Thermodynamics PYQs Set 13 (PDF)

Set 13 of 18 · Questions 361-390 of 511

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Mere Teacher · Previous Year Questions JEE Main Chemistry · Thermodynamics · Set 13 (Q361-390)
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361. $An ideal gas in a thermally insulated vessel at internal pressure = P_{1}, volume = V_{1} and absolute temperature = T_{1} expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P_{2}, V_{2} and T_{2}, respectively. For this expansion,$ (1) $q = 0$ (2) $T_{2} = T_{1}$ (3) $P_{2} V_{2} = P_{1} V_{1}$ (4) $P_{2} V_{2}^{γ} = P_{1} V_{1}^{γ}$ 362. $An ideal gas is expanded from (p_{1}, V_{1}, T_{1}) to (p_{2}, V_{2}, T_{2}) under different conditions. The correct statement(s) among the following is (are)$ (1) $The work done by the gas is less when it is expanded reversibly from V_{1} to V_{2} under adiabatic conditions as compared to that when expanded reversibly from V_{1} to V_{2} under isothermal conditions$ (2) $The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T1 = T2, and (ii) positive, if it is expanded reversibly under adiabatic conditions with T1 \neq T2$ (3) $If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic$ (4) $The work done on the gas is maximum when it is compressed irreversibly from (p_{2}, V_{2}) to (p_{1}, V_{1}) against constant pressure p_{1}$ 363. $For an endothermic reaction, energy of activation is E_{a} and enthalpy of reaction is Δ H (both of these in kJ/mol). Minimum value of E_{a} will be$ (1) $less than Δ H$ (2) $equal to Δ H$ (3) $more than Δ H$ (4) $equal to zero$ 364. $Using the data provided, calculate the multiple bond energy (kJ m o l^{-1}) of a CºC bond C_{2} H_{2} . That energy is (take the bond energy of a C-H bond as 350 kJ m o l^{-1}) 2C(s) + H_{2} (g) ¾® C_{2} H_{2} (g) DH = 225 kJ m o l^{-1} 2C(s) ¾® 2C (g) DH = 1410 kJ m o l^{-1} H_{2} (g) ¾® 2H(g) DH = 330 kJ m o l^{-1}$ (1) $1165$ (2) $837$ (3) $865$ (4) $815$ 365. $Match List-I with List-II List-I (A) Spontaneous process (B) Process with Δ P = 0, Δ T=0 (C) Δ H_{r e a c tl o n} (D) Exothermic process List-II (I) Δ H < 0 (II) Δ G_{T . P} < 0 (III) Isothermal and isobaric process (IV) [Bond energies of molecules in reactants] [Bond energies of product molecules] Choose the correct answer from the options given below:$ (1) $(A) - (III), (B) - (II), (C) - (IV), (D) - (I)$ (2) $(A) - (II), (B) - (III), (C) - (IV), (D) - (I)$ (3) $(A) - (II), (B) - (III), (C) - (I), (D) - (IV)$ (4) $(A) - (II), (B) - (I), (C) - (III), (D) - (IV)$ 366. $The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct ?$ (1) $T_{1} = T_{2}$ (2) $T_{3} > T_{1}$ (3) $wisothermal > wadiabatic$ (4) $ΔUisothermal > ΔUadiabatic$ 367. $(T = 300 K P = 15 bar 1 mole) (T = 300 K P = 10 bar 1 mole) (T = 300 K P = 5 bar 1 mole) Above shows a cyclic process. Calculate the total work done during one complete cycle..$ (1) $25/3 L bar$ (2) $- 25/3 L bar$ (3) $50/3 L bar$ (4) $- 50/3 L bar$ 368. $For a perfectly crystalline solid C_{p, m} = a T^{3} + b T, where a and b are constants. If C_{p, m} is 0.40 J / K m o l at 10 K and 0.92 J / K m o l at 20 K, then molar entropy at 20 K is :$ (1) $0.92 J / K m o l$ (2) $8.66 J / K m o l$ (3) $0.813 J / K m o l$ (4) $None of these$ 369. $Given: (i) C (g r a p hi t e) + O_{2} (g) \to C O_{2} (g); Δ_{r} H^{⊖} = x k J m o l^{- 1} (ii) C (g r a p hi t e) + \frac{1}{2} O_{2} (g) \to C O_{2} (g); Δ_{r} H^{⊖} = y k J m o l^{- 1} (iii) C O (g) + \frac{1}{2} O_{2} (g) \to C O_{2} (g); Δ_{r} H^{⊖} = z k J m o l^{- 1} Based on the above thermochemical equations, find out which one of the following algebraic relationship is correct?$ (1) $x = y - z$ (2) $y = 2z - x$ (3) $x = y + z$ (4) $z = x + y$ 370. $The effect of temperature on spontaneity of reactions are represented as: Δ H Δ S Temperature Spontaneity (A) + ◻ any T Non spontaneous (B) + + low T spontaneous (C) - - low T Non spontaneous (D) - + any T spontaneous$ (1) $(B) and (C) only$ (2) $(B) and (D) only$ (3) $(A) and (D) only$ (4) $(A) and (C) only$ 371. $Formation of a solution from two components can be considered as (i) Pure solvent \to separated solvent molecules, Δ H_{1} (ii) Pure solute \to separated solute molecules, Δ H_{2} (iii) Separated solvent and solute molecules \to solution, Δ H_{3} Solution so formed will be ideal if$ (1) $Δ H_{soln} = Δ H_{1} + Δ H_{2} + Δ H_{3}$ (2) $Δ H_{soln} = Δ H_{1} + Δ H_{2} - Δ H_{3}$ (3) $Δ H_{soln} = Δ H_{1} - Δ H_{2} - Δ H_{3}$ (4) $Δ H_{soln} = Δ H_{3} - Δ H_{1} - Δ H_{2}$ 372. $For the reaction, A (g) + B (g) \to C (g) + D (g), Δ H^{\circ} and Δ S^{\circ} are, respectively, - 29.8 kJ mo l^{- 1} and - 0.100 kJ K^{- 1} mo l^{- 1} at 298 K. The equilibrium constant for the reaction at 298 K is:$ (1) $1$ (2) $10$ (3) $1.0 \times 1 0^{-10}$ (4) $1.0 \times 1 0^{10}$ 373. $The incorrect expression among the following is:$ (1) $\frac{Δ G _{sy s t e m}}{Δ S _{t o t a l}} = - T$ (2) $In isothermal process, w_{r e v er s ib l e} = - n R T ℓ n \frac{V _{f}}{V _{i}}$ (3) $ln K = \frac{Δ H ^{0} - T Δ S ^{0}}{R T}$ (4) $K = e^{- Δ G^{0} / R T}$ 374. $Find the heat required to make water of 3 0^{\circ} C from 10 g of ice at 0. 0^{\circ} C . (Enthalpy of fusion of ice = 333.55 J g^{- 1}, C_{P} of water = 4.18 J g^{- 1} K^{- 1})$ (1) $4.0 kJ$ (2) $5.0 kJ$ (3) $3.59 kJ$ (4) $4.59 kJ$ 375. $Match the LIST-I with LIST-II List-I (Thermodynamic Process) (A) Work done in reversible, isothermal expansion of 2 mol ideal gas from 2 dm^{3} to 20 dm^{3} at 300 K (B) Work done in irreversible isothermal expansion of 1 mol ideal gas from 1 m^{3} to 3 m^{3} at 300 K against constant pressure 3 kPa (C) Change in internal energy for adiabatic expansion of 1 mol ideal gas, Δ T = 320 K, C_{V} = \frac{3}{2} R (D) Change in enthalpy at constant pressure of 1 mol ideal gas, Δ T = 337 K, C_{p} = \frac{5}{2} R List-II (Magnitude in kJ) (I) 4 (II) 11.5 (III) 6 (IV) 7 Choose the correct answer from the options given below:$ (1) $A-II, B-III, C-I, D-IV$ (2) $A-III, B-II, C-IV, D-I$ (3) $A-II, B-I, C-III, D-IV$ (4) $A-I, B-II, C-III, D-IV$ 376. $Given below are two statements: Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted. Statement II: At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point. In the light of the above statements, choose the correct answer from the options given below$ (1) $Both Statement I and Statement II are false$ (2) $Statement I is true but Statement II is false$ (3) $Both Statement I and Statement II are true$ (4) $Statement I is false but Statement II is true$ 377. $Calculate Δ_{r} H (kJ mol^{- 1}) of the following reaction C_{2} H_{5} OH (I) + 7/2 O_{2} (g) \to 2 CO_{2} (g) + 3 H_{2} O (I) Molecule Δ_{f} H^{0} (kJ mol^{- 1}) C_{2} H_{5} OH (I) -280 CO_{2} (g) -400 H_{2} O (l) -290$ (1) $-1950$ (2) $-1100$ (3) $-1390$ (4) $-700$ 378. $For a reaction to occur spontaneously$ (1) $Δ H must be negative$ (2) $Δ S must be negative$ (3) $(Δ H - TS) must be negative$ (4) $(Δ H + TS) must be negative.$ 379. $The value of entropy of solar system is$ (1) $increasing$ (2) $decreasing$ (3) $constant$ (4) $zero.$ 380. $Consider the following reactions: (i) H_{(aq)}^{+} + O H_{(aq)}^{-} = H_{2} O_{(l)}, Δ H = - X_{1} kJmo l^{- 1} (ii) H_{2 (g)} + 1/2 O_{2 (g)} = H_{2} O_{(l)}, Δ H = - X_{2} kJmo l^{- 1} (iii) C O_{2 (g)} + H_{2 (g)} = C O_{(g)} + H_{2} O_{(l)}, Δ H = - X_{3} kJmo k^{- 1} (iv) C_{2} H_{2 (g)} + 5/2 O_{2 (g)} = 2 C O_{2 (g)} + H_{2} O_{(l)}, Δ H = + X_{4} kJmo k^{- 1} Enthalpy of formation of H_{2} O_{(l)} is$ (1) $+ X_{3} kJmo 1^{- 1}$ (2) $- X_{4} kJmo 1^{- 1}$ (3) $+ X_{1} kJmo 1^{- 1}$ (4) $- X_{2} kJmo l^{- 1}$ 381. $CNG is an important transportation fuel. When 100 g CNG is mixed with 208 oxygen in vehicles, it leads to the formation of C O_{2} and H_{2} O and produces large quantity of heat during this combustion, then the amount of carbon dioxide, produced in grams is________. [nearest integer][Assume CNG to be methane]$ 382. $Consider the graph of Gibbs free energy G vs extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is______(a) Reaction is spontaneous at (a) and (b) (b) Reaction is at equilibrium at point (b) and non-spontaneous at point (c) Reaction is spontaneous at (a) and non-spontaneous at (c) (d) Reaction is non-spontaneous at (a) and (b) 1$ 383. $2.2 g of nitrous oxide (N_{2} O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ∆ U is ‘-x’ J. The value of ‘x’ is__. [nearest integer](Given: atomic mass of N = 14 g m o l^{- 1} and of O = 16 g m o l^{- 1} Molar heat capacity of N_{2} O is 100 J K^{- 1} m o l^{- 1})$ 384. $An ideal monoatomic gas was at 1 atm and 300 K. If one mole of such that ideal gas is allowed to expand adiabatically against a constant pressure of 0.3 atm till double its volume, determine ΔS \times 1 0^{3} in J K^{-1} m o l^{-1} for the process in the nearest possible integers. Given: log 2 = 0.3 ; log 3 = 0.48 ; log 5 = 0.7$ 385. $The incorrect statements from the following is: (a) The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy. (b) E°ell is dependent on the pressure. (c) \frac{d E _{cell}^{0}}{dT} = \frac{Δ _{r} S ^{0}}{nF} (d) A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.$ 386. $For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, ∆_{C} H^{-} = -601.70 kJ m o l^{- 1}, the magnitude of change in internal energy for the reaction is _____ kJ.(Nearest integer)(Given :R = 8.3 J K^{- 1} m o l^{- 1})$ 387. $The number of endothermic process/es from the following is_______. (a) I_{2} (g) \to 2I(g) (b) HCl(g) \to H(g) + Cl(g) (c) H_{2} O(a) \to H_{2} O(g) (d) C(s) + O_{2} ( g) \to C O_{2} ( g)$ 388. $For a certain reaction at 300 K, K = 10, then Δ G^{\circ} for the same reaction is_________\times 10^{- 1} kJ mol^{- 1} . (Given (R = 8.314 JK^{- 1} mol^{- 1})$ 389. $The reaction of cyanamide, N H_{2} C N_{(s)} with oxygen was run in a bomb calorimeter and Δ U was found to be - 742.24 k J m o l^{- 1} . The magnitude of for the reaction N H_{2} C N_{(s)} + \frac{3}{2} O_{2} (g) \to N_{2 (g)} + O_{2 (g)} + H_{2} O_{(l)} is ____ kJ. (Rounded off to the nearest integer) [Assume ideal gases and R = 8.314 J m o l^{- 1} K^{- 1}]$ 390. $Two reactions are given below: 2 Fe_{(s)} + \frac{3}{2} O_{2 (g)} \to Fe_{2} O_{3 (s)}, Δ H^{\circ} = - 822 kJ / mol C_{(s)} + \frac{1}{2} O_{2 (g)} \to CO_{(g)}, Δ H^{\circ} = - 110 kJ / mol Then enthalpy change for following reaction 3 C_{(s)} + Fe_{2} O_{3 (s)} \to 2 Fe_{(s)} + 3 CO_{(g)}$