TIFR GS 2012 Question Paper Chemistry X

Correct Answers are ticked in green.

CHM-X
GS-2012 (Chemistry)
TATA INSTITUTE OF FUNDAMENTAL RESEARCH

Written Test in CHEMISTRY - December 11, 2011
Duration : Three hours (3 hours)

Name : _______________________________________________ Ref. Code : ____________

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SOME USEFUL DATA

Avogadro number = 6.02×1023 mol-1 e = 1.6×10−19 C
RT/F = 0.0257 V at 25°C h = 6.626×10−34 J⋅s
Faraday = 96500 C/eq. wt. c = 3×108 m s−1
Boltzmann constant k = 1.38×10−23 J K−1 R = 8.314 J K-1 mol-1
Z2
En = − a.u. for hydrogen like atom
2n 2
Mass of an electron = 9.109×10−31 kg
8kT
Average velocity =
π ⋅m

1. A quantum mechanical state Q is a superposition of two normalized energy
eigenstates A and B in an amplitude ratio 2:1. If the two states are degenerate with
a common eigenvalue E, what is the energy of the state Q?

A) 0,
B) 3E
C) 5E
D) E

2. For the above, if the states were non-degenerate and with energy eigenvalues E
and −E respectively, then what would be the expectation value of the energy?

A) 3E
B) 5E
C) E
D) None of the above

3. Suppose we inscribe a circle inside an equilateral triangle, and then inscribe a
square inside this circle. What is the ratio of the side of the square to the side of
the triangle?

A) 1: ¥3
B) 2:5
C) 1: ¥6
D) 1:2

Page 1 of 16

4. The reversible reaction S ļ P is catalyzed by a catalyst. The equilibrium
constant Keq = [P]/[S] is 2 x 103. The forward rate constant was found to be 5 x
104 sec-1 and 4 x 10-6 sec-1 in the presence and in the absence of the catalyst
respectively. What is the expected rate constant for the reverse reaction in the
absence of the catalyst?

A) 5 x 108 sec-1
B) 2 x 10-9 sec-1
C) 0.8 x 10-10 sec-1
D) 5 x 10-9 sec-1

5. The molar extinction coefficient (at 550 nm) of compounds A and B are 1x104 M-1
cm-1 and 1 x 105 M-1 cm-1 respectively. Solutions of A and B are made at
concentrations of 1 x 10-4 M and 2 x 10-5 M respectively. In a spectrophotometer
set at 550 nm, the percentage of light transmitted by solutions A and B (in two
separate experiments) will be:

A) the same
B) B will transmit 10 times less light compared to A
C) B will transmit 5 times less light compared to A
D) B will transmit 2 times less light compared to A.

6. What are the configurations (R or S) of the chiral centers in the following
molecules:

H OH NH2
HOOC NH2
SH
H OH
1 2 3

A) Compound 1 = R; Compound 2 = R; Compound 3 = 1S, 2S
B) Compound 1 = R; Compound 2 = S; Compound 3= 1R, 2S
C) Compound 1 = S; Compound 2 = S; Compound 3 = 1S, 2R
D) Compound 1 = R; Compound 2 = S; Compound 3 = 1S, 2R

Page 2 of 16

7. What are the oxidation states of the metal ion in the following compounds

1. PdCl2
2. Pd(PPh3)4
3. Pd(OAc)2
4. ArPdBr where Ar is Aryl

A) 2, 4, 2, 2
B) 2, 0, 2, 1
C) 2, 0, 2, 2
D) 0, 0, 0, 2

8. Methanesulfonyl chloride is used commonly to form methanesulfonates upon
reaction with alcohols. Methanesulfonates are good leaving groups in nucleophilic
substitution reaction. In the following reaction calculate the volumes of
methanesulfonyl chloride and triethylamine required in ȝL. The amount of starting
material and the number of equivalents of each reagent is given.

O S O O S O
HO OH O O

N N
O
N Ethyl Acetate
+ S Cl +
O
solid liquid liquid

Amount (mg) 100

equivalents 1 2 3

Density (g/mL) 1.48 0.73

μL D E

A) D = 126, E = 167
B) D = 0.085, E = 0.229
C) D = 85, E = 229
D) D = 1.1, E = 1.65

Page 3 of 16

9. The vibrational Raman effect, a considerably weak scattering phenomena, was
first reported by Late Sir CV Raman in 1928. The intensity of the individual
vibrational resonances observed in a Raman spectrum is proportional to

A) Number of molecules
B) Polarizibility of the bond
C) Wavelength of radiation used
D) All of the above

10. The Wittig reaction is a reaction with an aldehyde or ketone with a phosphonium
ylide. Predict the product of the following reaction:

O
PPh3 + H

A)

B)

C)

D)

Page 4 of 16

11. The standard redox potential of water oxidation to dioxygen is −1.23 V.

2 H2O Æ O2 + 4H+ + 4e-

The redox potential of the same reaction at pH = 7 would be:

A) -0.41 V
B) -1 V
C) -0.82 V
D) -1.64 V

12. Amino acid side-chains in proteins have hydrogen bonds for structural and
catalytic reasons. One such combination of H-bonding partners is Histidine
associated with a partnering residue such as Tyrosine (X-H…N-His, where X is the
partnering amino acid). If the pKa of Histidine is 6.1, estimate the pKa of the
partnering residue (X-H) such that protonation of His at pH 6.5 is a favourable
process.

A) pKa >10
B) pKa <1
C) pKa < 6
D) 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) q2/4πİr
B) q2/16πİr
C) q2/ 4πİr2
D) 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) zero
B) first-order
C) second-order
D) 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 ֎ Glucose-6-phosphate

A) 0.06
B) 16.9
C) 4798
D) 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) 5’AGATCC3’
B) 5’CCTAGA3’
C) 5’GGATCT3’
D) 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-Ala-
Gly, Gly-Ser-Gly, and Ser-Gly-Ala peptides. What is the amino acid repeat?

A) Gly-Gly-Ser-Ala-Gly-Ala
B) Gly-Gly-Gly-Ala-Ala-Ser
C) Ser-Ala-Ala-Gly-Gly-Gly
D) 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 O
R N R C O N R C I
RS S N

O O
R1 R2 R3 R4

A) R1, R2 and R3
B) R2, R3 and R4
C) R4, R2 and R1
D) 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) drdθdφ
B) rsinθdrdθdφ
C) r2sin2θdrdθdφ
D) 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) 1.33 × 10-19 sec
B) 5.0 × 10-15 sec
C) 5.46 × 10-13 sec
D) 7.39 × 10-7 sec

Page 8 of 16

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

COO -
H2
A) HO C CH

+NH3

COO -
H2
-O C CH
B)
NH 2

COO -
H2
HO C CH
C)
NH 2

COO -

H2
-O C CH
D)

+NH3

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

A) 1
B) 1000
C) 0.605
D) 1.653

24. The reaction of sodium ethoxide with ethyliodide to form diethyl ether is termed

A) electrophilic substitution
B) nucleophilic substitution
C) electrophilic addition
D) radical substitution

Page 9 of 16

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

A) Fe3+
B) Co3+
C) Co2+
D) 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) 0ƫ2
B) 1ƫ2
C) 2ƫ2
D) 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) 79°
B) 45°
C) 11°
D) 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) 3.90 x 103
B) 1.54 x 104
C) 1.54 x 102
D) 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) 4 x 10-4 cm2 s-1 V-1
B) 1 x 10-4 s-1 V-1
C) 4 V cm2 s-1
D) 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) Only (i) and (ii)
B) Only (ii) and (iii)
C) Only (iv)
D) (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) Benzene
B) Benzenehexachloride
C) Chlorobenzene
D) Dichlorobenzene

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

2
§ 64 π 4ν mn
3
· §¨ ∧ ·
¸
A m → n = ¨¨ ¸¸ ⋅ m d n
¹ ¨© ¸
3
© 3 hc 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) electronic < vibrational < rotational
B) vibrational < rotational < electronic
C) rotational < vibrational < electronic
D) 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) ΔS˚ = 0
B) ΔS˚ = +ve
C) ΔS˚ = −ve
D) 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) −2
B) 0
C) 1
D) 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) 1011
B) 1031
C) 10-31
D) 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) The entropy increases, and the free energy decreases.
B) The entropy decreases, and the free energy decreases.
C) The entropy increases, and the free energy increases.
D) 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.

Flask 1 Flask 2 Flask 3 Flask 4 Flask 5
1 M HCl 25 ml 25 ml 25 ml 25 ml 25 ml
NaHCO3 0.70 g 1.00 g 2.10 g 4.20 g 6.30 g

A) The size of Balloon 1 = Balloon 2 = Balloon 3 = Balloon 4 = Balloon 5.
B) The size of Balloon 1 < Balloon 2 < Balloon 3 < Balloon 4 < Balloon 5.
C) The size of Balloon 1 < Balloon 2 < Balloon 3 = Balloon 4 = Balloon 5.
D) 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) 1
B) 3
C) 6
D) 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) 2 x 10-9 M
B) 1.98 x 10-7 M
C) 2 x 10-6 M
D) 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) Less than 1 hour.
B) Between 1 to 2 hours.
C) Between 2 to 3 hours.
D) Insufficient time was given.

Page 16 of 16

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CHM-X
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