PYQ 2011 - VedPrep

GATE Chemistry 2011
Previous Year Question Paper with Solution.

1. Jahn-Teller distortion of CuSO₄.5H₂O acts to

(a) raise symmetry

(b) remove an electronic degeneracy

(d) promote a d-electron to an antibonding molecular orbital

Ans. (b)

Sol. In CuSO₄ · 5H₂O, Cu is present as Cu²⁺.

Cu²⁺ = [Ar] 3d⁹

It is clear that the two out of three electrons in e_g orbitals can occupy either orbital or orbital.

Since, the e_g level is not symmetrically filled, Jahn-Teller distortion occurs. This removes the degeneracy of the e_g and t_2g levels. Thus, the complex is distorted.

Correct option is (b)

2. Among the following, the group of molecules that undergoes rapid hydrolysis is:

(a) SF₆, Al₂Cl₆, SiMe₄

(b) BCl₃, SF₆, SiCl₄

(d) [Xe₂F₃]⁺[AsF₆]^–

Ans. (c)

Sol. Out of these compounds BCl₃, SiCl₄ have vacant orbitals, hence H₂O can attack to them easily and they show rapid hydrolysis.

SF₆ is spherical with stronger S–F bonds as well as steric hinderance hence it is not hydrolysed. PCl₅ also vacant orbitals and hence can show hydrolysis.

PCl₅ + H₂O POCl₃ + 2HCl (partial hydrolysis)

PCl₅ + 4H₂O H₃PO₄ + 5HCl (complete hydrolysis)

SiMe₄ has steric repulsion hence H₂O can't attack, showing no hydrolysis. Hence BCl₃, SiCl₄, PCl₅ show more rate of hydrolysis.

Correct option is (c)

3. The reaction of solid XeF₂ with AsF₅ in 1:1 ratio affords

(a) XeF₄ and AsF₃

(b) XeF₆ and AsF₃

(d) [Xe₂F₃]⁺[AsF₆]^–

Ans. (c)

Sol. XeF₂ + AsF₅ [XeF]⁺ [AsF₆]^–

Correct option is (c)

4. A well known naturally occuring organometallic compound is:

(a) vitamin B₁₂ coenzyme

(b) chlorophyll

(d) myoglobin

Ans. (a)

Sol. Vitamin B₁₂ co-enzyme is naturally occuring organometallic compound.

Correct option is (a)

5. The complex that exists as a pair of enantiomers is

(a) trans-[Co(H₂NCH₂CH₂NH₂)₂Cl₂]⁺

(b) cis-[Co(NH₃)₄Cl₂]⁺

(d) [Co(H₂NCH₂CH₂NH₂)₃]³⁺

Ans. (d)

Sol. Complexes of the type [M(aa)₃], [M(aa)₂b₂], M[(aa) b₂c₂] exhibit optical isomerism and exist as a pair of enantiomers.

Thus, [Co(H₂NCH₂CH₂NH₂)₃]³⁺ exists as a pair of enantiomers. The structure of its enantiomers are as

Correct option is (d)

6. The region of electromagnetic spectrum employed in the electron spin resonance (ESR) spectroscopy is:

(a) radiowave

(b) microwave

(d) visible

Ans. (b)

Sol. The region of electromagnetic spectrum employed in the electron spin resonance (ESR) is microwave [3 × 10¹⁰ – 3 × 10¹² Hz]

Correct option is (b)

7. The red color of oxyhemoglobin is mainly due to the

(a) d-d transition

(b) metal to ligand charge transfer transition

(d) intraligand transition.

Ans. (d)

Sol. Red colour of oxyhemoglobin is mainly due to transition in porphyrin system

Correct option is (d)

8. The band structure in an n-type semiconductor is

(a) I

(b) II

(d) IV

Ans. (a)

Sol. In semiconductors there appears an impurity band between valence band and conductivity band.

In n-type of semiconductor the impurity band contain electrons while in p-type conductors impurity band is empty.

But in both case the impurity band show bridge between valence band and conduction band.

Correct option is (a)

9. In the following reaction

The major product [X] is:

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

10. In the following reaction sequence

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

11. The diene which undergoes Diels-Alder reaction with maleic anhydride is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

12. The sequence of an mRNA molecule produced from a DNA template strand with the composition 5'–AGCTACACT–3' is

(a) 5'–AGUGUAGCU–3'

(b) 5'–UCGAUGUGA–3'

(d) 5'–TCGATGTGA–3'

Ans. (c)

Sol.

Correct option is (c)

13. In the following reaction,

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

14. The structure of the dipeptide Ala-Pro derived from the natural amino acids is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol. Ala-Pro

In this dipeptide alanine is at N–T-A.A. So, NH₂ group of Ala should be free and proline is at C-T-AA. So, group should be free at Pro and both amino acid have 'S' configuration. So, it should be maintained ion the product also.

Correct option is (a)

15. In the following reaction

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Correct option is (c)

16. In the following reaction,

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

17. For a given first order reaction, the reactant reduces to 1/4^th its initial value in 10 minutes. The rate constant of the reaction is:

(a) 0.1386 min^–1

(b) 0.0693 min^–1

(d) 0.0693 mol L^–1 min^–1

Ans. (a)

Sol.

Correct option is (a)

18. The freezing point constant for water is 1.86 K (mol kg^–1)^–1. The change in freezing point when 0.01 mol glucose is added to 1 kg water is:

(a) 1.86 K

(b) –1.86 K

(d) –0.0186 K

Ans. (d)

Sol. Depression in freezing point

= i.k_f.x

Glucose is non electrolyte i = 1

k_f = 1.86k (mol/kg)^–1

Molality (m) = = 0.01

= 1 × 1.86 × 0.01 = 0.0186

T_f = 0 – 0.0186 = – 0.0186

Correct option is (d)

19. On the pressure-temperature diagram for a one-component system, the point where the solid-liquid and the liquid-gas curves intersect is:

(a) triple point

(b) critical point

(d) boiling point

Ans. (a)

Sol. Triple point is the piont on the P – T diagram for one compnent systement at which the solid-liquid and the liquid gas curves intersect. At this point all three phases (solid and vapour) can co-exist in equilibrium.

Correct option is (a)

20. The wave function for a harmonic oscillator described by Nx has

(a) One maximum only

(b) One maximum, one minimum only

(d) Two maxima, two minima only

Ans. (b)

Sol.

Further differentiation,

Hence, one maxima and one minima.

Correct option is (b)

21. If an arbitrary wave function is used to calculate the energy of a quantum mechanical system, the value calculated is never less than the true energy.

The above statement relates to

(a) Perturbation theory

(b) Variation principle

(d) quantization of energy

Ans. (b)

Sol. From variation principle, if we are used an arbitary wave function and calculate the energy of a quantum mechanical system the value calculated is never less than the true energy. This principle used for the validity of function.

> E₀

Where, = energy calculated

E₀ = energy system.

Correct option is (b)

22. The point group symmetry of the given planar shape is:

(a) D_3h

(b) C₃

(d) C_3v

Ans. (c)

Sol.

1C₃ axis, Hence, C_3h point group

Correct option is (c)

23.

(a) V

(b) S

(d) –V

Ans. (a)

Sol. dG = VdP – SdT (from Maxwell)

At constant temperature dT = 0

Correct option is (a)

24.

According to Ehrenfest classification of phase transitions, the above diagram refers to

(a) Zeroth order phase transition

(b) First order phase transition

(d) transition

Ans. (b)

Sol. Main characteristics of first-order transitions are:

(1) The chemical potential is a continuous function of temperature.

(2) The derivatives of chemical potential are discontinuous.

Correct option is (b)

25. According to conventional transition state theory, for elementary bimolecular reactions, the molar entropy of activation is:

(a) Positive

(b) Zero

(d) Positive for endothermic and negative for exothermic reactions.

Ans. (c)

Sol. According to conventional transition state theory for elementary bimolecular reactions the molar entropy of activation . is negative because two reactant species come together to form one species.

for Bimolecular Reactions is – 1

Correct option is (c)

26. The crystal field stabilization energy (CFSE) value, for [Ti(H₂O)₆]³⁺ that has an absorption maximum at 492 nm is

(a) 20,325 cm^–1

(b) 12,195 cm^–1

(d) 8,130 cm^–1

Ans. (d)

Sol. Absorption maximum, = 492 nm

= 492 × 10^–7 cm

= 20325 cm^–1

CFSE = – 0.4

= – 0.4 × 20325

= 8130 cm^–1

Correct option is (d)

27. For Et₂AlX (X = , Ph^–, Cl^–1 and H^–), the tendency towards dimeric structure follows the order

(a)

(b)

(c)

(d)

Ans. (d)

Sol. Correct option is (d)

28. In the isoelectronic series, VO₄^3–, CrO₄^2– and MnO₄^– all members have intense charge transfer (CT) transitions. The incorrect statement is

(a) CT transitions are attributed to excitations of electrons from ligand (σ) to metal (e)

(b) MnO₄^– exhibits charge transfer at shortest wavelength among the three

(d) The charge on metal nucleus increases in the order VO₄^–3 < CrO₄^–2 < MnO₄^–

Ans. (b)

Sol. CT (charge transfer) transitions are attributed to excitations of electron from ligand to metal or vice-versa.

Higher the oxidation state of metal, higher is the wavelength of transition.

Order of oxidation state is

V⁵⁺ < Cr⁶⁺ < Mn⁷⁺

The order of wavelength of transition is

MnO₄^– have high oxidation state.

So, energy gap will be less and wavelength will be maximum.

Correct option is (b)

29. The increasing order of wavelength of absorption for the complex ions

(i) [Cr(NH₃)₆]³⁺

(ii) [CrCl₆]^3–

(iii) [Cr(OH₂)₆]³⁺

(iv) [Cr(CN)₆]^3– is

(a) iv < ii < i < iii

(b) iv < iii < ii < i

(d) ii < iii < i < iv

Ans. (c)

Sol. Ligand strengh Cl^– < H₂O < NH₃ < CN^–

Cr³⁺ CFSE = Cl^– < H₂O < NH₃ < CN^–

So, Cl^– > H₂O > NH₃ > CN^–

So, correct option is (c)

30. The total number of metal-metal bonds in Ru₃(CO)₁₂ and Co₄(CO)₁₂, respectively, is

(a) 3 and 6

(b) 4 and 5

(d) 3 and 4

Ans. (a)

Sol. Ru₃(CO)₁₂ TVE 3 Ru 8 × 3 = 24 electron

12CO 12 × 2 = 24 electron

TVE = 48 electron

B = n × 18 – TVE, n = number of metal

= 3 × 18 – 48

= 54 – 48 = 6

= number of M—M bond ; = 3 (M—M bond)

Co₄(CO)₁₂ = TVE

4Co 4 × 4 = 36 electron

12CO 12 × 2 =

B = n × 18 – TVE = 4 × 18 – 60 = 12 ; = 6 (M—M bond)

Correct option is (a)

31. According to VSEPR theory the shapes of [SF₂Cl]⁺ and [S₂O₄]^2– should be

(a) trigonal planar for [S₂O₄]^2– and trigonal pyramidal for [SF₂Cl]⁺

(b) both trigonal planar

(d) both trigonal pyramidal

Ans. (d)

Sol. The Hybridised sp³ in [SF₂Cl]⁺.

hence, the shape will by trigonal pyramidal.

In [S₂O₄]^2– (Dithionite ion) 's' is sp³ hybridised by the S–S bond length are longer than that in polysulphites hence lp–lp repulsion is minimum.

Due to this here SO₂ planes almost parallel (dihedral angle is 30°) giving if (especially (SO₂^–) unit) a planar eclipsed structure.

Correct option is (d)

32. The product of the reaction between CH₃Mn(CO)₅ and ¹³CO is:

(a) (CH₃¹³CO)Mn(CO)₅

(b) (CH₃CO)Mn(CO)₄(¹³CO)

(d) CH₃Mn(CO)₄

Ans. (b)

Sol.

Correct option is (b)

33. The correct pair of ¹H and ³¹P NMR spectral patterns for C(H)(F)(PCl₂)₂ is:

(a)

(b)

(c)

(d)

Ans. (c)

Sol. The correct pair ¹H and ³¹P NMR

C(H) (F) (PCl₂)₂

¹H NMR (2NI + 1) (2NI_P + 1)

31P NMR (2NI_F + 1) (2NI_H+ 1)

Correct option is (c)

34. In the following reaction

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

35. In the following reaction,

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Correct option is (c)

36. In the following reaction,

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

37. The most appropriate sequence of reactions for carrying out the following conversion

(a) (i) Peracid; (ii) H⁺; (iii) Zn/dil. HCl

(b) (i) Alkaline KMnO₄; (ii) NaIO₄; (iii) N₂H₄/KOH

(d) (i) O₃/Me₂S; (ii) NaOEt; (iii) N₂H₄/KOH

Ans. (d)

Sol.

Correct option is (d)

38. In the following reaction sequence

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

39. In the following conversion

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

40. In the following reaction,

the major product [X] is:

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

41. In the reaction,

Optically pure (+)-trans-2-acetoxycyclohexyl tosylate

the major product [X] is:

(a) racemic trans-1, 2-cyclohexanediol diacetate

(b) optically active trans-1, 2-cyclohexanediol diacetate

(d) optically active cis-1, 2-cyclohexanediol diacetate.

Ans. (a)

Sol.

Correct option is (a)

42. The activity of water at 11 bar and 298K is:

(a) 1.101

(b) 1.007

(d) 0.898

Ans. (a)

Sol. At NTP concentration of water = 55.5 mol/L

Correct option is (a)

43. For the process

assuming ideal gas behavior, the change in molar entropy is:

(a) –27.57 J K^–1 mol^–1

(b) +27.57 JK^–1 mol^–1

(d) +24.20 JK^–1 mol^–1

Ans. (a)

Sol.

Correct option is (a)

44. The wave function for a quantum mechanical particle in a 1-dimensional box of length 'a' is given by

The value of 'A' for a box of length 200 nm is

(a) 4 × 10⁴ (nm)²

(b)

(c)

(d) 0.1 (nm)^–1/2

Ans. (d)

Sol. For one elimensional box

A = for one dimensional box normalisation constant

a = 200 nm

A =

Correct option is (d)

45. For 1 mole of a monoatomic ideal gas, the relation between pressure (p), volume (V) and average molecular kinetic energy is

(a)

(b)

(c)

(d)

Ans. (c)

Sol. PV = 1/3 MNu^–2

PV = 2/3 N ×

Correct option is (c)

46. For a 1 molal aqueous NaCl solution, the mean ionic activity coefficient and the Deby-Huckel Limiting Law constant (A) are related as

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

47. For the concentration cell

M | M⁺ (aq, 0.01 mol dm^–3) || M⁺ (aq, 0.1 mol dm^–3) | M

the EMF (E) of the cell at a temperature (T) equals

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

Commond Data Questions:

Commond data for Q.48 and Q.49:

A hypothetical molecule XY has the following properties

Reduced mass: 2 × 10^–26 kg

X–Y bond length: 100 pm

Force constant of the bond: 8 × 10² N.m^–1

48. The frequency of radiation (in cm^–1 units) required to vibrationally excite the molecule from v = 0 to v = 1 state is

(a) 3184.8

(b) 2123.2

(d) 840.0

Ans. (c)

Sol.

Wave number

Correct option is (c)

49. The frequency of radiation (in cm^–1 units) required to rotationally excite the molecule from J = 0 to J = 1 state is

(a) 1.4

(b) 2.8

(d) 3.6

Ans. (b)

Sol. J = 0 to J = 1

Correct option is (b)

Common data for Q.50 and Q.51:

Na₂HPO₄ and NaH₂PO₄ on heating at high temperature produce a chain sodium pentaphosphate quantitatively.

50. The ideal molar ratio of Na₂HPO₄ to NaH₂PO₄ is:

(a) 4 : 1

(b) 1 : 4

(d) 2 : 3

Ans. (d)

Sol.

Correct option is (d)

51. The total charge on pentaphosphate anion is:

(a) –5

(b) –3

(d) –9

Ans. (c)

Sol. Na₇P₅O₁₆ 7Na⁺ + P₅O₁₆^7–

Correct option is (c)

Linked Answer Q.52 and Q.53:

The decomposition of ozone to oxygen 2O₃(g) 3O₂(g) occurs by mechanism

where, M is the catalyst molecule.

k_i' are rate constants and K_a,i's the activation energies for the elementary steps,

52. Under the steady state approximation for the intermediates, the rate of decomposition of ozone, , is

(a)

(b)

(c)

(d)

Ans. (a)

Sol. r = K₃[O][O₃]

Applying SSA on [O]

Rate of formation = Rate of consumption

K₁[M][O₃] = K₂[O₂][O][M] + K₃[O][O₃]; [O] =

r = K₃[O₃]

Rate of decomposition of ozone, = 2r

Correct option is (a)

53. Assuming k₃[O₃] >> k₂[O₂][M], the activation of the overall reaction is

(a)

(b) E_a,3 + E_a,1 – E_a,2

(d) E_a,1

Ans. (d)

Sol.

Correct option is (d)

Statement for Linked Answer Q.54 and Q.55:

A ketone on treatment with bromine in methanol gives the corresponding monobromo compound[X] having molecular formula C₅H₉BrO. The compound [X] when treated with NaOMe in MeOH produces [Y] as the major product. The spectral data for compound [X] are: ¹H NMR: 1.17(d, 6H), 3.02 (m, 1H), 4.10(s, 2H); ¹³C NMR: 17, 37, 39, 210.