1.    For an ideal gas, the plot that is Nonlinear is:

    (a) PV vs T

    (b) PV vs P, at constant T

    (c) P vs V, at constant T

    (d) In P vs ln V at constant T

Ans.    c

Sol.    PV vs T graph is same as, nRT vs T, so as T increases, nRT increases too, So there is linear relationship between PV vs T.

    

    

    Correct option is (c)

2.    Consider two identical containers, one with 1 mole of H₂ and the other with 1 mole of He. If the root-mean square (RMS) velocities of the two gases are the same, then the ratio of the temperature, T(H₂)/T(He) is

    (a) 1/2

    (b) 2

    (c)

    (d)

Ans.    a

Sol.    

3.    An electron moves around the nucleus in a circular orbit, according to the Bohr model. The radial vector and the instaneous linear momentum vector are shown in the diagram below.

    

    The direction of the angular momentum vector is

    (a)

    (b)

    (c)

    (d)

Ans.    d

Sol.    

4.    X and Y transformed co-ordinates obtained from p and q as follows:

    

    The correct set of linear equations that represent X and Y are

    (a)

    (b)

    (c)

    (d)

Ans.    b

Sol.    

5.    Which of the following is NOT a solution of the equation

    (a)

    (b)

    (c)

    (d)

Ans.    c

Sol.    As only x = Ar², do not satisfy the differential equation, so it is not the solution.

    Correct option is (c)

6.    An electron is found in an orbital with one radial node and two angular nodes. Which orbital the electron is in?

    (a) 1s

    (b) 2s

    (c) 3s

    (d) 4s

Ans.    d

Sol.    

7.    The acceptable valence shell electronic arrangement is:

    (a)

    (b)

    (c)

    (d)

Ans.    c

Sol.    According to Hund's rule of maximum multiplicity states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pair, and, "According to Pauli exclusion principle, it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers".

    So, from the above rule only (c) is the acceptable valence shell electronic arrangement.

    Correct option is (c)

8.    If K_sp is the solubility product of a sparingly soluble salt A₃X₂, then its solubility is

    (a) (K_sp/108)^1/5

    (b) (K_sp)^1/5

    (c) (K_sp/72)^1/5

    (d) (K_sp)^1/2

Ans.    a

Sol.    

    Correct option is (a)

9.    For the formation of B from A, heat liberated is 20 kJ mol^–1. If the activation energy for the reaction is 100 kJ mol^–1, then the activation energy (in kJ mol^–1) for the reaction is

    (a) 120

    (b) 100

    (c) 80

    (d) 60

Ans.    a

Sol.    The activation energy for the reaction can be calculated after drawing energy profile diagram as:

    

    E_a(A – B) = E_a + 20 kJ mol^–1 = 100 + 20 = 120 kJ mole^–1

    Correct option is (a)

10.    For the reaction the concentration of Z at time t is given by

     where k is the rate constant. The rate law is:

    (a)

    (b)

    (c)

    (d)

Ans.    b

Sol.    

    

    

    

11.    Identify the correct option:

    In the periodic table, on moving from left to right along a period,

    (a) The atomic size of the element increases.

    (b) The first ionization potential of the element decreases.

    (c) The oxide of the element becomes less basic

    (d) The oxide of the element becomes more basic.

Ans.    c

Sol.    As we move from left to right in periodic table, then we move from metal to non-metal. So, their oxides will change its character from basic to acidic.

    Correct option is (c)

12.    Among the following, the incorrect statement is

    (a) Diamond and graphite are two allotrops of carbon

    (b) In diamond, each carbon is sp³ hybridized.

    (c) In graphite, each carbon is sp² hybridized

    (d) Graphite shows high electrical conductivity in one direction only

Ans.    d

Sol.    Graphite has a layered, planer structure. In each layer, the carbon atom are arranged in a honeycomb lattice with separation of 0.142 nm, and the distance between planes is 0.335 nm. Atoms in the plane are bonded covalently, with only three of the four potential bonding sites satisfied. The fourth electron is free to migrate in the plane, making graphite electrically conductive. However, it does not conduct at right angles to the plane.

    Correct option is (d)

13.    The pH of a 1 × 10^–8 M HCl solution is close to

    (a) 8.0

    (b) 7.1

    (c) 6.9

    (d) 6.0

Ans.    c

Sol.    [H⁺] = 10^–8 M (from HCl dissociation) + 10^–7 M (from H₂O dissociation)

    = 1.1 × 10^–7 M

    

    Correct option is (c)

 

 

14.    The indicator phenophthalein changes colour at pH ~ 9. This indictor is NOT suitable for accurate determination of the end point in the titration of

    (a) CH₃COOH with NaOH

    (b) HCl with NH₄OH

    (c) HCl with NaOH

    (d) HCl with KOH

Ans.    b

Sol.    Titration curve for strong acid vs. weak base

 

 

    Here, pehnolphthalein would be completely useless for strong acid versus weak base.

    Correct option is (b)

15.    In the thermite process, iron oxide is reduced to molten iron by aluminium powder because

    (a) The melting point of iron is low

    (b) The reaction is highly endothermic

    (c) Large amount of heat is liberated in the formation of Al₂O₃

    (d) Aluminium is an amphoteric element.

Ans.    c

Sol.    Al has high affinity for oxygen, because Al₂O₃ is highly stable compound, So, conversion of Al to Al₂O₃ (thermite process for reduction of metal) generates a lot of heat –ve, exothermic process), which reduces iron oxide to molten iron (due to high (–ve) value).

    Correct option is (c)

16.    The number of P = O bonds present in the tetrabasic acid H₄P₂O₇ is:

    (a) Three

    (b) Two

    (c) One

    (d) None

Ans.    b

Sol.    

17.    Egyption blue CaCuSi₄O₁₀ is an example of:

    (a) sheet silicate

    (b) cyclic silicate

    (c) pyrosilicate

    (d) chain silicate

Ans.    a

Sol.    

    

18.    The formal charges on the nitrogen atom from left to right in the azide anion, [N = N = N]^– are

    (a) + 1, –1, –1

    (b) –1, +1, –1

    (c) –1, –1, +1

    (d) –2, +1, 0

Ans.    b

Sol.    

19.    The unit cell of diamond can be obtained from the unit cell of

    (a) ZnS

    (b) NaCl

    (c) CsCl

    (d) AgCl

Ans.    a

Sol.    The unit cell of diamond is cubic and has the same overall geometry as ZnS.

    Correct option is (a)

20.    Calgon used for water softening is Na₂[Na₄(PO₃)₆] and it is prepared by heating microscosmic salt. The microscosmic salt is:

    (a) Na₂HPO₃

    (b) NaH₂PO₄

    (c) Na₂HPO₄

    (d) Na(NH₄)HPO₄

Ans.    d

Sol.    Microcosmic salt is sodium ammonium hydrogen phosphate Na(NH₄)HPO₄.

    Correct option is (d)

21.    The major product obtained in the following reaction

    

    (a)

    (b)

    (c)

    (d)

Ans.    a

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

    

    Chlorination with retention of relative configuration.

    Correct option is (a)

22.    The structure of D-galactose is

    

    Which one of these structures is L-galactose?

    (a)

    (b)

    (c)

    (d)

Ans.    D

Sol.    D galactose and L-galactose are enantiomer.

    L-Galactose is mirror image of D-galactose.

    Correct option is (d)

23.    The maximum number of stereoisomers possible for 4-phenylbut-3-en-2ol is

    (a) 1

    (b) 2

    (c) 3

    (d) 4

Ans.    d

Sol.    

24.    The major product of the reaction

    (a)

    (b)

    (c)

    (d)

Ans.    b

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

    

    Correct option is (b)

25.    Which of the following is achiral?

    (a) Alanine

    (b) Glycine

    (c) Proline

    (d) Phenylalanine

Ans.    b

Sol.     because it doesn't contain all four different substituents.

    Because it has a plane of symmetry.

    Correct option is (b)

26.    The reactivity order of the indicated functional group towards a nucleophile.

    

    (a) P > Q > R

    (b) Q > P > R

    (c) Q > R > P

    (d) R > P > Q

Ans.    a

Sol.    As oxygen is more electronegative than nitrogen so aldehyde is more prone to be attached by nucleophile.

    In ester, the –OCH₃ group reduces the electrophilic character at carbonyl carbon by donating it l.p., so ester is least reactive towards the attach of nucleophile.

    Correct option is (a)

27.    The major product formed in the reaction

    

    (a)

    (b)

    (c)

    (d)

Ans.    a

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

    

    Correct option is (a)

28.    Arrange the following in the correct order of acidity of the hydrogen indicated in bold.

    

    (a) P > Q > R

    (b) R > Q > P

    (c) Q > R > P

    (d) P > R > Q

Ans.    2

Sol.    

    

    Conjugate base of P, Q and R are all aromatic

    Carbanion of the conjugate base of Q and R are stabilized by 3-nearby ring, while P's carbanion is stabilized by 2-rings only. So, Q and R are more acidic than 'P'.

    As carbanion of R is planar with all 3 rings, so better stabilized w.r.t. Q's conjugate base (which is a bit pyramidal) due to non-rigidity of structure.

    Correct option is (b)

29.    Among the following the major product obtained in the reaction below is:

    (a)

    (b)

    (c)

    (d)

Ans.    d

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

    

    Correct option is (d)

30.    Which of the following are aromatic?

    

    (a) P and Q

    (b) Q and R

    (c) R and S

    (d) Q and S

Ans.    d

Sol.    

    Only Q and S are aromatic so correct option is (d)

31.    (a) A container is partitioned into two compartments, one of which contains 2 moles of He while the other contains 3 moles of Ar. The gases are ideal. The temperature is 300 K and the pressure is 1 bar:

    R = 0.083 L bar mol^–1 K^–1, ln (2/5) = –0.92, ln (3/5) = –0.51

    (i) What is the total Gibbs free energy of the two gases?

    (ii) If the partition between the two compartments is removed and the gases are allowed to mix, then what is the Gibbs free energy of the mixture?

    (iii) What is the change in enthalpy in this process?

    (b) Obtain (i) the molar heat of formation of CH₄(g) and (ii) the average C-H bond energy, to the nearest kilojoule (kJ), from the given data:

    

Sol.    

    (i) At T = 300ºK and P = 1 bar is close to standard conditions i.e. T = 298 K and P = 1 bar.

    

    Partition between gases has been removed.

    As the gases are ideal, so there will not be any change in temperature and pressure, even after removal of partition.

    

    

    Molar heat of formation of CH₄(g)

     = (Sublimation energy of graphite + atomisation energy at H₂(g))–Energy released for formation of C(g) to CH₄(g).

    = (717 + 436) kJ/mole – (339 + 444 + 444 + 435) kJ/mole = –509 kJ/mole

    (ii)    Average C-H bond energy

    

32.    (a) (i) Draw the P-T phase diagram of water.

    (ii) Label the different regions in this diagram.

    (iii) On the diagram, show the liquid-vapour equilibrium for a dilute solution of NaCl, with the help of a dashed curve.

    (b) The temperature dependence of the Gibb's free energy G is

    Obtain the expression for the temperature dependence of the equilibrium constant K given that = A + BT (Where A and B are constants)

Sol.    

     Slope has decreased and normal boiling point has increased. For NaCl solution

    

    

    Where k₂ is equilibrium constant at T₂ temperature and k₁ is equilibrium constant at T₁ temperature.

33.    (a) In the space provided, plot :

    (i) Conductometric titration curve of 0.1 M AgNO₃ with NaCl, extended beyond the end point

    

    

    (ii) pH vs. Volume of HCl, for a potentiometric titration of 0.1 (N) NH₄OH with 0.1 N HCl.

    

    (iii) Variation of the molar conductivity of NaCl with the square root of its concentration.

    

    (b) The Zn²⁺ | Zn half cell is connected to a Cu²⁺ | Cu half cell What is the value of Eº_cell for spontaneous conversion of chemical energy to electrical energy? What is the value of log₁₀ K, where K is the equilibrium constant? Use (2.303 RT/F) = 0.06.

Sol.    

    

    So, in the net cell reaction Zn will get oxidized and Cu⁺² will get reduced.

    

    For spontaneous, conversion of chemical energy to electrical energy.

    

34.    (a) The following initial rate data were obtained for the reaction

    

    (i) What is the rate law for this reaction?

    (ii) One of the mechanism proposed for this reaction is

    

    Obtain the rate law predicted for this mechanism, assuming a steady state concentration of NO₃.

    (iii) Predict the rate law for this mechanism, if the first equilibrium step is established quickly and the second step is slow.

    (b) (i) Write the expression for the vibrational contribution to the total energy of CH₄(g) at 500 K. All the vibrational modes are active a this temperature.

    (ii) Calculate the total internal energy of 1 mole of the gas at this temperature. R=8.314 J mol^–1K^–1.

Sol.    (a) (i) On doubling the pressure of NO, keeping the pressure of O₂ constant, the rate becomes 4 times.

    Order with respect to [NO] = 2

    On doubling the pressure of O₂, keeping P_NO = constant.

    The rate becomes double.

    Order with respect to O₂ = 1

    Hence, rate law:

    R = k[NO]²[O₂]¹

 

    As NO₃ is an intermediate

    So applying steady state approximation on NO₃.

    

    

    

    (iii) If first equilibrium step is established quickly and second step is slow, then k_–1 >> k₂

    

    (b)    (i)    For CH₄,

    Number of atoms N = 5

     Number of vibrational modes for nonlinear polyatomic molecule

    = 3N – 6

    = 3 × 5 – 6 = 9 modes

    Vibrational contribution to the total energy    = 9 × kT per molecule

    = 9 × RT per mole

    = 9 × 8.314 × 500

    = 37.4 kJ/mole

    (ii)    Total internal energy of 1 mole CH₄(g)

    = Translational contribution + Rotational contribution + Vibrational contribution

    

35.    (a) In the Bohr model of a hydrogen-like atom with atomic number Z.

    The angular momentum of an electron (of mass m_e and charge e) is a non-zero integral (n) multiple of where h is the Plank's constant, and

    The electrostatic attraction exerted by the nucleus on the electron is balanced by the centrifugal force experienced by the electron.

    (i) Write mathematical expressions for the above statements.

    (ii) Hence obtain the expression for the radius r of the Bohr orbit of the electron in terms of e, n and Z.

    (b) Complete the following nuclear reactions:

    

Sol.    

    

    Substituting the value of V_n from equation (1) in equation (2),

    

    On rearranging and cancelling the similar term we get,

    

    

    Total energy of electron in n^th Bohr orbit, = E_n = K.E. + P.E.

    

    From equation (2) and (4)

    

    Substituting the value of r_n from equation (3) in the above expression,

    

    

36.    (a) Highly pure nickel metal can be prepared from its sulphide ore via Ni(CO)₄. Write the chemical equations involved.

    (b) Addition of excess of aqueous NH₃ followed by ethanolic solution of dimethylglyoxime to a dilute aqueous solution of nickel sulphate changes the solution colour from green to blue to red. Write the structures of the metal complexes corresponding to green, blue and red colours.

Sol.    (a)    Sulfide ore in first roasted in air to give NiO.

    

    NiO is then reduced by water gas.

    

    To refine Ni, it is heated to about 50–60ºC in a steam of CO gas. Nickel passes off as its volatile carbonyl, Ni(CO)₄, this volatile product is passed over nickel shot at about 200ºC. Nickel is deposited by Ni(CO)₄ and is almost pure.

    

    

    

37.    The element E on burning in the presence of O₂ gives F. Compound F on heating with carbon in an electric furnace gives G. On passing nitrogen over a heated mixture of F and carbon produces H. Steam can decompose H to produce boric acid and a colourless gas that gives white fumes with HCl. Identify F, G and H and give balanced equations for their formation.

Sol.    

    

38.    (a) Provide IUPAC names for the following complexes:

    (i) [CoCl(NH₃)₅]Cl₂         (ii) K₂[PdCl₄]

    (b) The magnetic moment of [Mn(H₂O)₆] (NO₃)₂ is approximately Find the number of unpaired electrons, show crystal field splitting and calculate the CFSE.

Sol.    (a)     (i)    [CoCl(NH₃)₅]Cl₂

    Pentaamminechlorocobalt (III) chloride

    (ii)    K₂[PdCl₄]

    Potassium tetrachloropalladiate (II)

    (b)    [Mn(H₂O)₆](NO₃)₂ has Mn⁺² ion.

    Mn⁺² has 5 unpaired electron in 3d-orbitals

    

39.    A metal salt on heating with a mixture of KCl and conc. H₂SO₄ yields a deep red vapour J. The vapour on passing through an aqueous solution of KOH gives a yellow solution of compound K. Passing SO₂ gas through acidified solution (with H₂SO₄) of K leads to green colouration of the solution due to the formation of M. Identify J, K and M giving balanced equations for the transformations,

Sol.    

40.    (a) Identify E and F in the following reactions and suggest a suitable reason for their formation.

    

    (b) Predict the product in each of the following reactions.

    

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

    

    Product (F) is kinetically controlled and product (E) is thermodynamic controlled product.

    Greater unstability of 1-acid (i.e. F) is due to steric repulsion of H at C–8 with SO₃H group.

    

    In case of attack of SO₃, electrophile at C₂, the stabilization of carbocation is only at the cost of loss of aromaticity of nearby ring, but attack at C₁ gets some extra stability via resonance with nearby double bond without costing the aromaticity of other ring, thats why kinetically favourable at lower temperature.

    

    

    

    

41.    (a) A compound G having molecular formula C₆H₁₂ decolourless both permagnanate and bromine water. G on ozonolysis followed by reductive work-up (Zn/H₃O⁺) produces equal amounts of H and J with identical molecular C₃H₆O. Both H and J form 2, 4-dinitrophenyl hydrazones, however, only J shows positive test with Tollen's reagent. Identify the compounds G, H and J.

    (b) Identify K and M in the following reaction sequence.

    

Sol.    Since both H and J give 2,4 DNP test. It means both are carbonyl group containg ketone or aldehyde.

    Since, Only J give positive tollen's test, so it must be aldehyde and H must be ketone.

    Only possible structure of J and H having molecular formula C₃H₆O.

    

    

42.    (a) Identify N, P and Q in the following synthetic transformation.

    

    (b) Draw the most as well as the least stable chair conformations of trans-1-tert-butyl-4-methylcyclohexane.

Sol.    

    

43.    Identify R, S, T, X and Y in the following reaction sequences.

    

    

Sol.    

44.    (a) Compute the following reaction sequences with the structures of X, Y, and Z.

 

    (b) Calculate the isoelectric point (p.I.) of lysine, given the pK_a of NH₃ is 8.95 pK_a of side chain NH₃ is 10.53 and pK_a of α.COOH is 2.18.

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