1.    The molar internal energy of a gas at temperature T is U_m(T). The molar internal energy at T = 0 is U_m(0). The correct expression that relates these two with appropriate contributions is :

    (a) U_m(T) = U_m(0) + 3RT [Linear molecule; translation only]

    (b) U_m(T) = U_m(0) + 5/2 RT [Linear molecule; translation and rotation only]

    (c) U_m(T) = U_m(0) + 3/2 RT (Nonlinear molecule; translation and rotation only)

    (d) U_m(T) = U_m(0) + RT (Nonlinear molecule; translation only)

Ans.    b

Sol.    

    

    

    

    Correct option is (b)

2.    If a particle has linear momentum at position then its angular momentum is

    (a)

    (b)

    (c)

    (d)

Ans.    b

Sol.    

    Correct option is (b)

3.    If is the eigenfunction to the Hamiltonian operator with as the eigenvalue, then MUST be

    (a) positive

    (b) negative

    (c) an integer

    (d) real

Ans.    d

Sol.    As eigen value represents the property (e.g. energy, momentum etc.) of real physical quantity. So must real.

    Correct option is (d)

4.    A quantum mechanical particle of mass m free to rotate on the surface of a sphere of radius r is in the state with energy The degeneracy of this state is

    (a) 20

    (b) 10

    (c) 9

    (d) 4

Ans.    c

Sol.    

    (g_J) = 2J + 1 = 2 × 4 + 1 = 9

    Correct option is (c)

5.    Choose the INCORECT statement among the following :

    (a) When ideal gases are mixed, the entropy of mixing is always positive

    (b) At equilibrium, the chemical potential of a species is the same in all of the phases of the system

    (c) The total pressure of a mixture of ideal gases is equal to the sum of the partial pressure of each gas in the mixture.

    (d) When a gas is allowed to expand, the maximum work is obtained when the process is carried out irreversibly.

Ans.    d

Sol.    Maximum work is obtained in reversible process only.

    Correct option is (d)

6.    The work done during the free expansion of one mole of an ideal gas at 27°C to twice its original volume is (given : RT = 2494 J mol^–1, ln 2 = 0.7, log 2 = 0.3)

    (a) 1746 J mol^–1

    (b) –1746 J mol^–1

    (c) zero

    (d) 748.2 J mol^–1

Ans.    c

Sol.    

    Correct option is (c)

7.    Choose the correct order of the diffusion coefficients of the following at 298 K.

    P : H⁺ in water

    Q : QH^– in water

    R : H₂O in water

    S : Sucrose in water

    (a) P > Q > R > S

    (b) S > R > Q > P

    (c) S > Q > R > P

    (d) P > R > Q > S

Ans.    a

Sol.    H⁺ and OH^– diffusion follows Grothus type mechanism and their diffusion is very fast w.r.t. other molecules and ions.

    

    Similar mechanism for migration of OH^–, but OH^– migrates slower than H⁺.

    Correct option is (a)

8.    Two matrices are given as If X^T is the transpose of X then what would be X^TY?

    (a)

    (b)

    (c)

    (d)

Ans.    b

Sol.    

    Transpose of matrix is obtained when rows and column of a matrix are interchanged (i.e. rows have been converted in column and column in rows.)

    

    Correct option is (b)

9.    Addition of 1.0 g of a compound to 10 g of water increases the boiling point by 0.3°C. The amount of compound needed to prepare a 500 ml or 0.1 M solution is (given : assume negligible dissociation or association of the compound, boiling point constant K_b of water = 0.513 K kg mol^–1)

    (a) 0.855 g

    (b) 17.1 g

    (c) 8.55 g

    (d) 85.5 g

Ans.    c

Sol.    

    

    Correct option is (c)

10.    The molar conductivity of 0.009 M aqueous solution of a weak acid (HA) is 0.005 S m² mol^–1 and the limiting molar conductivity of HA is 0.05 S m² mol^–1 at 298 K. Assuming activity coefficient to be unity, the acid dissociation constant (K_a) of HA at this temperature is

    (a) 1 × 10^–4

    (b) 0.1

    (c) 9 × 10^–4

    (d) 1.1 × 10^–5

Ans.    a

Sol.    Given:

    

    

    Correct option is (a)

11.    The colour of potassium dichromate is due to

    (a) d-d transition

    (b) transition in K⁺ ion

    (c) ligand-to-metal charge transfer

    (d) Metal-to-ligand charge transfer

Ans.    c

Sol.    Orange colour of K₂Cr₂O₇ is due charge transfer from ligand (O^2–) to metal ion (Cr⁺⁶).

    Correct option is (c)

12.    Which one of the following configuration will show John-Teller distortion in an octahedral field?

    (a) high spin d⁸

    (b) high spin d⁴

    (c) high spin d⁵

    (d) low spin d⁶

Ans.    b

Sol.    In case of high spin d⁴, e_g level is asymmetrically filled in octahedral field, so Jahn-Teller distortion is observed.

    Correct otpion is (b)

13.    B₂H₆ and B₄H₁₀, respectively, are examples of

    (a) Nido and arachno boranes

    (b) Nido and closo boranes

    (c) Closo and arachno boranes

    (d) Nido boranes

Ans.    a

Sol.    

    

    Correct option is (a)

14.    Which of the following has a square planar geometry according to the VSEPR theory? Atomic number: B = 5, S = 16, Xe = 54.

    (a) XeO₂F₂

    (b) SF₄

    (c) BF₄^–

    (d) XeF₄

Ans.    d

Sol.    

    Correct option is (d)

15.    The structure of rock salt consists of

    (a) A cubic close-packed array of anions with cations in all the octahedral sites

    (b) A cubic close-packed array of cations with anions in all the tetrahedral sites

    (c) A hexagonal close-packed array of anions with cations in all the octahedral sites

    (d) A cubic close-packed array of anions with cations in all the tetrahedral sites

Ans.    a

Sol.    

    The rock salt face-centered cubic structure and each atom has six nearest neighbours, with octahedral geometry.

    Correct option is (a)

16.    Among lithium, nitrogen, carbon and oxygen, which element has the highest first ionization potential?

    (a) Lithium

    (b) Nitrogen

    (c) Carbon

    (d) Oxygen

Ans.    b

Sol.    As N has half filled 2p orbital, which is more stable configuration than oxygen which has 2p⁴ and carbon has 2p² configuration.

    As half filled are more stable, so it requires higher energy to remove the outermost electron.

    Correct option is (b)

17.    In which of the following C–H bond has the highest 's' character?

    (a) Acetylene

    (b) Ethylene

    (c) Methane

    (d) CH radical

Ans.    a

Sol.    

    Correct option is (a)

18.    Which one of the following is an electron deficient molecule according to the octet rule?

    (a) CH₄

    (b) H₃N : BH₃

    (c) AlH₃

    (d) GeH₄

Ans.    c

Sol.    

    AlH₃ has 3C-2e^– bond.

    So, there are only 6e^– around Al, So it is electron deficient

    Correct option is (c)

19.    Which one of the following has the highest lattice energy?

    (a) LiCl

    (b) CaCl₂

    (c) LiF

    (d) KCl

Ans.    b

Sol.    

    

20.    At room temperature, HCl is a gas while HF is a liquid because

    (a) Of a strong bond between H and F in HF

    (b) HF is less acidic as compared to HCl

    (c) Of strong intermolecular H-bonding in HF

    (d) HCl is less acidic as compared to HF

Ans.    c

Sol.    The electronegativity of F is higher than Cl. So, strong intermolecular hydrogen bonding in HF than HCl.

    Correct option is (c)

21.    Benzene and Dewar benzene are

    

    (a) Canonical forms

    (b) Structural isomers

    (c) Tautomers

    (d) Conformational isomers

Ans.    b

Sol.    Structural isomer have different connectivity of atoms.

    Correct option is (b)

22.    The IUPAC name of the following compound is:

    

    (a) 2-cyano-3-chlorobutane

    (b) 2-chloro-3-cyanobutane

    (c) 2-methyl-3-chlorobutanenitrile

    (d) 3-chloro-2-methylbutanenitrile

Ans.    d

Sol.    Correct option is (d)

23.    Which chemical test will distinguish the compounds shown below?

    

    (a) Beilstein's flame test

    (b) Ethanolic silver nitrate test

    (c) Sodium fusion test

    (d) Fehling's test

Ans.    b

Sol.    

    Correct option is (b)

24.    The reaction of the bromo compound shown below with sodium ethoxide gives predominantly

    

    (a)

    (b)

    (c)

    (d)

Ans.    c

Sol.    Chemical transformation involved in above chemical reaction can be illustrated as

    Since E₂ reaction is anti-elimination reaction. Here Br and D are anti to each other. So D-Br will remove.

    

25.    Choose the correct order of reactivity for dehydration of the given alcohols using concentrated sulfuric acid

    (a) 2-methylpropan-2-ol > 2-butanol > 1-butanol

    (b) 2-methylpropan-2-ol > 1-butanol > 2-butanol

    (c) 2-butanol > 2-methylpropan-2-ol > 1-butanol

    (d) 1-butanol > 2-butanol > 2-methylpropan-2-ol

Ans.    a

Sol.    As both E₁ and E₂–elimination is prefered if leaving group is at 3º carbon, then 2º carbon and then at 1º carbon.

    In case of 2-methylpropan-2-ol, 2-butanol, and 1-butanol and leaving group H₃O⁺ is at 3º, 2º and 1º carbon respectively. So dehyration follows the order given in option (A).

    Correct option is (a)

26.    The titration curve of alanine hydrochloride is given below

    

    The position in the graph that corresponds to the isoelectric point of alanine is:

    (a) P

    (b) Q

    (c) R

    (d) S

Ans.    b

Sol.    

    Correct option is (b)

27.    The absolute configurations at the two chiral centers in D-Ribulose are

    

    (a) 3R, 4R

    (b) 3R, 4S

    (c) 3S, 4R

    (d) 3S, 4S

Ans.    a

Sol.    

28.    The most stable conformation of the molecule shown below is correctly represented by

    

    (a)

    (b)

    (c)

    (d)

Ans.    d

Sol.    

29.    Thermal rearrangement of the following compound would give

    (a)

    (b)

    (c)

    (d)

Ans.    c

Sol.    Chemical transformation involved in above chemical reaction can be illustrated as

    

    Correct option is (c)

30.    The energy profile diagram that corresponds to 1,2-dihydroxyethane for rotation around the C–C bond is

    (a)

    (b)

    (c)

    (d)

Ans.    c

Sol.    

    

    Correct option is (c)

31.    (a) Equilibrium constant for a reaction doubles as the temperature is increased from 300 K to 600 K. Calculate the standard reaction enthalpy (in kJ mol^–1) assuming it to be constant in this temperature range. (Given R = 8.3 J K^–1 mol^–1, ln 2 = 0.7).

    (b) A 50 mL solution of 0.1 M monoprotic acid (K_a = 1 × 10^–5 at 298 K) is titrated with 0.1 M NaOH at 298 K. Calculate the solution after the addition of 50 mL of NaOH at this temperature. (Given K_w = 1 × 10^–14 at 298 K)

Sol.    (a) From van't Hoff equation,

    

    Where K₁ and K₂ are equilibrium constant at temperature T₁ and T₂ and standard enthalpy of reaction

    Given,        T₁ = 300 K,    T₂ = 600 K

    K₂ = 2K₁

    From equation (1),

    

    Na⁺A^– will undergo hydrolysis,

    pH for the above hydrolysis can be approximated as,

    (where c = constant of NaA salt)

    

32.    For the reaction, H₂(g) + Br₂(g) 2HBr(g)

    the following mechanism has been proposed.

    

    

    (a) Write the differential rate equations for the formation of the two intermediates H^• and Br^•.

    (b) Using the steady-state approximate calculate the concentration of the intermediate H^• and Br^• and obtain the rate law for the formation of HBr.

Sol.    

    

    

    

    

    

33.    

    Assume that at 273 K the molar enthalpy of fusion of ice is 6006 J mol^–1, the heat capacity C_p,m (s) of ice is 38 J K^–1 mol^–1 and heat capacity C_p,m of liquid water is 76 J K^–1 mol^–1. Consider the heat capacities to be constants. Consider the heat capacities to be constants. (given: ln = 263 = 5.57 and ln 273 = 5.61)

Sol.    

    

    

34.    Two beakers, one containing 0.02 M KMnO₄, 0.2 M MnSO₄ and 0.5 M H₂SO₄, and another containing 0.15 M FeSO₄ and 0.05 M Fe₂(SO₄)₃, are connected by a salt-bridge. Platinum electrodes are placed in each beaker and these two electrodes are connected via a wire with a voltmeter in between. H₂SO₄ is present in equal volumes in each beaker. Assume H₂SO₄ is completely ionized.

    Given :    

    (a) Write the complete balanced redox reaction for this cell.

    (b) What would be the potential of each half-cell after the reactions has reached equilibrium?

Sol.    

     will oxidize Fe⁺² to Fe⁺³ and will itself get reduced to Mn⁺².

    

    Therefore, Net balanced redox reaction for this cell, is obtained by adding equation (2) with 5 × equation (1).

    

    

    Large value of K_eq signifies that, the reaction will reach to completion.

    

    At equilibrium or after completion of reaction, (can be seen from balanced net reaction)

    

    

    As two half cell potentials will be identical at any stage of equilibrium,

    

35.    An atomic orbital is described by the wavefunction

    

    

    (a) Identify the atomic orbital and calculate the mean or the average radius of this orbital in terms of a₀.

    (b) Calculate the most probable radius (in terms of a₀) at which an electron will be found when it occupies this orbital.

Sol.    

     is a function of radial distance from nucleus (i.e. 'r'), only and has no angular dependence

    Also has no radial angular node, so can only be '1s' orbital.

    

    

    

    (b) Probability of finding electron in a spherical shell of thickness 'dr', at a distance 'r' from the nucleus is given by

    

    

36.    Identify W, X, Y and Z in the following sequence.

    

    Y turns moist litmus paper blue. Write balanced chemical equation for the conversion of Y to Z.

Sol.    

37.    (a) Draw the crystal field splitting diagram with appropriate labels for [NiCl₄]^2–. Determine the spin only magnetic moment and the crystal field stabilization energy (CFSE) for this complex. (Given : Atomic number of Ni = 28)

    (b) Write the balanced equations for the reactions involved in the iodometric estimation of Cu²⁺ using thiosulfate.

Sol.    (a) In case of [NiCl₄]^2–, there is crystal field splitting of 3d-orbitals in presence of tetrahedral field of 4Cl^– ligands.

    

    

    

38.    (a) In the reaction sequence given below P is an anionic Fe(II) complex.

    (b) Draw a properly labeled unit cell diagram of CsCl. Show through calculations that there is only one CsCl per unit cell.

Sol.    

    As Cs⁺ atom is at center only = number of Cs⁺ atoms/cell = 1

    Cl^– atoms are at all corners of the cube = Number of atoms of Cl^–/cell

    One formula unit of CsCl is present per unit cell.

39.    (a) Write the balanced chemical equations for the reactions involved in the synthesis of borazine using ammonium chloride as one of the starting materials. Write the structure of borazine.

    (b) Draw Lewis structures of SF₄ and NO₃^–.

Sol.    

    

    

40.    (a) Complete the following sequence by identifying E, F and G.

    

    (b) Identify H and I in the reactions below

    

Sol.    

    

41.    (a) Identify the products J, K and L in the following reactions. Lassigne's test for L shows the presence of nitrogen only.

    

    (b) Write the structure of M and N in the following reactions.

    

Sol.    

    

42.    (a) Write the structures of P, Q and R in the given reaction sequence.

    

    (b) Identify S and T in the reactions given below:

Sol.    

43.    (a) Identify X, Y and Z in the following reactions.

    (b) Suggest a suitable mechanism for the following reaction.

Sol.    

    

    

44.    Consider the following reactions for a compound with molecular formula C₁₀H₁₆.

    

    (a) Write structures that are consistent with the above data for the formula C₁₀H₁₆.

    (b) Given that myrcene is a terpene and has the molecular formula C₁₀H₁₆, using the isoprene rule identify the correct structure for myrcene among the structures elucidated in part (a).

Sol.    (a)

    (b) Structure (I), as shown above is myrecene because it follows isoprene rule.