TIFR Previous Year QP Chemistry

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SOME USEFUL DATA e = 1.6×10−19 C h = 6.626×10−34 J⋅s c = 3×108 ms−1 R = 8.314 J K-1 mol-1

Avogadro number = 6.02×1023 mol-1 RT/F = 0.0257 V at 25°C Faraday = 96500 C/eq. wt. Boltzmann constant k = 1.38×10−23 J K−1 Z2 a.u. for hydrogen like atom 2n 2 Mass of an electron = 9.109×10−31 kg Atomic radius of Cs = 266 pm, Atomic Wt. of Cs = 133

En = −

8kT π ⋅m 2+ Fe (aq) + 2e → Fe (s) 2H2O (l) + O2 (g) + 4e- → 4OH– (aq)

Average velocity =

1.

E° = –0.44 V E° = +0.40 V

The following curve is obtained when a solution of glycine hydrochloride (HOOC-CH2-NH4+Cl-) is titrated with a strong base. What are the predominant species present at point 1 shown on the curve?

a) b) c) d)

H3N+-CH2-COO- and H2N-CH2-COOH3N+-CH2-COOH3N+-CH2-COOH and H3N+-CH2-COOH2N-CH2-COO-

Page 1 of 17

2.

If the following probabilities were arranged in ascending order, which one would come third? a) The probability that a fair die will produce an even number. b) A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally probable. The probability that its square will end in 1. c) The probability that a letter chosen randomly from the English alphabet (all letters being equally probable) will be a vowel. d) A random number between 1 and 20 (inclusive) is chosen. The probability that its square root will not be an integer.

3.

What is the major product if HBr (in excess) is added to H2C=CH–CH2–OH a) b) c) d)

4.

CH3–CH(Br)–CH2–Br H2C=CH–CH2–Br CH3–CH(Br)–CH2–OH CH3–CH(OH)–CH2–OH Arrange the characteristic timescales of the following set of dynamical spectroscopic techniques in decreasing order of time (longest to shortest): NMR (Nuclear Magnetic Resonance), ESR (Electron Spin Resonance), Fluorescence, Raman and Absorption

a) b) c) d) 5.

Absorption > NMR > Fluorescence > ESR > Raman NMR > ESR > Fluorescence > Raman > Absorption Fluorescence > Absorption > ESR > NMR > Raman All have similar characteristic timescales. A segment of a protein under physiological conditions has a tendency to bury itself in the biological cell membrane. Which of the following is this segment more likely to be?

a) b) c) d)

Valine rich Lysine rich Glutamate rich Alanine rich

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Light of wavelength 500 nm is transmitted through a 10–4M dye solution which is contained in a glass cuvette of path length 1 cm. The extinction coefficient of the dye at 500 nm is 3010 M-1cm-1. Due to reflection, 4% of light is reflected in the front face of the cuvette (at the air/glass interface) and 4% at the back face before exiting the cuvette (at the glass/air interface). The percentage of the intensity of light transmitted through the dye and cuvette is:

6.

a) b) c) d)

42.6% 27.74% 30.1% 46.08% A 19th century iron bridge is protected from corrosion by connecting it to a block of metal (sacrificial anode), which is replaced annually. The corrosion of iron, represented by the chemical equation:

7.

2Fe (s) + 2H2O (l) + O2 (g) → 2Fe(OH)2 Which of the following metals is best suited as sacrificial anode? a) b) c) d)

Ag : Cd : Cu : Mg :

Ag+ + e- → Ag(s), Cd2+ + 2e- → Cd(s), Cu2+ + 2e- → Cu(s), Mg2+ + 2e- → Mg(s),

E0= +0.80 V E0= –0.40 V E0= +0.34 V E0= –2.36 V

An atom diffuses in one dimension on x-axis. At t=0, its position is x = x0. After a sufficiently long time, the probability of finding the atom is maximum at:

8.

a) b) c) d)

x = plus infinity or minus infinity x=0 x = x0 Indeterminate

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9.

Proton tunneling process has been implicated to be important part of many enzyme reaction mechanisms like in Aromatic Amine Dehydrogenase (AADH) which does oxidative deamination of substrates to aldehydes via a protein derived Aspartate residue (shown below).

Picture reproduced from Masgrau et al. Science (2006) Typically in such a reaction, the probability of a tunneling event should depend on: a) b) c) d)

Only the height (h) of the barrier Only the width (2a) of the barrier Both height (h) and width (2a) of the barrier None of the above

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10.

Structure of 1,2-dimethylcyclohexane is show below. Which of the following is an enantiomer to the given conformer?

11.

The pressure of a gas inside a spherical container is maintained at 2 atm. If the average velocity of the gas molecules inside the container is increased by a factor of two, keeping the pressure the same, by how much would the surface area of the container increase?

a) b) c) d) 12.

a) b) c) d)

22/3 24/3 2-1/3 1 A molecule normally absorbs in the green wavelength (ca. 500 nm). At some temperature, it is measured that for every 10 molecules in the excited state, there are about 27 molecules in the ground state. What is the approximate temperature of the molecule? 270 K 1000 K 500 K 30000 K

Page 5 of 17

13.

a) b) c) d) 14.

a) b) c) d) 15.

a) b) c) d) 16.

a) b) c) d)

The half-time for a chemical reaction: A Æ B is 2.3 sec. When a single molecule of A is observed during its conversion to B, what is the predicted time for this conversion to occur? e-2.3 sec 4.6 sec log 2.3 sec undefined The molar absorption coefficient of a compound in water at 532 nm is 2200 L mol-1cm-1. When light at that wavelength passes through an aqueous solution of this compound (kept in a 5 cm long cell), 50% of the light was absorbed. What is the concentration of the solution? 2.7 x 10-5 M 4.5 x 10-5 M 1.1 M Insufficient data A semi-permeable membrane, that is permeable only to cations, separates two compartments A and B. A solution of a monovalent electrolyte (of the type X+Y-) is contained in both the compartments. The concentrations are 0.1 M and 0.01 M in A and B respectively. When the voltage across the two compartments are measured, we find: No potential difference across the two solutions Compartment B shows +59mV with respect to A. Compartment A shows +10mV with respect to B. Compartment B shows -110 mV with respect to A. In an NMR experiment, the relative population difference (ΔN/N) for 13C nuclei in the magnetic fields of (a) 0.5 T, (b) 2.5 T and (c) 15.0 T at a temperature of 298 K are in the ratio: 1 : 5 : 30 e-1 : e-5 : e-30 e-0.5/298 : e-2.5/298 : e-15/298 30 : 5 : 1

Page 6 of 17

17.

a) b) c) d) 18.

A polymer chain has 500 segments. The length of each segment is 1.2 nm. If the polymer chain is totally flexible when dissolved in water, what would be the root mean square separation of the ends of the chain? 600 nm 417 nm 27 nm 300 nm An electronic state of a hydrogen atom is prepared to be a superposition energy of the eigenstates of the hydrogen atom, and for which the normalized wavefunction is written as:

φ=

1 1 1s + 2 s + C3 s 3s 2 4

.

Here |1s>, |2s> and |3s> are the exact energy eigenstates of the hydrogen atom, and C3s is a constant. What would be the average value of energy, associated with this wavefunction φ, in a.u.? a) b) c) d) 19.

– 0.2951 a.u. – 0.4161 a.u. – 0.2269 a.u. – 0.3929 a.u. For the reaction given below, Activation energy is 271kJ/mol. What is the value of k at 250 ºC? Note that A(frequency factor) =1 x 1015 sec-1

a) 8.568 x 10-12 s-1 b) 8.568 x 10-11 s-1 c) 5.141 x 10-11 min-1 d) 5.141 x 10-12 min-1

Page 7 of 17

20.

a) b) c) d)

21.

a) b) c) d) 22.

a) b) c) d) 23.

a) b) c) d)

In a polyatomic molecule the radiative lifetime of an allowed electronic transition is typically in the range of a few tens of nanoseconds. What will be the lifetimes of the allowed vibrationally excited states of the same molecule? nanoseconds picoseconds femtoseconds milliseconds

Vapour pressure of Cs (liq) contained in a cell of 1 litre volume is 80 Torr. If the Cs atoms are excited to an electronically excited state with a lifetime of 192 ns, how many collisions would the excited atoms suffer before they deactivate radiatively? ~100 ~200 2.83 x 1018 5.48 x 108 Arrange the pKas of the hydroxy groups of methanol, trifluoroacetic acid, phenol and benzyl alcohol in ascending order: Trifluoroacetic acid < phenol < benzyl alcohol < methanol Trifluoroacetic acid < benzyl alcohol < phenol < methanol Phenol < trifluoroacetic acid < benzyl alcohol < methanol Trifluoroacetic acid < methanol < phenol < benzyl alcohol Heme is a versatile molecule present in a large number of metalloproteins and enzymes. The absorption spectrum of heme is characterized by sharp band at near 400 nm and weaker bands at 520-550 nm. The origin of these absorption bands are: MLCT transitions LMCT transitions d-d transitions pi-pi* transitions

Page 8 of 17

24.

The proton NMR spectrum of a saturated hydrocarbon shows a single absorption line at 1.42 ppm with respect to TMS at room temperature. The area of the line is equivalent to 12 protons. Solely based on this observation, what are the tentative inferences you can draw about the nature of the hydrocarbon?

a) It is a pure compound i.e. there are no impurities present. b) More than one conformation of the molecules may be present and they are undergoing rapid interconversion. c) The hydrocarbon is cyclohexane. d) All of the above. 25.

a) b) c) d)

Below is a diagram by Maurits Cornelis Escher (1898-1972), a Dutch graphic artist. What elements of symmetry are present in this Escher diagram generated by tessellation of fish images?

no symmetry 2 fold rotation axis perpendicular to plane of paper mirror plane and 2-fold rotation axis perpendicular to plane of paper mirror plane

Page 9 of 17

26.

a) b) c) d)

27.

Imagine the world famous Koh-i-Noor diamond (mass 21.6 g) is completely burnt in the presence of oxygen, the amount of which is carefully controlled. After the completion of the burning process, the mass of the gaseous product is measured. What would you expect the amount of this gas to be? Less than 50 g. More than 50 g but less than 80 g. More than 80 g. Diamond will not decompose under the given conditions.

IrCl(CO)[P(C6H5)3]2 (trans-chlorocarbonylbis(triphenylphosphine)iridium(I)) also known as Vaska’s complex can undergo oxidative addition with dihydrogen. Which of the following structures is a correct depiction of the geometry and oxidation state of the ensuing product? H H

a) (C6H5)3P OC

Ir

H H

b) P(C 6H 5)3

(C 6H 5) 3P OC

Cl Ir (I)

(C6H5)3P OC

Ir H Ir (I)

P(C6H 5)3

Cl Ir (III)

H Cl

c)

Ir

H Cl

d) P(C 6H 5)3

(C 6H 5) 3P OC

Ir

P(C6H5)3

H Ir (III)

Page 10 of 17

28.

‘Click’ reactions can be used to join two molecular units with minimal side products, high chemical yield and stereospecificity. One such reaction is a thiol-yne reaction which is used in polymerization especially for dendrimer synthesis. Predict the final product of the following thiol-yne reaction between L-cysteine and 1-butyne: HO

SH

+ 2 O

HO

H sunlight

NH2

H S

O a)

b)

NH2

HO

H S

O S

HO H

NH2

O HO c)

NH2

H S

O

d)

NH2

HO

H S

O HO H

29.

S

NH2

NH2

O Two compartments X and Y are separated by an impermeable partition P. In the compartment X, the following reaction is going on: A2 + B2 ↔ 2AB in a solvent S, while compartment Y contains only the solvent S. Contents of both the compartments are continuously and vigorously stirred. After the reaction in the compartment X has reached equilibrium, the concentrations of A2, B2 and AB are measured and the equilibrium constant calculated. Then the partition is quickly removed. After waiting for a very long time, all the concentrations are measured again, and the new value of the equilibrium calculated. What is the most appropriate statement you can make about the result of this experiment? Assume that the chemicals are behaving ideally and the temperature is kept constant.

Page 11 of 17

X

Y

P a) The concentrations of all the chemicals and the equilibrium constant will be less than their values before the partition was removed. b) After removing the partition, the concentrations of A2, B2 will increase and that of AB will decrease, leading to a lower value of the equilibrium constant. c) After removing the partition, the concentrations of A2, B2 will decrease and that of AB will increase, leading to a higher value of the equilibrium constant. d) After removing the partition, the concentrations of all the chemicals will decrease, but value of the equilibrium constant will not change.

30.

What is the value of this continued fraction? 1 1 + 1 1 2 + 1 2 1 + 1 2 1 + 2 1 +L 2

a) b) c) d)

1/2 1 2 ∞

Page 12 of 17

31.

A rectangle with size given below is cut as shown. The two pieces are combined together to form a square. Determine the perimeter of the square.

12 m

27 m a) b) c) d)

32.

60 m 48 m 72 m 78 m

The reaction of nitric oxide with ozone takes place according to the following stoichiometry: NO + O3 → NO2 + O2 The observed rate law for the reaction is found to be

d [ NO] = α[O3]{[NO] + β[NO2]} dt where α and β are constants. To explain the above rate law, the following reaction scheme has been proposed: −

k1

NO + O3 → NO2 + O2

k2

NO2 + O3 → NO3 + O2

k3

NO + NO3 → 2NO2 Determine an expression for β.

a) b) c) d)

A unique expression of β cannot be determined from the given information. k2/k1 k3/k2 k1/k3

Page 13 of 17

33.

Given cos θ = α, π < θ < 3π/2, find cos (θ/2)

a) −

1+ α 2

b) −

1 + 2α 2

c)

1+ α 2

d)

1 + 2α 2

34.

a) b) c) d)

A student has measured the standard free energy change of a certain chemical reaction as a function of temperature. The data and a linear fit to them are shown below. From this diagram, determine approximately the standard entropy of the reaction. (Assume that the standard entropy of the reaction is independent of temperature.)

+50 J⋅mol−1⋅K−1 +75 J⋅mol−1⋅K−1 +100 J⋅mol−1⋅K−1 −100 J⋅mol−1⋅K−1

Page 14 of 17

35.

Consider the following electrochemical cell, from which current is drawn through an external resistor of 10 Ohms. During this process, the concentration of CuSO4 in the left and the right half-cells were measured, and the value of K ≡ [CuSO4]left/[ CuSO4]right was calculated. From the initial value of K = 10, predict the value of K after a very long time when the cell stopped giving any current. Cu| CuSO4(aq, 10 M)|| CuSO4(aq, 1M)|Cu

10 Ω a) An exact value cannot be predicted since CuSO4 solutions of such high concentrations, as used above, would not behave ideally. b) K ≈ 0.1 c) K = 1.0 d) K will be very small, possibly 10 pKa 6.5

13. The total energy expended to charge (total charge = +q) a sphere of radius ‘r’ in a dielectric medium (İ) is given by (in SI units): A) B) C) D)

q2/4πİr q2/16πİr q2/ 4πİr2 q2/8πİr

Page 5 of 16

14. A substance A is consumed by a reaction of unknown order. The initial concentration is 1mM, and concentrations at later times are as shown:

Time (min) [A] (mM) ____________________ 1 0.83 2 0.72 4 0.56 8 0.38 16 0.24 What is the order of the reaction? A) B) C) D)

zero first-order second-order pseudo-first order

15. ΔG0 values for the hydrolysis of glucose-1-phosphate and glucose-6-phosphate are −21 kJ/mol and –14 kJ/mol, respectively. What is the equilibrium constant for the following equilibrium at 250C? Glucose-1-phosphate A) B) C) D)

֎

Glucose-6-phosphate

0.06 16.9 4798 284

16. In a double stranded DNA, if the sequence 5’AGATCC3’ appears on one strand of DNA, what sequence in the complementary strand?

A) B) C) D)

5’AGATCC3’ 5’CCTAGA3’ 5’GGATCT3’ 5’TCTAGG3’

Page 6 of 16

17. One sequence of amino acids repeats for long distances in silk protein. Complete hydrolysis of one mole of a fragment with this sequence gives 2 mol alanine, 3 mol glycine, and 1 mol serine. Partial hydrolysis yields Ala-Gly-Ala, Gly-AlaGly, Gly-Ser-Gly, and Ser-Gly-Ala peptides. What is the amino acid repeat?

A) B) C) D)

Gly-Gly-Ser-Ala-Gly-Ala Gly-Gly-Gly-Ala-Ala-Ser Ser-Ala-Ala-Gly-Gly-Gly Gly-Ser-Gly-Ala-Gly-Ala

18. Which of the following compounds would give the 1H NMR spectrum shown below

A)

CH3CH(CH3)CH2X

B)

CH3C(CH3)2CH2CH2X

C)

CH3CH2(CH3)CH2X

D)

CH3CH2CH(CH3)X

Page 7 of 16

19. Which of the following compounds will react with R-SH in aqueous solutions between pH 6.5 and 8.5?

O

O O R C O N

R N O

R1

A) B) C) D)

O R2

O R C

R3

I

RS S

N R4

R1, R2 and R3 R2, R3 and R4 R4, R2 and R1 R1, R3 and R4

20. In a spherical polar coordinate system, a point A at (x, y, z) in the Cartesian coordinate system can be described by (r, θ, φ) where r, θ, and φ have their usual meaning. Expression for the volume of an infinitesimally small cube confined by dx, dy, and dz in terms of the spherical coordinate system is given by

A) B) C) D)

drdθdφ rsinθdrdθdφ r2sin2θdrdθdφ r2sinθdrdθdφ

21. Rotational energy of a diatomic molecule is given by Erot = J(J + 1)hBe, where Erot is in Joules. If the rotational constant for H2 molecule is given as Be = 1.8324 x 1012 Hz, the rotational period of the H2 molecule in J = 10 level will be A) B) C) D)

1.33 × 10-19 sec 5.0 × 10-15 sec 5.46 × 10-13 sec 7.39 × 10-7 sec

Page 8 of 16

22. Tyrosine, at pH 12, has the following structure COO -

A)

HO

H2 C

CH +NH3

COO -

B)

-O

H2 C

CH NH 2 COO -

HO

H2 C

CH

C) NH 2

COO -

D)

-O

H2 C

CH +NH3

23. Quartz crystal watches lose or gain about a second a week. What is the accuracy of these watches in ppm? A) B) C) D)

1 1000 0.605 1.653

24. The reaction of sodium ethoxide with ethyliodide to form diethyl ether is termed A) B) C) D)

electrophilic substitution nucleophilic substitution electrophilic addition radical substitution

Page 9 of 16

25. Of the following metal ions, which has the largest magnetic moment in its lowspin octahedral complexes?

A) B) C) D)

Fe3+ Co3+ Co2+ Cr2+

26. In a certain axis of quantization, the z-component of the spin angular momentum, Sz, has the following matrix representation.

ª1 0 0 º S z = ! ««0 0 0 »» «¬0 0 − 1»¼ What would be the trace of the matrix of Sx2 (square of the x-component) in the same representation? A) B) C) D)

0ƫ2 1ƫ2 2ƫ2 None of the above

Page 10 of 16

27. X-rays of CuKα (wavelength 154 pm) are diffracted by a set of atomic planes in a crystal in the following manner. The separation of the layers in the crystal is 404 pm. Find the angle α along which the first-order reflection will occur.

α

A) B) C) D)

79° 45° 11° None of the above

28. How many molecules of cetanol (of cross-sectional area 2.58 x 10-19 m2) can be adsorbed on the surface of a spherical drop of dodecane of radius 17.8 nm? A) B) C) D)

3.90 x 103 1.54 x 104 1.54 x 102 6.5 x 10-5

29. The velocity of Li+ ion in water is 2 x 10-2 cm/sec when 100 V is applied between two electrodes separated by 2 cm. The mobility of Li+ ion in water is,

A) B) C) D)

4 x 10-4 cm2 s-1 V-1 1 x 10-4 s-1 V-1 4 V cm2 s-1 2.5 x 105 V s cm-2

Page 11 of 16

30. The melting point of lithium metal is 454 K, and that of sodium is 371 K. Which of the following statements can explain this difference in their melting points? i. Metallic bonding in lithium is stronger than metallic bonding in sodium. ii. The delocalised electrons are more strongly attracted to the metal cation of lithium. iii. The lithium cations have a greater charge density than sodium cation. iv. Li+ cations are smaller than Na+ cations. A) B) C) D)

Only (i) and (ii) Only (ii) and (iii) Only (iv) (i), (ii), (iii), and (iv)

31. What is the final product after the following reaction has gone to completion? Benzene (liquid) + Chlorine (gas) Sunlight A) B) C) D)

?

Benzene Benzenehexachloride Chlorobenzene Dichlorobenzene

32. The transition probability for spontaneous emission from state m to state n is given by an expression

3 § 64 π 4ν mn A m → n = ¨¨ 3 © 3 hc

∧ · §¨ ¸¸ ⋅ m d n ¹ ¨©

2

· ¸ ¸ ¹

Where, νmn is the frequency of transition, and the term in the parenthesis is the transition dipole. Assuming that the magnitude of the transition dipole is same for all types of transitions, arrange the average lifetimes for the electronic, vibrational, and rotational transitions in the proper order. A) B) C) D)

electronic < vibrational < rotational vibrational < rotational < electronic rotational < vibrational < electronic electronic < rotational ≈ vibrational

Page 12 of 16

33. At 20 °C, the standard EMF of a certain cell is +0.2699V, and at 30 °C it is +0.2669V. What can you say about the standard entropy of this reaction? Assume that the standard ΔH˚ and ΔS˚ are independent of temperature.

A) B) C) D)

ΔS˚ = 0 ΔS˚ = +ve ΔS˚ = −ve Not enough information is given.

34. Which of the following most closely resembles the 13C NMR spectrum of ethanol? Assume a scalar coupling of 150 Hz among the 1H and the 13C nuclei within a functional group, a scalar coupling of 50 Hz between the 13C nuclei, a static magnetic field of 11.7 T, and a temperature of 300 K.

A)

13

C ppm

B) 13

C ppm

C)

13

C ppm

D) 13

C ppm

Page 13 of 16

35. The roots of the equation x3 + ax2 − bx + c = 0 are three consecutive integers. What is the maximum value of b? A) B) C) D)

−2 0 1 2

36. The corrosion of iron in contact with an acidic aqueous solution undergoes the following reaction Fe(s) + 2H+(aq) ⇔ Fe2+(aq) + H2(g)

(1)

in the anaerobic condition, and the following reaction 2Fe(s) + O2(aq) + 4H+(aq) ⇔ Fe2+(aq) + 2H2O(l)

(2)

in the aerobic condition. During the corrosion, Fe(II) ions are formed in both conditions. If the water is polluted with Cr(IV), the following reaction may take place. 7H+(aq) + 3Fe2+(aq) + HCrO4−(aq) ⇔ 3Fe3+(aq) + Cr3+ (aq) + 4H2O(l)

(3)

Reaction (3) be broken down to the following redox half-reactions: 3Fe3+ + 3e− ⇔ 3Fe2+(aq)

E0 = +0.77 V (4)

7H+(aq) + HCrO4−(aq) + 3e− ⇔ Cr3+ (aq) + 4H2O(l)

E0 = +1.38 V (3)

The standard potentials of these reactions are with respect to the normal hydrogen electrode. What would be the approximate value of the equilibrium constant of reaction 3 at 298 K? A) B) C) D)

1011 1031 10-31 10−11

Page 14 of 16

37. Consider a container of volume 5.0 L that is divided into two compartments of equal size. In the left compartment there is nitrogen at 1.0 atm and 25 °C; in the right compartment there is hydrogen at the same temperature and pressure. What will happen when the partition is removed? A) B) C) D)

The entropy increases, and the free energy decreases. The entropy decreases, and the free energy decreases. The entropy increases, and the free energy increases. The entropy decreases, and the free energy increases.

38. Each of the following flasks contains 25 ml of 1M HCl solution in water. To them a certain amount of solid sodium bicarbonate is added and, as shown the picture, then the mouths of the flasks are quickly closed by rubber balloons of identical size. The masses of NaHCO3 added to the flask 1 through the flask 5 are 0.70 g, 1.00 g, 2.10 g, 4.20 g and 6.30 g, respectively. After waiting for a sufficiently long time, predict the relative size of the 5 balloons.

1 M HCl NaHCO3

A) B) C) D)

Flask 1

Flask 2

Flask 3

Flask 4

Flask 5

25 ml 0.70 g

25 ml 1.00 g

25 ml 2.10 g

25 ml 4.20 g

25 ml 6.30 g

The size of Balloon 1 = Balloon 2 = Balloon 3 = Balloon 4 = Balloon 5. The size of Balloon 1 < Balloon 2 < Balloon 3 < Balloon 4 < Balloon 5. The size of Balloon 1 < Balloon 2 < Balloon 3 = Balloon 4 = Balloon 5. The size of Balloon 1 < Balloon 2 < Balloon 3 < Balloon 4 = Balloon 5.

39. The degeneracy of the energy level 12h2/8ma2 of a particle in a three dimensional cube of length “a” is A) B) C) D)

1 3 6 12

Page 15 of 16

40. Compound A is more soluble in solvent X when compared to solvent Y. X and Y are immiscible. The partition coefficient of A between the two solvents is 10. 10 mL of a 2 x 10-5M solution of A in solvent Y is mixed vigorously with 100 mL of solvent X and the two phases are allowed to separate out. The concentration of A in phase Y after the separation would be: A) B) C) D)

2 x 10-9 M 1.98 x 10-7 M 2 x 10-6 M 1.8 x 10-7M

The following question does NOT carry any marks and is given to collect information only:

41.

How much time did you take to complete this chemistry exam? A) B) C) D)

Less than 1 hour. Between 1 to 2 hours. Between 2 to 3 hours. Insufficient time was given.

Page 16 of 16

GS-2012 (CHEMISTRY)

CHM-X

ANSWER SHEET Please see reverse for instructions on filling of answer sheet.

Question Paper Set : X

Y

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Reference Code :

Ref Code

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2 3 4 5

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{ { { { { { { { { {

SECTION A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

{ { { { { { { { { {

{ { { { { { { { { {

{ { { { { { { { { {

{ { { { { { { { { {

SECTION A

(A)

(B)

(C)

(D)

{ { { { { { { { { { { { { { { { { { { {

{ { { { { { { { { { { { { { { { { { { {

{ { { { { { { { { { { { { { { { { { { {

{ { { { { { { { { { { { { { { { { { { {

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

(A)

(B)

(C)

(D)

{ { { { { { { { { { { { { { { { { { { { {

{ { { { { { { { { { { { { { { { { { { { {

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{ { { { { { { { { { { { { { { { { { { { {

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Correct answers are ticked in green.

CHM-X

GS-2013 (Chemistry) TATA INSTITUTE OF FUNDAMENTAL RESEARCH   Written Test in CHEMISTRY ‐ December 9, 2012  Duration : Three hours (3 hours)      Name : _______________________________________________ Ref. Code : ____________        Please read all instructions carefully before you attempt the questions.      1.   Please fill‐in details about name, reference code etc.  on the answer sheet.  The Answer  Sheet  is  machine‐readable.    Read  the  instructions  given  on  the  reverse  of  the  answer  sheet before you start filling it up.  Use only HB pencils to fill‐in the answer sheet.    2.   Indicate your ANSWER ON THE ANSWER SHEET by blackening the appropriate circle for  each question.  Do not mark more than one circle for any question : this will be treated  as a wrong answer.    3.   This is a multiple choice question paper with one section having a total of 40 questions.   Each  correct  answer  will  get  you  3  marks.    Every  wrong  answer  will  get  you  ‐1  mark.   Marks are not awarded or deducted when a question is not attempted.   It is better not  to answer a question if you are not sure.    4.  We advise you to first mark the correct answers on the QUESTION PAPER and then to  TRANSFER these to the ANSWER SHEET only when you are sure of your choice.    5.  Rough work may be done on blank pages of the question paper.  If needed, you may ask  for extra rough sheets from an Invigilator.      6.  Use  of  calculators  is  permitted.    Calculator  which  plots  graphs  is  NOT  allowed.  Multiple‐use devices such as cell phones, smart phones etc., CANNOT be used for this  purpose.    7.   Do  NOT  ask  for  clarifications  from  the  invigilators  regarding  the  questions.  They  have  been  instructed  not  to  respond  to  any  such  inquiries  from  candidates.  In  case  a  correction/clarification is deemed necessary, the invigilator(s) will announce it publicly.     

SOME USEFUL DATA e = 1.6×10−19 C h = 6.626×10−34 J⋅s c = 3×108 m s−1 R = 8.314 J K-1 mol-1

Avogadro number = 6.02×1023 mol-1 RT/F = 0.0257 V at 25°C Faraday constant = 96500 C/mol Boltzmann constant k = 1.38×10−23 J K−1 Z2 a.u. for hydrogen like atom 2n 2 Mass of an electron = 9.109×10−31 kg

En = −

8kT π ⋅m Standard reduction potential of Al3+ + 3e− → Al is −1.66 V at 25°C Standard reduction potential of Fe2+ + 2e− → Fe is −0.44 V at 25°C

Average velocity =

1. The Friedel-Crafts reactions are common in organic chemistry. Which of the following is expected to be a better catalyst? A) AlBr3 B) AlI3 C) AlCl3 D) MgCl2 2. If the CO stretching frequency of Ni(CO)3(P(OMe)3) is A, and that of Ni(CO)2(PMe3)2 is B, then A) B) C) D)

A>B A=B A ΔS2 > ΔS3 B) ΔS1 < ΔS2 < ΔS3 C) ΔS1 ≠ ΔS2 ≠ ΔS3 D) ΔS1 = ΔS2 = ΔS3

Page 10 of 12

33. Which of the following molecular species are expected to be paramagnetic? O2+, O2− and O22− ? A) All of them B) Only O2+ and O2− C) Only O2+ and O22− D) Only O2− and O22− 34. The reaction of sodium ethoxide with ethyliodide to form diethyl ether is termed A) B) C) D)

electrophilic substitution nucleophilic substitution electrophilic addition radical substitution

35. Point of group of 1,2-propadiene is A) C2h B) C2v C) D2h D) D2d 36. The 1H NMR spectrum of a compound with molecular formula C3H7NO shows the following features: Chemical shift (ppm) Shape

6.50 broad singlet

2.25 quartet

1.10 triplet

Which of the following is in agreement with this information? A) (CH3)2C=NOH B) CH3COCH2NH2 C) CH3CH2CONH2 D) HCON(CH3)2 37. Electrospray ionization mass spectroscopy produces multiply charged ions of proteins. On application of this technique to hemeprotein it gave a large number of peaks corresponding to different charge-states of the protein. The three consecutive peaks are observed at the m/z values: 2061, 1767, 1546 The approximate m/z value of the consecutive fourth peak in the series would be: A) 1252 B) 1374 C) 1498 D) 1325 Page 11 of 12

38. The cell potential for the following electrochemical system at 25 0C is: Al(s) | Al3+ (0.01 M) || Fe2+ (0.1 M) | Fe(s) A) 1.23 V B) 1.21 V C) 1.22 V D) −2.10 V 39. Real gases behave differently from ideal gases because: (i) the molecules of real gases are in constant motion. (ii) molecules of real gases collide with the walls of the container. (iii) molecules of real gases have volume. (iv) molecules of real gases attract each other. A) i and ii B) iii only C) iii and iv D) all of the above 40. Global warming is due to increase of A) Methane in atmosphere B) CO2 in atmosphere C) Water vapour D) Methane and CO2

The following question does NOT carry any marks and is given to collect information only: 41.

How much time did you take to complete this chemistry exam? A) B) C) D)

Less than 1 hour. Between 1 to 2 hours. Between 2 to 3 hours. Insufficient time was given.

Page 12 of 12

Correct answers are ticked in green.

CHM-X GS-2014 (Chemistry) TATA INSTITUTE OF FUNDAMENTAL RESEARCH Written Test in CHEMISTRY - December 8, 2013 Duration : Three hours (3 hours) Name : _______________________________________________ Ref. Code : ____________

Please read all instructions carefully before you attempt the questions.

1.

Please fill-in details about name, reference code etc. on the answer sheet. The Answer Sheet is machine-readable. Read the instructions given on the reverse of the answer sheet before you start filling it up. Use only HB pencils to fill-in the answer sheet.

2.

Indicate your ANSWER ON THE ANSWER SHEET by blackening the appropriate circle for each question. Do not mark more than one circle for any question : this will be treated as a wrong answer.

3.

This is a multiple choice question paper with one section having a total of 40 questions. Each correct answer will get you 3 marks. Every wrong answer will get you -1 mark. Marks are not awarded or deducted when a question is not attempted. It is better not to answer a question if you are not sure.

4.

We advise you to first mark the correct answers on the QUESTION PAPER and then to TRANSFER these to the ANSWER SHEET only when you are sure of your choice.

5.

Rough work may be done on blank pages of the question paper. If needed, you may ask for extra rough sheets from an Invigilator.

6.

Use of calculators is permitted. Calculator which plots graphs is NOT allowed. Multiple-use devices such as cell phones, smart phones etc., CANNOT be used for this purpose.

7.

Do NOT ask for clariĮcations from the invigilators regarding the questions. They have been instructed not to respond to any such inquiries from candidates. In case a correction/clariĮcation is deemed necessary, the invigilator(s) will announce it publicly.

Page 1 of 14

SOM ME USEFU UL DATA Avoogadro num mber = 6.02× ×1023 mol−1 RT/F F = 0.0257 V at 25°C Faraaday constaant = 96500 C/mol Bolttzmann connstant k = 1.38×10−23 J K−1

e = 1.6× ×10−19 C h = 6.6226×10−34 J s c = 3×1008 m s−1 R = 8.3114 J K−1 mo ol−1

Z2 a.u. for hydroggen like atom m 2n 2 Masss of an elecctron = 9.1009×10−31 kgg En = −

Aveerage velociity =

8kT

π m

1. For the following f reeaction,

CO2 + H2O → H2CO3 the entroppy change (ΔS ( system) waas calculated to be −96 J K−1 mol−−1. The enthaalpy − change (Δ ΔH) was meeasured to be b −45 kJ K−1 mol−1. Thhis reaction is expected d to be a spontaneoous process. The total change c in en ntropy (ΔSsystem+surroundi s ings) is A) +54 J K−1 mol−1 B) −96 J K−1 mol−1 C) −45096 J K−1 mol−11 D) −44004 J K−1 mol−1

2. What is the t product of the folloowing electrrocyclic ringg-closing reeaction?

X

A)

B)

a B C) both A and

D) nonee of the aboove

Pag ge 2 of 14

3. For the following f chhemical reacctions

The ratee constants k1 and k2 arre at least 10 000 times slower than either k3 or k4. During the course of the abovve reactions the ratio off the products B and C will w be A) B) C) D)

[B]/[C] = k3/k4 [B]/[C] = k4/k3 [B]/[C] = k2k3/ k1k4 [B]/[C] = k1/k2

4. Transitioon states in chemical c reeactions are generally not n directly observed in n experim ments becauuse A) their struuctures are different from reactantts and produucts B) they havve the higheest kinetic energy and hence h difficult to captu ure C) they havve the higheest potentiall energy andd their lifetimes are sho ort D) all of the above 5. A single--stranded RNA R has 12000 bases. Th he total base content off this RNA was found to have h the folllowing ratiio A:U:G:C C = 0.2:0.3:00.3:0.2. Thee probability y of a randomlyy chosen 5 nucleotide n loong sequencce as GAUG GA is A) 0.000988 B) 0.002433 C) 0.000322 D) 0.001088 6. Phosphorescence is a slower prrocess than fluorescencce because A) phosphoorescence occurs at lon nger wavelengths than ffluorescencce B) spin anggular momentum is nott conserved in phosphoorescence prrocess C) both A and a B D) none off the above 7. The partiition constaant of a com mpound betw ween two im mmiscible soolvents A an nd B is 10. Solvvent A is prreferred oveer solvent B.. You are giiven 10ml oof 0.1M solu ution of the com mpound in soolvent B. Thhis solution n is vigoroussly shaken aand equilibrrated with 100ml of solveent A. After phase separration, the concentratio c on of the compound in solveent B is A) 0.09 M B) 0.099 M C) 0.009 M D) 0.05 M

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8. A molecuule has a grround state and a two exccited electroonic energy levels, all of o −20 which aree nondegeneerate with thhe energies: E0=0, E1=1×10 J, aand E2 = 3× ×10−20 J. If P0, P1 and a P3 are frractions of molecules m occupied o in ground, firsst and secon nd excited sttates, respecctively, at 298K, then, P0 : P1 : P2 = ? A) 0.919 : 0.081 0 : 0.0001 B) 0.900 : 0.098 0 : 0.0002 C) 0.666 : 0.333 0 : 0.1111 D) 0.880 : 0.088 0 : 0.0222 9. While caarrying out the t titrationn of a weak acid a with a strong basee, the pH off the solutionn is measureed as a funcction of the added titrannt. The resuult is shown below.

Three pH H values haave been marked, m corrresponding to 3 differrent volumees of the added base. b V0 coorresponds to t the ‘end d point’ or the ‘stoichhiometric point’ p of neutralizzation. Whaat is the pka of the acid?? A) pH1 B) pH2 A) pH3 D) cannot be b answeredd because of insufficiennt informatiion

10. Althouggh both NF3 and NCl3 are covalen nt, NCl3 unddergoes hyddrolysis wheereas NF3 does not because A) NF3 is more m stable than NCl3 B) dipole moment m of NF N 3 is moree than NCl3 C) electronnegativity off F > Cl D) Cl can expand e its octet o by usin ng d-orbitalss

Pag ge 4 of 14

11. The potential energy of a diatomic molecule, as a function of the internuclear separation r, is approximated as

ܷ ሺ‫ ݎ‬ሻ ൌ

‫ܣ‬ ‫ܤ‬ െ ‫ݎ‬௔ ‫ݎ‬௕

where A and B are positive constants and a > b.

As shown in the above figure, r0 is the equilibrium bond length. What is the energy necessary to break the bond from its equilibrium position? A)

஺

஻

௥బ

௥బ್

ೌ െ

B)



C)



஻

௥బ್

െ

஺

௔

௥బ

௕

஺ ௥బೌ

ೌ ቀ െ ͳቁ

D) both B and C 12. The heme is present at the active site of many proteins and enzymes including hemoglobin, cytochromes etc. It is an iron complex of a cyclic aromatic ligand named porphyrin. Several metal complexes of porphyrin synthesized in the laboratory have similar absorption spectra, except that the most intense absorption band position is either red shifted or blue shifted around 400 nm depending on the nature of the metal ion. The origin of this most intense absorption band in these porphyrin complexes is: A) MLCT transitions B) LMCT transitions C) d-d transitions D) π- π* transitions Page 5 of 14

13. Which of the follow wing statem ments is truee about ferroomagnets? A) In the presence of a magnetic field, the unnpaired spinns of a ferro omagnet all alignn with the external e field. In the abbsence of thee external magnetic m field, sppins then revert back im mmediately to their origginal state. B) The orrigin of magnetism in n a ferrom magnet arises from raandomly arrangeed paired spins in a lattiice. C) A ferroomagnetic material m is weaker (inn its attracttion to an external magnettic field) thaan a paramaagnetic mateerial. D) none off the above 14. An elecctron can bee transferredd between tw wo moleculles X and Y either direcctly with a rate kXYY = k1 or thrrough an inttermediate molecule Z with rates kXZ = kZY = k2. If at time t = 0 the electron is situated at X then n average time t it willl take to reeach Y is given by:

A) t = 1/(k1 + k2/2) B) t = 1/k1 + 1/k2 C) t = 1/(k1 + 2k2) D) t = (k1 + k2)/( k1 k2) 15. For a coonservative force field (e.g., graviity): F, workk done in m moving a parrticle by distance dr d is W=F.ddr. which off the following is true A) W arounnd a closed path is zero o and W is path p indepenndent B) W arounnd a closed path p is zero o and W is path p dependeent C) W arounnd a closed path p is non--zero and W is path inddependent D) W arounnd a closed path is non--zero and W is path deppendent

16. 0.050 mol m of aceticc acid and 0.20 0 mol of sodium aceetate are mixxed and totaal volumee is adjustedd to 500 ml in i water. Th he pKa for acetic a acid ((CH3COOH H) is 4.75. Iff now 0.0100 mol of NaaOH is addeed to the aboove mixturee, what will the final pH H of the soluution be? A) > pH 7 B) pH will stay at 4.755 because it is a buffereed solution C) > pH 4.775 D) not suffi ficient inform mation has been given

Pag ge 6 of 14

17. Given below is a figure showing three X-ray diffraction patterns for (a) bulk metallic gold (commercially available) deposited on a flat polymeric substrate

(along with lattice planes) and (b) nanoparticles of gold that were synthesized in a research lab. These were deposited on the same flat polymeric substrate and (c) is a blank polymeric substrate. Which of the following statements is true regarding structural quality of the gold nanoparticles that have been synthesized? A) the gold nanoparticles that have been synthesized are amorphous in nature and not crystalline. As such they do not belong to the FCC lattice B) there are many impurities present in the sample containing gold nanoparticles C) insufficient information is given to make a conclusive statement D) none of the above 18. An artificial soft drink contains 11.0 g/L of tartaric acid C4H6O6, and 20 g/L of its potassium salt C4H5O6K. What is the pH of the drink? (Given: Ka tartaric acid = 1.0 × 10−3) A) 4.24 B) 5.21 C) 3.82 D) 3.16 19. Which of the catalytic protocols listed below demonstrate a homogeneous catalysis? I. Pt(s) catalyzing the reaction of O2(g) with CO(g) II. Cl(g) catalyzing the decomposition of O3(g) III. H2O2(aq) decomposition catalyzed by Br − (aq) A) I only B) II only C) I and III only D) II and III only

Page 7 of 14

20. FAD is a redox-active molecule which takes part in many important biological reactions. The redox potential of FAD at pH 7.0 is given below.

Calculate the redox potential when the media is acidified to pH 0. A) 0 V B) 0.24 V C) 0.12 V D) none of the above 21. What is ii ? (Given, ݅ ଶ ൌ െͳ) A) a real number B) a complex number C) an imaginary number D) none of the above 22. The two fine-structure components of a nuclear magnetic resonance transition are observed at chemical shifts of 2.142 and 2.208 ppm in a 300 MHz NMR spectrometer. Calculate the coupling constant. A) 19.8 Hz B) 0.066 Hz C) 6.6 Hz D) data is insufficient

23. The concentration of a molecule in aqueous solution is (C/1000) L−1, where C is the number of molecules. Assuming the molecule is a sphere of radius r0 Angstrom, one can estimate the intermolecular (centre-to-centre) separation by: ଵ

A) య − 2×r0 metre ξ஼ ଵ

B) య metre ξ஼ ଵ

C) య −2×10−10 ×r0 metre ξ஼

D) cannot be estimated based on the information above

Page 8 of 14

24. Paraformaldehyde (4% by wt), acrylamide (4% wt/vol), and an azo initiator (0.25% wt/vol) were added to a protein. What are the expected products X and Y?

25. Raman scattering is often seen overlapping with fluorescence emanating from the sample. However, fundamentally Raman process is different from fluorescence. This is because A) Raman scattering is a two-photon process and fluorescence is not B) Raman process is a scattering process while fluorescence is not C) Raman process need not be Stokes shifted D) all of above

Page 9 of 14

26. Predict the products X and Y for the following de-protection reactions:

27. Calculate the change in entropy when 1 mol of solid iodine, I2, at a temperature of 360 K is heated at constant pressure to produce liquid iodine at a temperature of 410 K. The constant pressure molar heat capacity of solid iodine is 54.44 J K−1mol−1 and of liquid iodine is 80.67 J K−1 mol−1. The melting temperature of iodine is 387 K, and the molar enthalpy of fusion of iodine is 7.87 kJ mol−1. A) 8.6 J K−1 mol−1 B) 28.9 J K−1 mol−1 C) 20.3 J K−1 mol−1 D) 11.7 J K−1 mol−1

Page 10 of 14

28. What is the product X in the following reaction?

X

A) tetrahedral

B) octahedral

C) distorted octahedral

D) square pyramid

29. How many molecular orbitals may be constructed from the valence shell orbitals of the constituent atoms in CH4? A) 2 B) 4 C) 6 D) 8

Page 11 of 14

30. Write down the matrix representing a two-step transformation of a general point (x, y, z): rotation through 1800 (about the z-axis) followed by reflection in an yz mirror plane ͳ A) ൥Ͳ Ͳ ͳ C) ൥Ͳ Ͳ

Ͳ െͳ Ͳ Ͳ െͳ Ͳ

Ͳ Ͳ൩ ͳ

െͳ B) ൥ Ͳ Ͳ

Ͳ ͳ Ͳ

Ͳ Ͳ൩ ͳ

Ͳ Ͳ൩ െͳ

െͳ D) ൥ Ͳ Ͳ

Ͳ ͳ Ͳ

Ͳ Ͳ൩ െͳ

31. What is the side product (X) of the following ring closing metathesis reaction?

32. What is the nature of silicon-oxygen bonds in silica (SiO2)? A) polar covalent B) ionic C) nonpolar covalent D) coordinate covalent

Page 12 of 14

33. The Sharpless epoxidation catalyst Ti(OiPr)4 converts allylic alcohols to epoxides steroselectively. What is the stereochemistry of the products obtained in the following oxidation reactions?

A) X: ((2R,3S)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol Y: ((2S,3R)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol B) X: ((2S,3R)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol Y: ((2R,3S)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol C) X: ((2R,3R)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol Y: ((2S,3S)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol D) X: ((2R,3S)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol Y: ((2S,3S)-3-benzyl-2,3-dimethyloxiran-2-yl)methanol

34. When 10 mL of each liquid of liquid pairs listed below are mixed and then allowed to stand, which pair is most likely to separate into two layers? A) carbon tetrachloride and hexane B) ethanol and methanol C) carbon tetrachloride and methanol D) hexane and pentane 35. The mathematical expression ei(kx−wt) represents A) a wave stationary in space but oscillating in time B) a travelling wave moving in the positive x direction C) a wave stationary in time but periodically varying in space D) a travelling wave moving in the negative x direction 36. Blue copper proteins consist of mono-nuclear copper center bound to 2 imidazole groups (histidine), one thiol group (cysteine) and one thioether group (methionine). The coordination geometry around the metal ion is distorted tetrahedral. What will be the relative value of the redox potential of the metal center (Cu2+/Cu+) in the protein compared to that of CuSO4 in water? A) more positive B) more negative C) equal D) redox potential of the metal center in the protein will be zero.

Page 13 of 14

37. Vapor pressure of a liquid in a closed container depends upon A) the volume of the container B) the volume of the liquid C) the temperature D) both B and C 38. Which of the following statements is/are true? (i) HCl absorbs IR radiation (ii) CO2 absorbs IR radiation (iii) H atom absorbs IR radiation (iv) H atom absorbs UV-vis and microwave radiation A) (i) only B) (i) and (ii) only C) (i), (ii) and (iii) only D) (i), (ii), (iii) and (iv) 39. N2 does not show pure vibrational spectra because A) triple bond in N2 is very strong B) the dipole moment of is N2 zero C) both A and B D) none of the above 40. What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100 V? A) 0.123 nm B) 0.123 Angstrom C) 1.23 × 10−11 cm D) none of the above

The following question does NOT carry any marks and is given to collect information only: 41. How much time did you take to complete this chemistry exam? A) B) C) D)

Less than 1 hour. Between 1 to 2 hours. Between 2 to 3 hours. Insufficient time was given.

Page 14 of 14

Correct answers are ticked in green.

CHM-X

GS-2015 (Chemistry) TATA INSTITUTE OF FUNDAMENTAL RESEARCH   Written Test in CHEMISTRY ‐ December 14, 2014  Duration : Three hours (3 hours)      Name : _______________________________________________ Ref. Code : ____________        Please read all instructions carefully before you attempt the questions.      1.   Please fill‐in details about name, reference code etc.  on the answer sheet.  The Answer  Sheet  is  machine‐readable.    Use  only  Blue/Black  ball  point  pen  to  fill‐in  the  answer  sheet.    2.   Indicate your ANSWER ON THE ANSWER SHEET by blackening the appropriate circle for  each question.  Do not mark more than one circle for any question : this will be treated  as a wrong answer.    3.   This is a multiple choice question paper with one section having a total of 40 questions.   Each  correct  answer  will  get  you  3  marks.    Every  wrong  answer  will  get  you  ‐1  mark.   Marks are not awarded or deducted when a question is not attempted.   It is better not  to answer a question if you are not sure.    4.  We advise you to first mark the correct answers on the QUESTION PAPER and then to  TRANSFER these to the ANSWER SHEET only when you are sure of your choice.    5.  Rough work may be done on blank pages of the question paper.  If needed, you may ask  for extra rough sheets from an Invigilator.      6.  Use  of  calculators  is  permitted.    Calculator  which  plots  graphs  is  NOT  allowed.  Multiple‐use devices such as cell phones, smart phones etc., CANNOT be used for this  purpose.    7.   Do  NOT  ask  for  clarifications  from  the  invigilators  regarding  the  questions.  They  have  been  instructed  not  to  respond  to  any  such  inquiries  from  candidates.  In  case  a  correction/clarification is deemed necessary, the invigilator(s) will announce it publicly.          Page 1 of 16 

SOME USEFUL DATA Avogadro number = 6.02×1023 mol−1 RT/F = 0.0257 V at 25°C Faraday constant = 96500 C/mol Boltzmann constant k = 1.38×10−23 J K−1 En = −

e = 1.6×10−19 C h = 6.626×10−34 J s c = 3×108 m s−1 R = 8.314 J K−1 mol−1

Z2 a.u. for hydrogen like atom 2n 2

Mass of an electron = 9.109×10−31 kg Average velocity =

8kT π m

For H3PO4, pK1 = 2.16, pK2 = 7.21, pK3 = 12.32

1. Predict the product for the following sugar functionalization reaction:

2. Which of the following cannot act as a chelating agent? A) HC(CH2CH2NH2)3 B) CH3NHCH2CH2CH3 C) N(CH2CH2NH2)3 D) H2NCH2CH2CH2NH2

Page 2 of 16

3. In the following setup, two chambers 1 and 2 are enclosed by a thermally insulated material. Chamber 1 contains an ideal gas at 100 atm. Chambers 2 is completely

2

1

Seal evacuated. The two chambers are separated by a breakable seal. Before the seal is broken, the temperature of the chamber 1 is T1, initial. Then the seal is broken, and the gas is allowed to rush to chamber 2. The volume of chamber 2 is 100 times the volume of chamber 1. When the pressure in the two chambers becomes equal, their respective temperature is T1, final and T2, final. Which of the following statements is true? A) T1, final = T2, final = T1, initial B) T2, final = T1, final < T1, initial C) T2, final < T1, initial , T1, final = T1, initial D) Only a very small drop in temperature is expected. So T1, final, T2, final will be approximately equal to T1, initial 4. Consider the trigonometric function

A)

cos A − sin A + 1 . It can be simplified as cos A + sin A − 1

1 + sec A − tan A 1 − sec A + tan A

B) cosec A + cot A C) 1 /(cosec A − cot A) D) All of the above

5. The combustion of ethane (C2H6) is represented by the following reaction: 2 C2H6(g) + 7 O2(g)  4 CO2(g) + 6 H2O(l) Which of the following is TRUE for the above reaction? A) The rate of consumption of ethane is seven times faster than the rate of consumption of oxygen B) Water is formed at a rate equal to two-thirds the rate of formation of CO2 C) The rate of consumption of oxygen equals the rate of formation of water D) CO2 is formed twice as fast as ethane is consumed

Page 3 of 16

6. Consider the following reaction: Au + O2 + 3F2 → [O2]+ + [AuF6]– Which statement is correct about the redox changes in this reaction? A) Au is oxidized; O is oxidized; F is reduced B) Au is reduced; O is oxidized; F is reduced C) Au is oxidized; O does not undergo a redox change; F is reduced D) Au is reduced; O is oxidized; F does not undergo a redox change

7. Formation of Z from X is theoretically expected to obey the following kinetic scheme.

X

k1 k−1

Y

k2 k−2

Z

An experimentalist wants to verify the above scheme, but can observe and measure the concentration of only X or Z. Is it possible that under certain conditions, the measurements of [X] or [Z] as function of time would lead the experimenter to conclude that the kinetic scheme is as given below, and that the species Y is absent?

X

kobs k−obs

Z

A) No, that is not possible B) Yes, if k−1 >> k1 and k−2 >> k2 C) Yes, if

k1 k = 2 k −1 k −2

D) Yes, if [Y] attains a steady-state concentration during the experiment

8. NaCl, KCl, NaBr and KBr crystallize in FCC lattices. Their anion and cation touch along the edge of the unit cell. The dimensions of their unit cells are 562.8 pm, 627.7 pm, 596.2 pm, and 658.6 pm, respectively. From these data, what can you say about the size of the ionic radii (within an error of about 5%)? A) Ionic radii of the cations depend on the nature of the anions B) Ionic radii of the anions depend on the nature of the cations C) Both (A) and (B) D) Ionic radii are independent of the counter ions

Page 4 of 16

9. Indicate which of the following is/are “acceptable” wave function(s) in quantum mechanics in the range -∞ < x < +∞ ii) ψ = x2

i) ψ = x

iii) ψ = sin x

v) ψ = exp(-x2)

iv) ψ = exp(-x)

A) iii and v B) iv only C) iv and v D) i and iii 10. For a harmonic oscillator in its ground state i.e. v = 0 state, the energy is given by E= ½hν, where ν is the vibrational frequency. This is due to its A) Kinetic energy B) Potential energy C) Sum of kinetic and potential energy D) Heat of formation 11. The state of a certain amount of a gas, not necessarily ideal, is changed from A to B in various hypothetical paths, as shown below. The total amount of the gas remains constant. Which of the following paths are physically realizable?

A

(i)

(ii)

P

P

(iii) P

B

B V (iv)

A

A

B V

V A

A

(v)

P B V

P B V

A) All of them B) Only (i), (ii) and (iii) C) Only (iii) and (v) D) Only (i) and (iii) Page 5 of 16

12. Thiols are important molecular species present in cells and can mediate cell signaling processes. A procedure for detecting thiols has been recently reported based on the following reaction. Predict the structures of reaction products. N

O O O S

pH 7.6

+

O

SH O

13. If the peak in the mass spectrum of C2F6 at mass number 138 is 100 units tall, what will be the heights of the peaks at mass numbers 139 and 140. (Isotopic abundances: 12C, 98.89%; 13C, 1.11%; 19F, 100%) A) 2.24 and 0.0126 B) 1.12 and 0.0126 C) 50 and 25 D) 2.24 and 0.025 14. According to the Nernst equation, the potential of an electrode changes by 59.2 mV whenever the ratio of the oxidized and the reduced species changes by a factor of 10 at 25 °C. What would be the corresponding change in the electrode potential if the experiment is carried out at 30 °C? A) 59.2 mV B) 71.0 mV C) 60.2 mV D) None of the above

Page 6 of 16

15. Degenerate C-C coupling reactions are very important for synthesizing supramolecular organic structures. Name the reagents X, Y and Z that would be necessary to make the C3 symmetric product?

A)

B)

C)

D)

16. What is the point group of Fe2(CO)9 ? A) C3h B) D3h C) C3v D) D3d Page 7 of 16

17. Which of the following is the curve x = y2.

A) i

B) ii

C) iii

D) iv

18. For a particle undergoing quantum tunneling through a barrier, which of the following is NOT true: A) The amplitude of particle wave function after passing the barrier decreases with an increase in tunneling distance B) The probability of finding the particle after passing the barrier decreases with increase in tunneling barrier height C) The energy of the particle after crossing the barrier decreases with increase in tunneling distance D) The change in the phase of the particle wave function upon transmission is proportional to the tunneling distance Page 8 of 16

Signal

19. A magnetic resonance spectrum, recorded using a radiation of frequency 100 MHz, is shown below. What can you say about the nature of this spectrum?

Magnetic field A) It is a continuous-wave NMR spectrum B) It is a Fourier transform NMR spectrum C) It is an ESR spectrum D) None of the above 20. An electron can transfer from state D to state A with a rate kDA. The intrinsic (in the absence of any charge transfer between states D and A) lifetimes of charge transfer states D and A are τD and τA, respectively. Assuming that initially the electron is in state D, under what conditions would kDA be completely determined in terms of the overall rate at which the electron leaves the combined D+A system. A) kDA >> 1/τD and kDA >> 1/τA B) kDA >> 1/τD and kDA 1/τA D) kDA f where the initial (i) and final (f) configurations each comprise of simple additive combinations of purely folded (e.g. F1, F1+F2, F1+F2+F3) or unfolded states (e.g. U1, U1+U2, U1+U2+U3). Transitions between folded (or unfolded) configurations are also allowed unless a state is part of both the initial and final configurations. Assuming Ti -->f = Tf -->i the total number of distinct transitions are: A) 61

B) 49

C) 73

D) 9

17) A set of N vectors  ,  , ….  satisfy the eigenvalue equation for an operator with scalar eigenvalues ,  ,….  (i.e.,   ). The linear combination vector ∑ , where ’s are non-zero scalar coefficients A) is not an eigenvector of A B) is an eigenvector of A only if the ’s are all distinct (no two eigenvalues are equal) C) is an eigenvector of A only if the  ’s are all equal D) is an eigenvector of only if ’s are equal 18) A C5H12O2 compound has strong infrared absorption at 3300 to 3400 cm-1. The 1H NMR spectrum has three singlets at δ 0.9, δ 3.45 and δ 3.2 ppm with relative areas 3:2:1. Addition of D2O to the sample eliminates the lower field signal. The 13C NMR spectrum shows three signals all at higher field than δ 100 ppm. Which of the following compounds best fits this data? A) 1,5-pentanediol B) 1,3-dimethoxypropane C) 2,2-dimethyl-1,3-propanediol D) 2,4-pentanediol 19) A compound of formula C5H12 gives one signal in the 1H NMR and two signals in the 13 C NMR spectra. The compound is A) pentane B) 2-methylbutane D) cannot tell without more information

C) 2,2-dimethylpropane

Page 6 of 12     

 

20) Predict the products X and Y of the following peptide ligation reaction.

A)

B)

C)

D) 21) The 1H NMR spectrum of a compound A shows a doublet and a septet. Which one of the following statements is true? A) The spectrum is consistent with A containing a CH3CH2CH2 group B) The spectrum is consistent with A being (CH3)2CHCl C) The spectrum is consistent with A containing a CH3CH2 group D) The spectrum is consistent with A being (CH3)2CCl2 22) For a binary mixture of ideal gas, free energy of mixing is given by Δ 1 1 , where x is the mole fraction of one of the components. What are the enthalpy and entropy of mixing of this system? A B C D

 Δ  Δ  Δ  Δ

0  0  0  0 

 Δ  Δ  Δ  Δ

0 0 0 0

Page 7 of 12     

 

23) Predict the products of the following reactions between cis-2-butene and singlet and triplet methylenes.

A)

B)

C)

D)

24) Which of the following is/are implied by the second law of thermodynamics? A) B) C) D)

Δ / for an irreversible process A B at temperature T Δ 0 for an isolated system in the course of a spontaneous change Entropy of the universe always tends to maximum All of the above

25) ABCD is a rectangle of area 50 m2. The mid-points AB, BC and AD are E, F and G, respectively. When EF is extended, it meets extended DC at H. Similarly, when EG is extended, it meets extended CD at J. What is the area of the triangle EHJ? B) 100 m2 C) 200 m2 A) 50 m2 D) The area cannot be determined without knowing the length and breadth of the rectangle Page 8 of 12     

 

26) Predict the products of the following reaction.

A)

B)

C)

D)

27) What is the value of A) B) C) D)

, where

√ 1

Real number Complex number Cannot be calculated None of the above

28) In a 1 g diamond crystal, a scientist wants to replace a few of the carbon atoms with nitrogen atoms. Which of the following statements best describes the resulting material? A) This is not possible as nitrogen has a coordination number of 3 and carbon has a coordination number of 4 B) The resulting material will NOT have a cubic diamond structure C) The resulting material will be a defective diamond as it will be p-doped D) The resulting material can be characterized as n-doped diamond

Page 9 of 12     

 

29) Chemical oxidation of water to produce O2 gas is an energy demanding reaction, done routinely by plants using the process called photosynthesis. By how many eV will it be uphill if the water oxidation reaction be carried out at pH = 0 versus at pH = 7.0? A) B) C) D)

0.41 eV -1.6 eV -0.41 eV Cannot be calculated based on the data given

30) In a face centered arrangement of A and B atoms. Where A atoms are at the corners of the unit cell and B atoms are at the face centers . For each unit cell, one A atom is missing from a corner position and one B atom is missing from one face position. The simplest formula of the resulting compound will be: A) B) C) D)

A14B40 A7B20 A1-xB3-x AB2

31) Proton pumps are ubiquitous in living organisms. They (shown in below figure) serve as an important regulator of pH gradients across membranes, which lead to ATP synthesis. Calculate the amount of CHEMICAL work done at temperature T by such a pump to maintain pH = 5 inside the cellular compartment against a neutral pH outside the membrane?

pH = 5 in

A) B) C) D)

pH = 7 out

2 RT 2.303 RT 4.606 RT 23.03 RT

32) The specific heat of a certain material monotonically increases with temperature. Two identical blocks of this material are kept at 50C and 100C, respectively. The two blocks are now brought in contact with each other. Assume that no heat is lost to the surrounding. When thermal equilibrium is reached after the two blocks are kept in contact, what would be the final temperature of the two blocks? A) 75 C B) > 75 C (C) < 75 C D) Tf can be either more than or less than 75 C, depending upon the precise variation of the specific heat with temperature Page 10 of 12     

 

33) What is the product of the following reaction?

(A)

Ph2P

P

PPh2

(B)

+

Ph2P

P

Br3

(C)

Ph2P

P

Br

PPh2

+

Br

Br

Br

PPh2

(D)

+

Br3

none of the above

Br

34) What is the product of the following reaction?

(A)

H3N

BH3

H3N

(B)

n

BH2

Bu

Li

(C)

H2N

Li

(D)

BH3

No reaction

Li

35) Predict the products of the following reactions: [Pt(PPh3)4]2+ + 2Cl[PtCl4]2- + 2PPh3 A) B) C) D)

---- > X ---- > Y

X = trans-[PtCl2(PPh3)2] and Y= cis-[PtCl2(PPh3)2] X = cis-[PtCl2(PPh3)2] and Y= trans-[PtCl2(PPh3)2] X = Y = cis-[PtCl2(PPh3)2] X = Y = trans-[PtCl2(PPh3)2] Page 11 of 12   

 

 

36) The 1H NMR of 1,1-dibromoethane consists of two well-separated signals, one large and another one small. Which one of the following statements is correct? A) The large signal is a quartet and the small signal is a doublet B) The large signal is a triplet and the small signal is a singlet C) The large signal is a singlet and the small signal is a triplet D) The large signal is a doublet and the small signal is a quartet 37) Far infrared and microwave radiation is useful in studying the following process A) Transition of inner electrons of atoms B) Transitions of outer (or valence) electrons in atoms or molecules C) Changes in vibrational-rotational states of molecules D) Changes in molecular rotational states only 38) The reaction of nitric oxide with oxygen gas is given by NO + O2  NO2. When 25 g of NO is allowed to react with 12 g of oxygen gas, the maximum amount of NO2 formed will be A) 38.3 g

B) 17.3 g

C) 34.5 g

D) None of these

39) Which of following observations reflect colligative properties? i. A 0.5 M NaCl solution has a higher vapor pressure than a 0.5 M BaCl2 solution. ii. A 0.5 M NaOH solution freezes at a lower temperature than pure water. iii. Pure water freezes at a higher temperature than pure methanol. A) i and ii only B) i and iii only C) ii and iii only D) i, ii and iii 40) For a canonical ensemble where each system has N, V, T fixed, which of the following statements regarding energy hold(s) true: A) B) C) D)

Energy of the system does not fluctuate At thermodynamic limit (large N) the fluctuation in energy is extremely narrow At thermodynamic limit (large N), the fluctuation in energy is extremely broad All of the above

The following question does NOT carry any marks and is given to collect information only: 41) How much time did you take to complete this chemistry exam? A) Less than 1 hour B) Between 1 to 2 hours C) Between 2 to 3 hours D) Insufficient time was given Page 12 of 12     

CHM-X GS-2017 (Chemistry) TATA INSTITUTE OF FUNDAMENTAL RESEARCH Written Test in CHEMISTRY ‐ December 11, 2016  Duration : Three hours (3 hours)  Name : _______________________________________________ Ref. Code : ____________ 

Please read all instructions carefully before you attempt the questions. 

1.

Please fill‐in details about name, reference code etc.  on the answer sheet.  The Answer Sheet  is  machine‐readable.    Use  only  Blue/Black  ball  point  pen  to  fill‐in  the  answer sheet.

2.

Indicate your ANSWER ON THE ANSWER SHEET by blackening the appropriate circle for each question.  Do not mark more than one circle for any question : this will be treated as a wrong answer.

3.

This is a multiple choice question paper with ONE section having a total of 40 questions. Each  correct  answer  will  get  you  3  marks.    Every  wrong  answer  will  get  you  ‐1  mark. Marks are not awarded or deducted when a question is not attempted.   It is better not to answer a question if you are not sure.

4.

We advise you to first mark the correct answers on the QUESTION PAPER and then to TRANSFER these to the ANSWER SHEET only when you are sure of your choice.

5.

Rough work may be done on blank pages of the question paper.  If needed, you may ask for extra rough sheets from an invigilator.

6.

Use  of  calculators  is  permitted.    Calculator  which  plots  graphs  is  NOT  allowed. Multiple‐use devices such as cell phones, smart phones etc., CANNOT be used for this purpose.

7.

In answering the questions, please choose the option that best describes the solution to the problem.

8.

Do  NOT  ask  for  clarifications  from  the  invigilators  regarding  the  questions.  They  have been  instructed  not  to  respond  to  any  such  inquiries  from  candidates.  In  case  a correction/clarification is deemed necessary, the invigilator(s) will announce it publicly. Page 1 of 18

SOME USEFUL DATA Avogadro number = 6.02u1023 mol1 RT/F = 0.0257 V at 25qC Faraday constant = 96500 C/mol Boltzmann constant k = 1.38u1023 J K1 Mass of an electron = 9.109u1031 kg

e = 1.6u1019 C h = 6.626u1034 J s c = 3u108 m s1 R = 8.314 J K1 mol1

1) For a hydrogen atom, which of the following orbital(s) have the lowest energy: A) 4s B) 4p C) 4d D) All of the above have same energy 2) Given an operator A and a set of vectors ࢄ which obey the following relationship ‫ ࢄܣ‬ൌ Oࢄ, where O is the set of scalars. If A commutes with B and B ≠ A, which of the following is correct: A) X are eigenvectors of A only if the ߣ are all distinct (no two eigenvalues are equal) B) X are eigenvectors of B C) X are eigenvectors of B with set of eigenvalues ߣ D) X need not be eigenvectors of A

3) The non-bonded interactions between two molecules consist of electrostatic (El) and van der Waals (vdW) forces. Which of the following is a correct description of the distance dependence intermolecular interactions between two molecules? A) At large distances, El interactions decay faster than the vdW interactions B) At large distances, vdW interactions decrease faster than the El interactions C) Which force drops faster depends on the net charge of the molecules D) Both interactions have same distance dependence

Page 2 of 18

4) In a cubic unit cell, identify the Miller plane (111)

A)

B)

C)

D)

None of the above

5) Predict the relative rates for the following reductive elimination for X = H, Cl, CH3, OCH3

A) Cl > H > CH3 > OCH3 B) H > Cl > OCH3 > CH3 C) OCH3 > CH3 > H > Cl D) CH3 > H > Cl > OCH3 Page 3 of 18

6) Predict the major product of the following hydroboration reaction:

A)

B)

C)

D)

7) Predict the multiplicities for hydrogens on C1, C3, and C4 of butanone associated with the spin-spin coupling in its 1H NMR spectrum. A) H’s on C1: Singlet; H’s on C3: Doublet; H’s on C4: Triplet B) H’s on C1: Singlet; H’s on C3: Triplet; H’s on C4: Quartet C) H’s on C1: Singlet; H’s on C3: Quartet; H’s on C4: Triplet D) H’s on C1: Triplet; H’s on C3: Doublet; H’s on C4, Triplet

Page 4 of 18

8) All natural amino acids, except one, react with cold nitrous acid and produce nitrogen gas. Which one of the following is that odd amino acid? A) Tryptophan B) Glycine C) Proline D) Histidine

9) Zinc solid has hcp (hexagonal close packed) structure. In a unit cell of solid Zinc, the Zinc atoms occupy A) 74% of volume of unit cell. B) 80% of volume of unit cell. C) 68% of volume of unit cell. D) 90% of volume of unit cell.

10) An organic compound has the following spectroscopic properties: Mass Spectrometry: m/z 102 (very small), 87 & 43 are the largest ions; 1H NMR: δ 1.4 & 3.9 ppm (both singlets, intensity ratio 3:2); 13C NMR: δ 108, 64 & 25 ppm; Infrared spectroscopy: several strong absorptions in the 1000 to 1300 cm-1 region. Which of the following is the most likely formula of this compound?

A)

B)

C)

D)

Page 5 of 18

11) An electron tunnels through a square barrier of width d and height h. If h is fixed and d is is normally distributed, then the electron transfer probability distribution is:

A) a normal distribution B) a delta function C) a log normal distribution D) a poisson distribution

12) In a rotational microwave spectrum of C12O16 lines were equally spaced by 3.863 cm-1. In a rotational Raman spectrum of N2 (normal isotope) the lines were equally spaced by 8.04 cm-1. Assuming that the force constant for the two molecules is inversely proportional to their bond lengths, the ratio of the vibrational frequency of CO to that of N2 will be:

A) 0.8368 B) 0.9952 C) 1.0258 D) 1.2198

13) If standard potential of the reaction 2H2O(l) = O2(g, 1bar) + 4H+(aq) + 4e- is E0 = -1.23 V. At 25oC and pH =7, what is the oxidation potential of pure water according to this reaction? A) +0.410 V B) -2.620 V C) -0.817 V D) -0.410 V

Page 6 of 18

14) Given the molecular formula of the hexa-coordinated complexes (I) Co Cl3 (NH3)6 (II) Co Cl3 (NH3)5 (III) Co Cl3 (NH3)4 If the number of coordinated NH3 molecules in (I), (II), and (III) respectively are 6, 5 and 4 then the oxidation state of Co in (I), (II) and (III) are respectively:

A) +6, +5, +4 B) +3, +2, +1 C) 0, +1, +2 D) +3, +3, +3 15) An aqueous solution contains 0.300 mole L1 of KH2PO4 and 0.015 mole L1 of K2HPO4. Which of the following statements is true about this solution? [Data: For H3PO4, pK1 = 2.16, pK2 = 7.21, pK3 = 12.32]

A) It can act as a buffer solution around pH = 2 B) It can act as a buffer solution around pH = 12 C) Its pH will approximately equal to 6.9 D) Both B and C.

16) The complex showing a spin-only magnetic moment of 2.82 B.M. is A) [Ni(CO)4] B) [NiCl4]2C) [Ni(NH3)4]2+ D) [Ni(CN)4]2-

Page 7 of 18

17) What are X and Y in the following reaction?

18) What is the value of ݅ ݈‫݃݋‬ଵ଴ ݅ ଶ , where ݅ ൌ ξെͳ ? A) Real and positive number B) Real and negative number C) Complex number D) Purely imaginary

19) Cyclooctatetraene is A) aromatic, because it is planar and it follows Hückel’s rule B) antiaromatic, because it is not planar and it does not follow Hückel’s rule C) antiaromatic, because it is planar and it does not follow Hückel’s rule D) nonaromatic, because it is not planar and it does not follow Hückel’s rule

Page 8 of 18

20) What are the products of the following reaction?

21) What is the value of the continued fraction given below?

ͳ൅

ଶ଴଴଴ ଶା

A) 1999

మబబబ మబబబ మశ మశ‫ڮ‬

B) ξʹͲͲͲ

C) ξʹͲͲͳ

D) None of them

22) A compound with molecular formula C5H12O2, has strong infrared absorption at 3300 to 3400 cm-1. The 1H NMR spectrum showed three singlets at δ 0.90, δ 3.45 and δ 3.20 ppm; with relative areas 3:2:1. Addition of D2O to the sample eliminates the lower field signal. The 13C NMR spectrum shows three signals all higher than δ 100 ppm. Which of the following compounds best fits this data?

A) 1,5-pentanediol B) 1,3-dimethoxypropane C) 2,2-dimethyl-1,3-propanediol D) 2,4-pentanediol

Page 9 of 18

o

23) For angular momentum vector operator

o

A)

B)

C)

D)

o

L

, which of the following relation is true:

o2

Lu L i! L o

o

o

o

o

o

o

Lu L i! L o

Lu L i! L

Lu L 0

24) Isotopic substitution is an often-used procedure in assigning vibrational spectroscopic features but the difference in isotopic masses of the vibrating atoms has to be sufficiently large to make the vibrational shift observable. In a double isotopic replacement experiment, a proline with a 13C=18O carbonyl group is inserted in the middle of the polypeptide using molecular recombinant techniques. Given that in the naturally found proline the 12C=16O group exhibits a narrow vibrational feature at 1,711 cm−1, what is the shift of the carbonyl stretching vibration for the 13C=18O proline isotopomer.

Assume: a) The force constant for different isotopes can be considered identical. b) The isotopic changes in the carbonyl group will have little effect on the vibrations of other atoms in proline.

A) 80 cm-1 B) 165 cm-1 C) 85 cm-1 D) 42.5 cm-1

Page 10 of 18

25)

NMR spectroscopy can be used to assay for drug binding to certain protein targets. One of the primary objectives of any binding assay is the quantification of the free and the bound forms of a drug molecule at a certain concentration of the protein target. Let us assume that the fully bound drug exhibits a 1H chemical shift of δA while that of the free form resonates at δB for the same proton (see figure above). If the exchange timescale (i.e.; proportional to kOFF as kON is diffusion limited) between the free form of the drug and its bound form is in microseconds, which of the following statements cannot be true assuming that the drug is only 50% bound with its protein target?

A) The NMR linewidth of the observed transition(s) will be different from the free form of the drug. B) There will be two resonances obtained in the NMR spectrum of the Protein-Drug complex: one for the free form while other for the bound form. C) We will see a single resonance at a position δeff which is in between δA and δB. D) Varying the concentration of the drug molecule while observing the NMR signatures will provide an estimate of the binding constant.

26) At 25 0C, if the pKa value for a weak acid is smaller than its aqueous solution pH by 2, what is the fraction of the acid in dissociated form?

A) 1.10 % B) 99.01 % C) 0.99% D) More information is needed

Page 11 of 18

27) The heat of formation ('Hf) for the reaction 2Cu(s) + O2(g) Æ 2CuO(s) is measured and plotted as a function of temperature (T). Of the 4 possible graphs shown below, which one would most likely represent the observed trend?

A) 1 B) 2 C) 3 D) 4 28) If the outer circle radius is ‘Z’, in the diagram given below, then what is the line segment AB? The ratio of inner circles’ diameters is 2.

A)

ସξଶ ଷ

‫ݖ‬ 

B) close to 2 Z ξହ C) ‫ݖ‬ ξଶ

D)

ଶξହ ଷ

‫ݖ‬

Page 12 of 18

29) Assume that the temperature (T) dependence of ∆G for a chemical reaction can be represented by an equation of the form ∆G = x +›ܶ+zT2 What is the expression for the heat capacity change at constant pressure, 'Cp? A) x/T B) -y C) -2zT D) Insufficient information

30) During isothermal expansion of an ideal gas which of the following happen: (i)

Temperature does not change

(ii)

Process is spontaneous

(iii)

The energy of the system does not change

(iv)

Entropy increases

A) i and iii only B) i, ii, and iv only C) i, iii, and iv only D) i, ii, iii and iv

31) In an experiment measuring the weight of the object, 100 repeats were performed by one student. He found the mean weight of 332 grams with standard error of the mean as 5 grams. A lazier student only performs 10 measurements on the same object. Which of the following values will her result be closest to? A) 330 ± 50 grams B) 400 ± 15 grams C) 330 ± 15 grams D) 330 ± 5 grams

Page 13 of 18

32) Two compartments X and Y are separated by an impermeable partition P. In the compartment X, the following reaction is going on in a solvent S, while the compartment Y contains only the solvent S: A2 + B2 l 2AB Contents of both the compartments are continuously and vigorously stirred. After the reaction in the compartment X has reached equilibrium, the concentrations of A2, B2 and AB are measured and the equilibrium constant calculated. Then the partition is quickly removed. After waiting for a very long time, all the concentrations are measured again, and the new value of the equilibrium calculated. What is the most appropriate statement you can make about the result of this experiment? Assume that the chemicals are behaving ideally and the temperature is kept constant.

X

Y

P A) The concentrations of all the chemicals and the equilibrium constant will be less than their values before the partition was removed. B) After removing the partition, the concentrations of A2 and B2 will increase, and that of AB will decrease. C) After removing the partition, the concentrations of A2 and B2 will decrease, and that of AB will increase. D) After removing the partition, the concentrations of all the chemicals will decrease.

33) A kid has been playing with an inflated balloon. Suddenly, a reaction happens inside the balloon. This causes the inside surface of the balloon to become sticky, so that some of the air molecules inside which collide against the surface get stuck to it. As a result, immediately after the reaction, the balloon will A) Inflate B) Deflate C) Remain unaltered D) Will change its shape without changing its volume

Page 14 of 18

34) “Doping” and “Alloying” are two common terms used to describe the presence of two different elements in one material. Which one of the following statements is false?

A) Doping is the process of intentionally introducing impurities into an semiconductor in order to change its electrical properties. B) Doping means making one solid solution. C) Alloying is a homogeneous mixture of two or more elements, at least one of which is a metal. D) In an alloy, the combined mixture has different properties from those of its component elements.

35) The graph below plots the progress of a dimerization reaction involving species A. It depicts a straight line with slope k (the rate constant). What is the value of the intercept, c in the graph?

A) [A(0)] B) [A(0)]2 C) [A(0)]-1 D) k x [A(0)]2

Page 15 of 18

36) A particle in a 1-D box of length L has eigenstates ߰௡ ሺ‫ݔ‬ሻ with energies‫ܧ‬௡ . Consider two initial states of the particle at time t = 0: case 1) Ȳሺ‫ݔ‬ǡ ‫ ݐ‬ൌ Ͳሻ ൌ ߰௡ (arbitrary n), and case 2) Ȳሺ‫ݔ‬ǡ ‫ ݐ‬ൌ Ͳሻ ൌ ߰௡ ൅ ߰௠ (arbitrary n and m; n ≠ m). The probability to find the particle at a specific position within the box: A) Varies with time for case 1 but not for case 2 B) Is time dependent for both cases C) Is time independent for both cases D) Varies with time for case 2 but not for case 1

37) What major products are obtained in the following Mitsunobu reaction?

A)

B)

C)

D)

Page 16 of 18

38) A bio-conjugation reaction can be used to modify a specific residue on a protein to attach therapeutics and diagnostic agents. Predict the major product of the following bioconjugation reaction with Fluorescein.

A)

B)

C)

D)

Page 17 of 18

39) The acidity of molecules is usually measured by a parameter called the pKa. Metal ions (Mn+) solubilized in water form solvated aqua complexes commonly denoted by [M(H2O)m]n+ or Maqn+. It is known that the pKa of coordinated water in such metal-aqua complexes will be different from that of bulk water. For the following set of metal-aqua complexes: Caaq2+, Feaq2+, Mnaq2+, Feaq3+; arrange the complexes with decreasing value of expected pKa of the coordinated water molecule: A) Feaq2+ > Mnaq2+ > Caaq2+ > Feaq3+ B) Caaq2+ > Mnaq2+ > Feaq2+ > Feaq3+ C) Feaq2+ > Feaq3+ > Mnaq2+ > Caaq2+ D) Mnaq2+ > Caaq2+ > Feaq2+ > Feaq3+

40) Solid inorganic materials are commonly classified as conductors, semi-conductors or insulators as determined by their bandgap. Carbon has many allotropes such as diamond, graphite, carbon nanotubes and graphene with distinct bandgaps. Considering the properties of diamond, what should be its bandgap:

A) 7.0 eV B) 1.0 eV C) 0.01 eV D) 0 eV

The following question does NOT carry any marks and is given to collect information only:

41) How much time did you take to complete this chemistry exam? A) Less than 1 hour B) Between 1 to 2 hours C) Between 2 to 3 hours D) Insufficient time was given

Page 18 of 18

CHM-X GS-2018 (Chemistry) TATA INSTITUTE OF FUNDAMENTAL RESEARCH  WrittenTestinCHEMISTRYͲDecember10,2017 Duration:Threehours(3hours)   Name:_______________________________________________Ref.Code:____________    Pleasereadallinstructionscarefullybeforeyouattemptthequestions.   1. PleasefillͲindetailsaboutname,referencecodeetc.ontheanswersheet.TheAnswer Sheet is machineͲreadable.  Use only Blue/Black ball point pen to fillͲin the answer sheet.  2. IndicateyourANSWERONTHEANSWERSHEETbyblackeningtheappropriatecirclefor eachquestion.Donotmarkmorethanonecircleforanyquestion:thiswillbetreated asawronganswer.  3. ThisisamultiplechoicequestionpaperwithONEsectionhavingatotalof40questions. Each correct answer will get you 3 marks.  Every wrong answer will get you Ͳ1 mark. Marksarenotawardedordeductedwhenaquestionisnotattempted.Itisbetternot toansweraquestionifyouarenotsure.  4. WeadviseyoutofirstmarkthecorrectanswersontheQUESTIONPAPERandthento TRANSFERthesetotheANSWERSHEETonlywhenyouaresureofyourchoice.  5. Roughworkmaybedoneonblankpagesofthequestionpaper.Ifneeded,youmayask forextraroughsheetsfromaninvigilator.  6. Use of calculators is permitted.  Calculator which plots graphs is NOT allowed. MultipleͲusedevicessuchascellphones,smartphonesetc.,CANNOTbeusedforthis purpose.  7. Inansweringthequestions,pleasechoosetheoptionthatbestdescribesthesolutionto theproblem.  8. Do NOT ask for clariĮcations from the invigilators regarding the questions. They have been instructed not to respond to any such inquiries from candidates. In case a correction/clariĮcationisdeemednecessary,theinvigilator(s)willannounceitpublicly. 

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