## GATE Chemistry 2018

Previous Year Question Paper with Solution.

1. For low partial pressure of ozone , the adsorption of ozone on graphite surface is the fully dissociative in nature and follows Langmuir isotherm. Under these conditions, if the dependence of the surface coverage of graphite on partial pressure of ozone is given by , the value of x is ____________ (Upto two decimal places)

Ans. (0.33)

Sol.

2. According to Eyring state theory for a bimolecular reaction, the activated complex has

(a) no vibrational degrees of freedom

(b) vibrational degrees of freedom but they never participate in product formation

(c) one high frequency vibration that leads to product formation

(d) one low frequency vibration that leads to product formation

Ans. (d)

Sol. E_{wb} = hv = k_{b}T hv = k_{B}T, v =

The frequency of such vibration will be low and average energy will be of the order of k_{B}T.

Correct option is (d)

3. The major product formed in the following reaction is

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

4. The major product of the following intramolecular cycloaddition reaction is

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

5. The coordination geometries around the copper ion of plastocyanin (a blue-copper protein) in oxidized and reduced form, respectively are

(a) tetrahedral and square-planar

(b) square-planar and tetrahedral

(c) distorted tetrahedral for both

(d) ideal tetrahedral for both

Ans. (c)

Sol. Both oxidised and reduced form of plastocyanin have distorted Td geometry.

6. The major product formed in the following reactions is

(a)

(b)

(c)

(d)

Ans. (d)

Sol. Hantzsch Dihydropyridine synthesis

7. The spherical harmonic function with appropriate values of and m, is an eigenfunction of operator. The corresponding eigenvalue is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

8. The temperature derivative of electrochemical potential E at constant pressure, is given by

(a)

(b)

(c)

(d)

Ans. (b)a

Sol.

9. The water exchange rates for the complex ions follow the order

(a)

(b)

(c)

(d)

Ans. (d)

Sol. Rate of water exchange

It also depend upon electronic configuration (for ion having same o.s.) ions having d^{3} configuration show alter exchange lesser as compared so d^{7} configuration. Hence order of H_{2}O exchange is

Correct option is (d)

10. For an ionic micelle-forming surfactant near its critical micelle concentration (CMC), the dependence of molar conductivity and surface tension on surfactant concentration is best represented by

(a)

(b)

(c)

(d)

Ans. (b)

Sol. Ionic micelle forming surfactant near its critical miscelle concentration (CMC)**
**

Correct option is (b)

11. The major product formed in the following reaction sequence is

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

12. Two moles of an ideal gas X and two moles of an ideal gas Y, initially at the same temperature and pressure, are mixed under isothermal-isobaric condition. The entropy change on mixing is ______________JK^{–1}.

(Upto one decimal place, Use R = 8.31 JK^{–1} mol^{–1})

Ans. (23.05 JK^{–1})

Sol.

.

Correct answer is (23.05 JK^{–1})

13. Consider the operators, where and are the position and linear momentum operators, respectively. The commutator, is equal to

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

14. In the 1H NMR spectrum of an organic compound recorded on a 300 MHz instrument, a proton resonates as a quartet at 4.20 ppm. The individual signals of quartet appear at , 4.19, 4.21 and 4.23 ppm. The coupling constant J in Hz is ___________

Ans. (6)

Sol. **J = 4.19 – 4.17 = 0.02 ppm (since, 1 ppm = 300 Hz)
**

0.02 ppm = 0.02 × ppm = 6Hz

Correct answer is (6)

15. The bond angle (Ti–C–C) in the crystal structure of

is severely distorted due to

(a) hydrogen-bonding interaction

(b) agostic interaction

(c) steric bulk of the phosphine ligand

(d) higher formal charge on metal.

Ans. (b)

Sol. Distortion in Ti–C–C bond angles is due to agostic interaction

Correct option is (b)

16. The major product formed in the following reaction sequence is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

17. The lowest energy transition of the complexes follow the order

(a)

(b)

(c)

(d)

Ans. (a)

Sol. Order of energy for d-d transition is

it depends upon ligand field strength.

Order of ligand field strength

H_{2}O < NH_{3} < CN^{–}

Correct option is (a)

18. The major product of the following reaction is

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

19. The total number of valence electrons in W is ____________ (Atomic number of W = 74)

Ans. (18)

Sol. w( – Cp) ( – Cp) (CO)_{2}**
**

Electron from w = 6

Electron from – Cp = 3

Electron from – Cp = 5

Electron from 2 CO =

Hence, number of valence electron is eqal to 18.

20. The energy of a hydrogen molecule in its ground state equilbrium configuration is –31.7eV. Its dissociation energy is ______________eV. (Upto one decimal place)

Ans. (4.5)

Sol.

21. The molar heat capacity of a substance is represented in the temperature range 298K to 400K by the empirical relation , where b is a constant. The molar enthalpy change when the substance is heated from 300K to 350K is 2 kJ mol^{–1}. The value of b is _____________ J K^{–2} mol^{–1}. (Upto two decimal places)

Ans.

Sol. T_{1} = 298 K; T_{2} = 400 K**
**

C_{p, m} = (14 + bT) JK^{–1 }mol^{–1
}

^{
}

^{
}

^{ }

22. In the electron ionization (EI) mass spectra, methly hexanoate, methyl heptanoated and methyl octanoate give the same base peak. The m/z value of the base peak is _____________

Ans. (74)

Sol.

23. For the radioactive isotope ^{131}I, the time required for 50% disintegration is 8 days. The time required for the 99.9% disintegration of 5.5 of ^{131}I is _____________ days. (Upto one decimal place)

Ans. (80.33)

Sol.

24. The symmetry label of valence p orbitals of a metal ion in an octahedral ligand field is

(a) t_{lg}

(b) t_{tu}

(c) e_{g} + a_{lg}

(d) t_{2g}

Ans. (b)

Sol. The symmetry of label of valence p orbital of a metal ion in an octahedral ligand field is t_{1u}.

25. Based on Wade's rule, the structure-type of [B_{5}H_{8}]^{–} is

(a) closo

(b) nido

(c) arachno

(d) hypho

Ans. (b)

Sol. [B_{5}H_{8}]^{–} = [B_{5}H_{5}]^{4–} = Nido

Correct option is (b)

26. Spectroscopic ground state term symbols of cobalt ions in respectively are

(a)

(b)

(c)

(d)

Ans. (b)

Sol. **[Co(H _{2}O)_{6}]^{2+}, high spin
**

**
**

** **

27. The reaction of equimolar quantities of Fe (CO)_{5} and OH^{–} gives a complex species X which on further reaction with MnO_{2} give species Y. X and Y, respectively, are

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

28. The enantiomeric pair, among the following is

(a)

(b)

(c)

(d) and

Ans.

Sol.

Both are enantiomers.

Hence the correct option is (d)

29. In a molecule XY, let and denote normalized atomic orbitals of atoms X and Y, respectively. A normalized molecular orbital of XY is given by . The value of the overlap integral of and is ___________ (Upto two decimal place)

Ans. (0.59)

Sol. For molecule XY if and are normalized atomic orbital for atoms X and Y**
**

where, S_{XY} = overalp integral

(0.56)^{2} + (0.56)^{2} + 2 × 0.56 × 0.56 × S_{XY} = 1 {S_{XY} = 0.59}

Correct answer is (0.59)

30. The absorption maxima of two dyes X and Y are 520 and 460 nm, respectively. The absorbance data of these measured in a 1cm path length cell are given in the table below.

The concentration of Y in the mixture is ___________ mM. (Upto two decimal places)

Ans. (7.7967 mM)

Sol.

Correct answer is (7.7967 mM)

31. The major product in the following reaction sequence is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

32. the elimination product of the following reaction is

(a) I_{2
}

(b) CH_{3}I

(c) CH_{3}COI

(d) I_{3}

Ans. (c)

Sol.

33. Number of carbonyl groups present in the final product of the following reaction sequence is

Ans. (4)

Sol.

Correct option is (4)

34. For the following reaction sequence,

X and Y, respectively, are

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

35. he major product of the following reaction sequence is

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

36. For a diatomic vibrating rotor, in vibrational level v = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm^{–1}. Its equilibrium oscillation frequency is 2998.3 cm^{–1}, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm^{–1}. The value of J is ___________. (Up to nearest integer)

Ans. (12)

Sol.

1454.99 = 9.716 J (J +1)

J (J + 1) = 149.7

Correct option is (12)

37. At temperature T, the canonical partition function of a harmonic oscillator with fundamental frequency (v) is given by

For , the probability of finding the harmonic oscillation in its ground vibrational state is ___________ (Upto two decimal places)

Ans. (**)

Sol. Probability of finding particle in ground state

p_{0} = 0.95

** Note:** Here partition function give is vibrational partition function with considering zero point energy.

** **

38. A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is ( is a constant). Using only the first order correction, the total ground state energy of the anharmonic oscillator is

Note: For aone-dimensional harmonic oscillator

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

39. The rate constant of a first order reaction, is 1.6×10^{–1} s^{–1} at 300K. Given that the activation energy of the reaction is 28 kJ mol^{–1} and assuming Arrhenium behaviur for the temperature dependence, the total time required to obtain 90% of Y at 350K is ___________s. (Upto to one decimal place, use R = 8.31 JK^{–1} mol^{–1}).

Ans. (289.6 sec)

Sol.

40. The strongest band observed in the IR spectrum of the final product of the following reaction appears, approximately at __________×100 cm^{–1} (Upto one decimal place)

.

Ans. (17.0)

Sol.

Correct answer is (17.0)

41. The reaction of PCl^{3} with PhLi in 1:3 molar ratio yields X as one of the products, which on further treatment with CH_{3}I gives Y. The reaction of Y with n-BuLi gives product Z. The product X, Y and Z respectively, are

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Correct option is (c)

42. The electrons in benzene can be modelled as particles in a ring that follow Pauli's exclusion principle. Given that the radius of benzene is 1.4Å, the longest wavelength of light that is absorbed during an electronic transition in benzene is __________________________________nm. (Upto one decimal place. Use h = 6.6 × 10^{–34}Js, c = 3.0 ×10^{8} ms^{–1})

Ans. (212.1 nm)

Sol. The longest wavelength absorption in the benzene spectrum according to model

43. Second-order are constant for the reaction between and H_{2}O; n = 2 for X = Cl^{–}) and at room temperature varies with the X as

(a)

(b)

(c)

(d)

Ans. (b)

Sol. Cl^{–}_{
} > H_{2}O > NH_{3}

Correct option is (b)

44. The Latimer diagram of oxygen is given below. The value of x is ___________ V. (Upto two decimal places)

Ans. (1.23)

Sol.

Correct answer is (1.23)

45. The major product formed in the following retro-aldol reaction is

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

46. The enthalpy of vaporization of a liquid at its boiling point (T_{b} = 200 K) is 15.3 kJ mol^{–1}. If the molar volumes of the liquid and the vapour at 200K are 100 and 12000 cm^{3} mol^{–1}, respectively, then the slope of the liquid-boundary is ___________kPa (Upto two decimal places. Note : 1 Pa = 1 J m^{–1})

Ans. (6.4339 kPaK^{–1})

Sol.

= 0.0064339 × 10^{6} = 6433.9 PaK^{–1} = 6.4339 kPaK^{–1}

47. The O_{2} coordinated to metal ion centres in oxy-myoglobin and oxy-hemocyanin exists, respectively, as

(a) superoxide and peroxide

(b) superoxide and superoxide

(c) peroxide and peroxide

(d) superoxide and oxygen

Ans. (a)

Sol. O_{2} coordinated to oxyhemoglobin exist as while in oxyhemocyanin as **
**

Correct option is (a)

48. For an inverse spinel, AB_{2}O_{4}, the A and B, respectively, can be

(a) Ni(II) and Ga(III)

(b) Zn(II) and Fe(III)

(c) Fe(II) and Cr(III)

(d) Mn(II) and Mn(III)

Ans. (a)

Sol. A spinel AB_{2}O_{4}, is inverse spinel if CFSE of A^{2+} ion in octahedral site is more than CFSE of B^{3+} ion in oh site.

CFSE of Ni^{2+} in oh site is more than CFSE of Ga(III).

Correct option is (a)

49. he molar conductivity of a 0.01 M weak acid (HX) at 298K, measured in a conductivity cell with cell constant of 0.4cm^{–1}, is 64.4 Scm^{2} mol^{–1}. The limiting molar conductivities at infinite dilution of H^{+} and X^{–} at 298K are 350 and 410 S cm^{2} mol^{–1}. Ignoring activity coefficients, the pK_{a} of HX at 298K is ___________ (Upto two decimal places)

Ans. (4.105)

Sol.

50. The spacing between the two adjacent lines of the microwave spectrum of H^{35}Cl , is 6.35 × 10^{11} Hz, given that bond length D^{35}Cl is 5% greater than that of H^{35}Cl the corresponding spacing for D^{35}Cl is ___________ × 10^{11} Hz. (Upto two decimal places)

Ans. (**)

Sol.

2B_{H – Cl} = 6.35 × 10^{11} Hz

B_{H – Cl} = 3.175 × 10^{11} Hz

= 2.95 × 10^{11} Hz

51. Generally, the coordination number and the nature of the electronic absorption band of lanthanide (III) ion in their complexes are respectively

(a) greater than 6 and sharp

(b) 6 and broad

(c) less than 6 and sharp

(d) greater than 6 and broad

Ans. (a)

Sol. Due to larger size of lanthanoid, they have coordination number generally greater than 6. Also due to deep buried nature of f-orbital they show sharp peak in their absorption spectrum.

Correct option is (a)

52. A tetrapeptide, made up of natural amino acids, has alanine as the N-terminal residue which is coupled to a chiral amino acid. Upon complete hydrolysis, the tetrapeptide gives glycine, alanine, phenylalanine and leucine. The number of possible sequences of the tetrapeptide is ___________

Ans. (4)

Sol. Ala-Phe-Gly-Leu

Ala-Leu-Gly-Phe

Ala-Phe-Leu-Gly

Ala-Leu-Phe-Gly

Correct answer is (4)

53. The major product formed in the following reaction sequence is

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

54. The major product formed in the flowing reaction sequence is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Correct option is (a)

55. In the following reaction,

(a) X is the major product and Y is the minor product

(b) X is the only product

(c) Y is the only product

(d) X is the minor product and Y is the major product

Ans. (a)

Sol. Cram's Product :**
**

Correct option is (a)