PYQ Vault

Chemistry · Textbook solutions

Thermodynamics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 36 questions

Worked Examples

14 q

Solved Examples

Worked · 14
  1. Eg 5.1
    Express the change in internal energy of a system when (i) No heat is absorbed by the system from the surroundings, but work (w) is done on the system. What type of wall does the system have? (ii) No work is done on the system, but qq amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have? (iii) w amount of work is done by the system and qq amount of heat is supplied to the system. What type of system would it be?
  2. Eg 5.2
    Two litres of an ideal gas at a pressure of 10 atm10\,\text{atm} expands isothermally at 25 ∘C25\,^\circ\text{C} into a vacuum until its total volume is 10 litres. How much heat is absorbed and how much work is done in the expansion?
  3. Eg 5.3
    Consider the same expansion, but this time against a constant external pressure of 1 atm1\,\text{atm}.
  4. Eg 5.4
    Consider the expansion given in problem 5.2, for 1 mol of an ideal gas conducted reversibly.
  5. Eg 5.5
    If water vapour is assumed to be a perfect gas, molar enthalpy change for vapourisation of 1 mol of water at 1 bar1\,\text{bar} and 100 ∘C100\,^\circ\text{C} is 41 kJ mol−141\,\text{kJ mol}^{-1}. Calculate the internal energy change, when 1 mol of water is vapourised at 1 bar1\,\text{bar} pressure and 100 ∘C100\,^\circ\text{C}.
  6. Eg 5.6
    1 g1\,\text{g} of graphite is burnt in a bomb calorimeter in excess of oxygen at 298 K298\,\text{K} and 1 atmospheric pressure according to the equation C (graphite)+O2(g)→CO2(g)\text{C (graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) During the reaction, temperature rises from 298 K298\,\text{K} to 299 K299\,\text{K}. If the heat capacity of the bomb calorimeter is 20.7 kJ/K20.7\,\text{kJ/K}, what is the enthalpy change for the above reaction at 298 K298\,\text{K} and 1 atm1\,\text{atm}?
  7. Eg 5.7
    A swimmer coming out from a pool is covered with a film of water weighing about 18 g18\,\text{g}. How much heat must be supplied to evaporate this water at 298 K298\,\text{K}? Calculate the internal energy of vaporisation at 298 K298\,\text{K}. ΔvapH⊖\Delta_{vap}H^{\ominus} for water at 298 K=44.01 kJ mol−1298\,\text{K} = 44.01\,\text{kJ mol}^{-1}
  8. Eg 5.8
    Assuming the water vapour to be a perfect gas, calculate the internal energy change when 1 mol of water at 100 ∘C100\,^\circ\text{C} and 1 bar1\,\text{bar} pressure is converted to ice at 0 ∘C0\,^\circ\text{C}. Given the enthalpy of fusion of ice is 6.00 kJ mol−16.00\,\text{kJ mol}^{-1}, heat capacity of water is 4.2 J/g ∘C4.2\,\text{J/g}\,^\circ\text{C}.
  9. Eg 5.9
    The combustion of one mole of benzene takes place at 298 K298\,\text{K} and 1 atm1\,\text{atm}. After combustion, CO2(g)\text{CO}_2(g) and H2O(l)\text{H}_2\text{O}(l) are produced and 3267.0 kJ3267.0\,\text{kJ} of heat is liberated. Calculate the standard enthalpy of formation, ΔfH⊖\Delta_f H^{\ominus} of benzene. Standard enthalpies of formation of CO2(g)\text{CO}_2(g) and H2O(l)\text{H}_2\text{O}(l) are −393.5 kJ mol−1-393.5\,\text{kJ mol}^{-1} and −285.83 kJ mol−1-285.83\,\text{kJ mol}^{-1} respectively.
  10. Eg 5.10
    Predict in which of the following, entropy increases/decreases: (i) A liquid crystallizes into a solid. (ii) Temperature of a crystalline solid is raised from 0 K0\,\text{K} to 115 K115\,\text{K}. (iii) 2NaHCO3(s)→Na2CO3(s)+CO2(g)+H2O(g)2\text{NaHCO}_3(s) \rightarrow \text{Na}_2\text{CO}_3(s) + \text{CO}_2(g) + \text{H}_2\text{O}(g) (iv) H2(g)→2H(g)\text{H}_2(g) \rightarrow 2\text{H}(g)
  11. Eg 5.11
    For oxidation of iron, 4Fe(s)+3O2(g)→2Fe2O3(s)4\text{Fe}(s) + 3\text{O}_2(g) \rightarrow 2\text{Fe}_2\text{O}_3(s) entropy change is −549.4 JK−1mol−1-549.4\,\text{JK}^{-1}\text{mol}^{-1} at 298 K298\,\text{K}. Inspite of negative entropy change of this reaction, why is the reaction spontaneous? (ΔrH⊖\Delta_r H^{\ominus} for this reaction is −1648×103 J mol−1-1648 \times 10^{3}\,\text{J mol}^{-1})
  12. Eg 5.12
    Calculate ΔrG⊖\Delta_r G^{\ominus} for conversion of oxygen to ozone, 32O2(g)→O3(g)\dfrac{3}{2}\text{O}_2(g) \rightarrow \text{O}_3(g) at 298 K298\,\text{K}, if KpK_p for this conversion is 2.47×10−292.47 \times 10^{-29}.
  13. Eg 5.13
    Find out the value of equilibrium constant for the following reaction at 298 K298\,\text{K}. 2NH3(g)+CO2(g)⇌NH2CONH2(aq)+H2O(l)2\text{NH}_3(g) + \text{CO}_2(g) \rightleftharpoons \text{NH}_2\text{CONH}_2(aq) + \text{H}_2\text{O}(l) Standard Gibbs energy change, ΔrG⊖\Delta_r G^{\ominus} at the given temperature is −13.6 kJ mol−1-13.6\,\text{kJ mol}^{-1}.
  14. Eg 5.14
    At 60 ∘C60\,^\circ\text{C}, dinitrogen tetroxide is 50 per cent dissociated. Calculate the standard free energy change at this temperature and at one atmosphere.

Exercises

22 q
  1. Ex 5.1
    Choose the correct answer. A thermodynamic state function is a quantity
    1. A.
      used to determine heat changes
    2. B.
      whose value is independent of path
    3. C.
      used to determine pressure volume work
    4. D.
      whose value depends on temperature only.
  2. Ex 5.2
    For the process to occur under adiabatic conditions, the correct condition is:
    1. A.
      ΔT=0\Delta T = 0
    2. B.
      Δp=0\Delta p = 0
    3. C.
      q=0q = 0
    4. D.
      w=0\text{w} = 0
  3. Ex 5.3
    The enthalpies of all elements in their standard states are:
    1. A.
      unity
    2. B.
      zero
    3. C.
      <0< 0
    4. D.
      different for each element
  4. Ex 5.4
    ΔU⊖\Delta U^{\ominus} of combustion of methane is −X kJ mol−1-X\,\text{kJ mol}^{-1}. The value of ΔH⊖\Delta H^{\ominus} is
    1. A.
      =ΔU⊖= \Delta U^{\ominus}
    2. B.
      >ΔU⊖> \Delta U^{\ominus}
    3. C.
      <ΔU⊖< \Delta U^{\ominus}
    4. D.
      =0= 0
  5. Ex 5.5
    The enthalpy of combustion of methane, graphite and dihydrogen at 298 K298\,\text{K} are, −890.3 kJ mol−1-890.3\,\text{kJ mol}^{-1}, −393.5 kJ mol−1-393.5\,\text{kJ mol}^{-1}, and −285.8 kJ mol−1-285.8\,\text{kJ mol}^{-1} respectively. Enthalpy of formation of CH4(g)\text{CH}_4(g) will be
    1. A.
      −74.8 kJ mol−1-74.8\,\text{kJ mol}^{-1}
    2. B.
      −52.27 kJ mol−1-52.27\,\text{kJ mol}^{-1}
    3. C.
      +74.8 kJ mol−1+74.8\,\text{kJ mol}^{-1}
    4. D.
      +52.26 kJ mol−1+52.26\,\text{kJ mol}^{-1}
  6. Ex 5.6
    A reaction, A+B→C+D+q\text{A} + \text{B} \rightarrow \text{C} + \text{D} + q is found to have a positive entropy change. The reaction will be
    1. A.
      possible at high temperature
    2. B.
      possible only at low temperature
    3. C.
      not possible at any temperature
    4. D.
      possible at any temperature
  7. Ex 5.7
    In a process, 701 J701\,\text{J} of heat is absorbed by a system and 394 J394\,\text{J} of work is done by the system. What is the change in internal energy for the process?
  8. Ex 5.8
    The reaction of cyanamide, NH2CN(s)\text{NH}_2\text{CN}(s), with dioxygen was carried out in a bomb calorimeter, and ΔU\Delta U was found to be −742.7 kJ mol−1-742.7\,\text{kJ mol}^{-1} at 298 K298\,\text{K}. Calculate enthalpy change for the reaction at 298 K298\,\text{K}. NH2CN(g)+32O2(g)→N2(g)+CO2(g)+H2O(l)\text{NH}_2\text{CN}(g) + \dfrac{3}{2}\text{O}_2(g) \rightarrow \text{N}_2(g) + \text{CO}_2(g) + \text{H}_2\text{O}(l)
  9. Ex 5.9
    Calculate the number of kJ of heat necessary to raise the temperature of 60.0 g60.0\,\text{g} of aluminium from 35 ∘C35\,^\circ\text{C} to 55 ∘C55\,^\circ\text{C}. Molar heat capacity of Al is 24 J mol−1K−124\,\text{J mol}^{-1}\text{K}^{-1}.
  10. Ex 5.10
    Calculate the enthalpy change on freezing of 1.0 mol1.0\,\text{mol} of water at 10.0 ∘C10.0\,^\circ\text{C} to ice at −10.0 ∘C-10.0\,^\circ\text{C}. ΔfusH=6.03 kJ mol−1\Delta_{fus}H = 6.03\,\text{kJ mol}^{-1} at 0 ∘C0\,^\circ\text{C}. Cp [H2O(l)]=75.3 J mol−1K−1C_p\,[\text{H}_2\text{O}(l)] = 75.3\,\text{J mol}^{-1}\text{K}^{-1} Cp [H2O(s)]=36.8 J mol−1K−1C_p\,[\text{H}_2\text{O}(s)] = 36.8\,\text{J mol}^{-1}\text{K}^{-1}
  11. Ex 5.11
    Enthalpy of combustion of carbon to CO2\text{CO}_2 is −393.5 kJ mol−1-393.5\,\text{kJ mol}^{-1}. Calculate the heat released upon formation of 35.2 g35.2\,\text{g} of CO2\text{CO}_2 from carbon and dioxygen gas.
  12. Ex 5.12
    Enthalpies of formation of CO(g)\text{CO}(g), CO2(g)\text{CO}_2(g), N2O(g)\text{N}_2\text{O}(g) and N2O4(g)\text{N}_2\text{O}_4(g) are −110-110, −393-393, 8181 and 9.7 kJ mol−19.7\,\text{kJ mol}^{-1} respectively. Find the value of ΔrH\Delta_r H for the reaction: N2O4(g)+3CO(g)→N2O(g)+3CO2(g)\text{N}_2\text{O}_4(g) + 3\text{CO}(g) \rightarrow \text{N}_2\text{O}(g) + 3\text{CO}_2(g)
  13. Ex 5.13
    Given N2(g)+3H2(g)→2NH3(g)\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g); ΔrH⊖=−92.4 kJ mol−1\Delta_r H^{\ominus} = -92.4\,\text{kJ mol}^{-1} What is the standard enthalpy of formation of NH3\text{NH}_3 gas?
  14. Ex 5.14
    Calculate the standard enthalpy of formation of CH3OH(l)\text{CH}_3\text{OH}(l) from the following data: CH3OH(l)+32O2(g)→CO2(g)+2H2O(l)\text{CH}_3\text{OH}(l) + \dfrac{3}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l); ΔrH⊖=−726 kJ mol−1\Delta_r H^{\ominus} = -726\,\text{kJ mol}^{-1} C(graphite)+O2(g)→CO2(g)\text{C}(\text{graphite}) + \text{O}_2(g) \rightarrow \text{CO}_2(g); ΔcH⊖=−393 kJ mol−1\Delta_c H^{\ominus} = -393\,\text{kJ mol}^{-1} H2(g)+12O2(g)→H2O(l)\text{H}_2(g) + \dfrac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l); ΔfH⊖=−286 kJ mol−1\Delta_f H^{\ominus} = -286\,\text{kJ mol}^{-1}
  15. Ex 5.15
    Calculate the enthalpy change for the process CCl4(g)→C(g)+4Cl(g)\text{CCl}_4(g) \rightarrow \text{C}(g) + 4\text{Cl}(g) and calculate bond enthalpy of C−Cl\text{C}-\text{Cl} in CCl4(g)\text{CCl}_4(g). ΔvapH⊖(CCl4)=30.5 kJ mol−1\Delta_{vap}H^{\ominus}(\text{CCl}_4) = 30.5\,\text{kJ mol}^{-1} ΔfH⊖(CCl4)=−135.5 kJ mol−1\Delta_f H^{\ominus}(\text{CCl}_4) = -135.5\,\text{kJ mol}^{-1} ΔaH⊖(C)=715.0 kJ mol−1\Delta_a H^{\ominus}(\text{C}) = 715.0\,\text{kJ mol}^{-1}, where ΔaH⊖\Delta_a H^{\ominus} is enthalpy of atomisation ΔaH⊖(Cl2)=242 kJ mol−1\Delta_a H^{\ominus}(\text{Cl}_2) = 242\,\text{kJ mol}^{-1}
  16. Ex 5.16
    For an isolated system, ΔU=0\Delta U = 0, what will be ΔS\Delta S?
  17. Ex 5.17
    For the reaction at 298 K298\,\text{K}, 2A+B→C2\text{A} + \text{B} \rightarrow \text{C} ΔH=400 kJ mol−1\Delta H = 400\,\text{kJ mol}^{-1} and ΔS=0.2 kJ K−1mol−1\Delta S = 0.2\,\text{kJ K}^{-1}\text{mol}^{-1} At what temperature will the reaction become spontaneous considering ΔH\Delta H and ΔS\Delta S to be constant over the temperature range.
  18. Ex 5.18
    For the reaction, 2Cl(g)→Cl2(g)2\text{Cl}(g) \rightarrow \text{Cl}_2(g), what are the signs of ΔH\Delta H and ΔS\Delta S?
  19. Ex 5.19
    For the reaction 2A(g)+B(g)→2D(g)2\text{A}(g) + \text{B}(g) \rightarrow 2\text{D}(g) ΔU⊖=−10.5 kJ\Delta U^{\ominus} = -10.5\,\text{kJ} and ΔS⊖=−44.1 JK−1\Delta S^{\ominus} = -44.1\,\text{JK}^{-1}. Calculate ΔG⊖\Delta G^{\ominus} for the reaction, and predict whether the reaction may occur spontaneously.
  20. Ex 5.20
    The equilibrium constant for a reaction is 10. What will be the value of ΔG⊖\Delta G^{\ominus}? R=8.314 JK−1mol−1\text{R} = 8.314\,\text{JK}^{-1}\text{mol}^{-1}, T=300 KT = 300\,\text{K}.
  21. Ex 5.21
    Comment on the thermodynamic stability of NO(g)\text{NO}(g), given 12N2(g)+12O2(g)→NO(g)\dfrac{1}{2}\text{N}_2(g) + \dfrac{1}{2}\text{O}_2(g) \rightarrow \text{NO}(g); ΔrH⊖=90 kJ mol−1\Delta_r H^{\ominus} = 90\,\text{kJ mol}^{-1} NO(g)+12O2(g)→NO2(g)\text{NO}(g) + \dfrac{1}{2}\text{O}_2(g) \rightarrow \text{NO}_2(g); ΔrH⊖=−74 kJ mol−1\Delta_r H^{\ominus} = -74\,\text{kJ mol}^{-1}
  22. Ex 5.22
    Calculate the entropy change in surroundings when 1.00 mol1.00\,\text{mol} of H2O(l)\text{H}_2\text{O}(l) is formed under standard conditions. ΔfH⊖=−286 kJ mol−1\Delta_f H^{\ominus} = -286\,\text{kJ mol}^{-1}.