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Chemistry · Textbook solutions

Chemical Thermodynamics

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 67 questions

4. Chemical Thermodynamics — worked examples

20 q

Problems / Examples 4.1 - 4.20

Worked · 20
  1. Solved Ex.4.1
    Three moles of an ideal gas are expanded isothermally from 15 dm3\mathrm{dm^3} to 20 dm3\mathrm{dm^3} at constant external pressure of 1.2 bar. Estimate the amount of work in dm3\mathrm{dm^3} bar and J.
  2. Solved Ex.4.2
    Calculate the constant external pressure required to compress 2 moles of an ideal gas from volume of 25 dm3\mathrm{dm^3} to 13 dm3\mathrm{dm^3} when the work obtained is 4862.4 J.
  3. Solved Ex.4.3
    200 mL ethylene gas and 150 mL of HCl gas were allowed to react at 1 bar pressure according to the reaction C2H4(g)+HCl(g)⟶C2H5Cl(g)\mathrm{C_2H_4(g) + HCl(g) \longrightarrow C_2H_5Cl(g)} Calculate the PVPV work in joules.
  4. Solved Ex.4.4
    2 moles of an ideal gas are expanded isothermally and reversibly from 20 L to 30 L at 300 K. Calculate the work done (R=8.314 J K−1 mol−1R = 8.314\ \mathrm{J\ K^{-1}\ mol^{-1}})
  5. Solved Ex.4.5
    22 g of CO2\mathrm{CO_2} are compressed isothermally and reversibly at 298 K from initial pressure of 100 kPa when the work obtained is 1.2 kJ. Find the final pressure.
  6. Solved Ex.4.6
    300 mmol of an ideal gas occupies 13.7 dm3\mathrm{dm^3} at 300 K. Calculate the work done when the gas is expanded until its volume has increased by 2.3 dm3\mathrm{dm^3} (a) isothermally against a constant external pressure of 0.3 bar (b) isothermally and reversibly (c) into vacuum.
  7. Solved Ex.4.7
    ΔH\Delta H for the reaction, 2C(s)+3H2(g)⟶C2H6(g)\mathrm{2C(s) + 3H_2(g) \longrightarrow C_2H_6(g)} is −84.4-84.4 kJ at 25∘C25^\circ\mathrm{C}. Calculate ΔU\Delta U for the reaction at 25∘C25^\circ\mathrm{C}. (R=8.314 J K−1 mol−1R = 8.314\ \mathrm{J\ K^{-1}\ mol^{-1}})
  8. Solved Ex.4.8
    In a particular reaction 2 kJ of heat is released by the system and 6 kJ of work is done on the system. Determine of ΔH\Delta H and ΔU\Delta U?
  9. Solved Ex.4.9
    Calculate the work done in oxidation of 4 moles of SO2\mathrm{SO_2} at 25∘C25^\circ\mathrm{C} if 2 SO2(g)+O2(g)⟶2 SO3(g)\mathrm{2\,SO_2(g) + O_2(g) \longrightarrow 2\,SO_3(g)} R=8.314 J K−1 mol−1R = 8.314\ \mathrm{J\ K^{-1}\,mol^{-1}} State whether work is done on the system or by the system.
  10. Solved Ex.4.10
    Calculate standard enthalpy of reaction, 2C2H6(g)+7O2(g)⟶4 CO2(g)+6 H2O(l)\mathrm{2C_2H_6(g) + 7O_2(g) \longrightarrow 4\,CO_2(g) + 6\,H_2O(\mathit{l})} Given that ΔfH0(CO2)=−393.5 kJ mol−1\Delta_f H^0(\mathrm{CO_2}) = -393.5\ \mathrm{kJ\ mol^{-1}}, ΔfH0(H2O)=−285.8 kJ mol−1\Delta_f H^0(\mathrm{H_2O}) = -285.8\ \mathrm{kJ\ mol^{-1}} and ΔfH0(C2H6)=−84.9 kJ mol−1\Delta_f H^0(\mathrm{C_2H_6}) = -84.9\ \mathrm{kJ\ mol^{-1}}
  11. Solved Ex.4.11
    Estimate the standard enthalpy of combustion of CH4(g)\mathrm{CH_4(g)} if ΔfH0(CH4)=−74.8 kJ mol−1\Delta_f H^0(\mathrm{CH_4}) = -74.8\ \mathrm{kJ\ mol^{-1}}, ΔfH0(CO2)=−393.5 kJ mol−1\Delta_f H^0(\mathrm{CO_2}) = -393.5\ \mathrm{kJ\ mol^{-1}} and ΔfH0(H2O)=−285.8 kJ mol−1\Delta_f H^0(\mathrm{H_2O}) = -285.8\ \mathrm{kJ\ mol^{-1}}
  12. Solved Ex.4.12
    Calculate the standard enthalpy of : N2H4(g)+H2(g)⟶2 NH3(g)\mathrm{N_2H_4(g) + H_2(g) \longrightarrow 2\,NH_3(g)} if ΔH0(N-H)=389 kJ mol−1\Delta H^0(\mathrm{N\text{-}H}) = 389\ \mathrm{kJ\ mol^{-1}}, ΔH0(H-H)=435 kJ mol−1\Delta H^0(\mathrm{H\text{-}H}) = 435\ \mathrm{kJ\ mol^{-1}}, ΔH0(N-N)=159 kJ mol−1\Delta H^0(\mathrm{N\text{-}N}) = 159\ \mathrm{kJ\ mol^{-1}}
  13. Solved Ex.4.13
    The enthalpy change of the following reaction CH4(g)+Cl2(g)⟶CH3Cl(g)+HCl(g)\mathrm{CH_4(g) + Cl_2(g) \longrightarrow CH_3Cl(g) + HCl(g)}, ΔrH0=−104\Delta_r H^0 = -104 kJ. Calculate C-Cl bond enthalpy. The bond enthalpies are
    BondC-HCl-ClH-Cl
    ΔH0/kJ mol−1\Delta H^0/\mathrm{kJ\ mol^{-1}}414243431
  14. Solved Ex.4.14
    Calculate the standard enthalpy of the reaction, 2Fe(s)+32 O2(g)⟶Fe2O3(s)\mathrm{2Fe(s) + \tfrac{3}{2}\,O_2(g) \longrightarrow Fe_2O_3(s)} Given : i. 2Al(s)+Fe2O3(s)⟶2Fe(s)+Al2O3(s)\mathrm{2Al(s) + Fe_2O_3(s) \longrightarrow 2Fe(s) + Al_2O_3(s)}, ΔrH0=−847.6 kJ\Delta_r H^0 = -847.6\ \mathrm{kJ} ii. 2 Al(s)+32 O2(g)⟶Al2O3(s)\mathrm{2\,Al(s) + \tfrac{3}{2}\,O_2(g) \longrightarrow Al_2O_3(s)}, ΔrH0=−1670 kJ\Delta_r H^0 = -1670\ \mathrm{kJ}
  15. Solved Ex.4.15
    Calculate the standard enthalpy of the reaction, SiO2(s)+3C(graphite)⟶SiC(s)+2 CO(g)\mathrm{SiO_2(s) + 3C(graphite) \longrightarrow SiC(s) + 2\,CO(g)} from the following reactions, i. Si(s)+O2(g)⟶SiO2(s)\mathrm{Si(s) + O_2(g) \longrightarrow SiO_2(s)}, ΔrH0=−911 kJ\Delta_r H^0 = -911\ \mathrm{kJ} ii. 2 C(graphite)+O2(g)⟶2CO(g)\mathrm{2\,C(graphite) + O_2(g) \longrightarrow 2CO(g)}, ΔrH0=−221 kJ\Delta_r H^0 = -221\ \mathrm{kJ} iii. Si(s)+C(graphite)⟶SiC(s)\mathrm{Si(s) + C(graphite) \longrightarrow SiC(s)}, ΔrH0=−65.3 kJ\Delta_r H^0 = -65.3\ \mathrm{kJ}
  16. Solved Ex.4.16
    State whether following reactions are spontaneous or not. Further state whether they are exothermic or endothermic. a. ΔH=−110 kJ\Delta H = -110\ \mathrm{kJ} and ΔS=+40 JK−1\Delta S = +40\ \mathrm{JK^{-1}} at 400 K b. ΔH=+50 kJ\Delta H = +50\ \mathrm{kJ} and ΔS=−130 JK−1\Delta S = -130\ \mathrm{JK^{-1}} at 250 K
  17. Solved Ex.4.17
    For a certain reaction ΔH0\Delta H^0 is −224-224 kJ and ΔS0\Delta S^0 is −153 J K−1-153\ \mathrm{J\ K^{-1}}. At what temperature the change over from spontaneous to nonspontaneous will occur?
  18. Solved Ex.4.18
    For the reaction, CH4(g)+H2(g)⟶C2H6(g)\mathrm{CH_4(g) + H_2(g) \longrightarrow C_2H_6(g)}, Kp=3.356×1017K_p = 3.356 \times 10^{17} Calculate ΔG0\Delta G^0 for the reaction at 25∘C25^\circ\mathrm{C}.
  19. Solved Ex.4.19
    Calculate ΔStotal\Delta S_{total} and state whether the reaction is spontaneous or nonspontaneous at 25∘C25^\circ\mathrm{C}. HgS(s)+O2(g)⟶Hg(l)+SO2(g)\mathrm{HgS(s) + O_2(g) \longrightarrow Hg(\mathit{l}) + SO_2(g)}, ΔH0=−238.6 kJ\Delta H^0 = -238.6\ \mathrm{kJ}, ΔS0=+36.7 J K−1\Delta S^0 = +36.7\ \mathrm{J\ K^{-1}}
  20. Solved Ex.4.20
    Calculate ΔG\Delta G for the reaction at 25∘C25^\circ\mathrm{C} CO(g)+2 H2(g)⟶CH3OH(g)\mathrm{CO(g) + 2\,H_2(g) \longrightarrow CH_3OH(g)}, ΔG0=−24.8 kJ mol−1\Delta G^0 = -24.8\ \mathrm{kJ\ mol^{-1}} The partial pressures of gases are PCO=4 barP_{CO} = 4\ \mathrm{bar}, PH2=2 barP_{H_2} = 2\ \mathrm{bar} and PCH3OH=2 barP_{CH_3OH} = 2\ \mathrm{bar}

Exercises

47 q

1. Select the most apropriate option.

Practice · 10
  1. Select the most apropriate option.
    Ex Q.1 (i)
    The correct thermodynamic conditions for the spontaneous reaction at all temperatures are

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  2. Ex Q.1 (ii)
    A gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 bar from an initial volume of 2.5 L to a final volume of 4.5 L. The change in internal energy, ΔU\Delta U of the gas will be

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  3. Ex Q.1 (iii)
    In which of the following, entropy of the system decreases?

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  4. Ex Q.1 (iv)
    The enthalpy of formation for all elements in their standard states is

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  5. Ex Q.1 (v)
    Which of the following reactions is exothermic?

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  6. Ex Q.1 (vi)
    6.24 g of ethanol are vaporized by supplying 5.89 kJ of heat. Enthalpy of vaporization of ethanol will be

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  7. Ex Q.1 (vii)
    If the standard enthalpy of formation of methanol is −238.9 kJ mol−1-238.9\ \mathrm{kJ\ mol^{-1}} then entropy change of the surroundings will be

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  8. Ex Q.1 (viii)
    Which of the following are not state functions? 1. Q+WQ + W 2. QQ 3. WW 4. H−TSH-TS

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  9. Ex Q.1 (ix)
    For vaporization of water at 1 bar, ΔH=40.63 kJ mol−1\Delta H = 40.63\ \mathrm{kJ\ mol^{-1}} and ΔS=108.8 J K−1 mol−1\Delta S = 108.8\ \mathrm{J\ K^{-1}\ mol^{-1}}. At what temperature, ΔG=0\Delta G = 0 ?

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  10. Ex Q.1 (x)
    Bond enthalpies of H-H, Cl-Cl and H-Cl bonds are 434 kJ mol−1434\ \mathrm{kJ\ mol^{-1}}, 242 kJ mol−1242\ \mathrm{kJ\ mol^{-1}} and 431 kJ mol−1431\ \mathrm{kJ\ mol^{-1}}, respectively. Enthalpy of formation of HCl is

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2. Answer the following in one or two sentences.

Practice · 8
  1. Answer the following in one or two sentences.
    Ex Q.2 (i)
    Comment on the statement: no work is involved in an expansion of gas in vacuum.
  2. Ex Q.2 (ii)
    State the first law of thermodynamics.
  3. Ex Q.2 (iii)
    What is enthalpy of fusion?
  4. Ex Q.2 (iv)
    What is standard state of a substance?
  5. Ex Q.2 (v)
    State whether ΔS\Delta S is positive, negative or zero for the reaction 2H(g)⟶H2(g)\mathrm{2H(g) \longrightarrow H_2(g)}. Explain.
  6. Ex Q.2 (vi)
    State second law of thermodynamics in terms of entropy.
  7. Ex Q.2 (vii)
    If the enthalpy change of a reaction is ΔH\Delta H how will you calculate entropy of surroundings?
  8. Ex Q.2 (viii)
    Comment on spontaneity of reactions for which ΔH\Delta H is positive and ΔS\Delta S is negative.

3. Answer in brief.

Practice · 9
  1. Answer in brief.
    Ex Q.3 (i)
    Obtain the relationship between ΔG0\Delta G^0 of a reaction and the equilibrium constant.
  2. Ex Q.3 (ii)
    What is entropy? Give its units.
  3. Ex Q.3 (iii)
    How will you calculate reaction enthalpy from data on bond enthalpies?
  4. Ex Q.3 (iv)
    What is the standard enthalpy of combustion ? Give an example.
  5. Ex Q.3 (v)
    What is the enthalpy of atomization? Give an example.
  6. Ex Q.3 (vi)
    Obtain the expression for work done in chemical reaction.
  7. Ex Q.3 (vii)
    Derive the expression for PVPV work
  8. Ex Q.3 (viii)
    What are intensive properties? Explain why density is intensive property.
  9. Ex Q.3 (ix)
    How much heat is evolved when 12 g of CO reacts with NO2\mathrm{NO_2} ? The reaction is : 4 CO(g)+2 NO2(g)⟶4 CO2(g)+N2(g)\mathrm{4\,CO(g) + 2\,NO_2(g) \longrightarrow 4\,CO_2(g) + N_2(g)}, ΔrH0=−1200 kJ\Delta_r H^0 = -1200\ \mathrm{kJ}

4. Answer the following questions.

Practice · 20
  1. Answer the following questions.
    Ex Q.4 (i)
    Derive the expression for the maximum work.
  2. Ex Q.4 (ii)
    Obtain the relatioship between ΔH\Delta H and ΔU\Delta U for gas phase reactions.
  3. Ex Q.4 (iii)
    State Hess's law of constant heat summation. Illustrate with an example. State its applications.
  4. Ex Q.4 (iv)
    Although ΔS\Delta S for the formation of two moles of water from H2\mathrm{H_2} and O2\mathrm{O_2} is −327 JK−1-327\ \mathrm{JK^{-1}}, it is spontaneous. Explain. (Given ΔH\Delta H for the reaction is −572-572 kJ).
  5. Ex Q.4 (v)
    Obtain the relation between ΔG\Delta G and ΔStotal\Delta S_{total}. Comment on spontaneity of the reaction.
  6. Ex Q.4 (vi)
    One mole of an ideal gas is compressed from 500 cm3\mathrm{cm^3} against a constant external pressure of 1.2×1051.2 \times 10^5 Pa. The work involved in the process is 36.0 J. Calculate the final volume.
  7. Ex Q.4 (vii)
    Calculate the maximum work when 24 g of O2\mathrm{O_2} are expanded isothermally and reversibly from the pressure of 1.6 bar to 1 bar at 298 K.
  8. Ex Q.4 (viii)
    Calculate the work done in the decomposition of 132 g of NH4NO3\mathrm{NH_4NO_3} at 100∘C100^\circ\mathrm{C}. NH4NO3(s)⟶N2O(g)+2 H2O(g)\mathrm{NH_4NO_3(s) \longrightarrow N_2O(g) + 2\,H_2O(g)} State whether work is done on the system or by the system.
  9. Ex Q.4 (ix)
    Calculate standard enthalpy of reaction, Fe2O3(s)+3CO(g)⟶2 Fe(s)+3CO2(g)\mathrm{Fe_2O_3(s) + 3CO(g) \longrightarrow 2\,Fe(s) + 3CO_2(g)}, from the following data. ΔfH0(Fe2O3)=−824 kJ/mol\Delta_f H^0(\mathrm{Fe_2O_3}) = -824\ \mathrm{kJ/mol}, ΔfH0(CO)=−110 kJ/mol\Delta_f H^0(\mathrm{CO}) = -110\ \mathrm{kJ/mol}, ΔfH0(CO2)=−393 kJ/mol\Delta_f H^0(\mathrm{CO_2}) = -393\ \mathrm{kJ/mol}
  10. Ex Q.4 (x)
    For a certain reaction ΔH0=219 kJ\Delta H^0 = 219\ \mathrm{kJ} and ΔS0=−21 J/K\Delta S^0 = -21\ \mathrm{J/K}. Determine whether the reaction is spontaneous or nonspontaneous.
  11. Ex Q.4 (xi)
    Determine whether the following reaction is spontaneous under standard state conditions. 2 H2O(l)+O2(g)⟶2H2O2(l)\mathrm{2\,H_2O(\mathit{l}) + O_2(g) \longrightarrow 2H_2O_2(\mathit{l})} if ΔH0=196 kJ\Delta H^0 = 196\ \mathrm{kJ}, ΔS0=−126 J/K\Delta S^0 = -126\ \mathrm{J/K} Does it have a cross-over temperature?
  12. Ex Q.4 (xii)
    Calculate ΔU\Delta U at 298 K for the reaction, C2H4(g)+HCl(g)⟶C2H5Cl(g)\mathrm{C_2H_4(g) + HCl(g) \longrightarrow C_2H_5Cl(g)}, ΔH=−72.3 kJ\Delta H = -72.3\ \mathrm{kJ} How much PVPV work is done?
  13. Ex Q.4 (xiii)
    Calculate the work done during synthesis of NH3\mathrm{NH_3} in which volume changes from 8.0 dm3\mathrm{dm^3} to 4.0 dm3\mathrm{dm^3} at a constant external pressure of 43 bar. In what direction the work energy flows?
  14. Ex Q.4 (xiv)
    Calculate the amount of work done in the (a) oxidation of 1 mole HCl(g) at 200∘C200^\circ\mathrm{C} according to reaction. 4HCl(g)+O2(g)⟶2 Cl2(g)+2 H2O(g)\mathrm{4HCl(g) + O_2(g) \longrightarrow 2\,Cl_2(g) + 2\,H_2O(g)} (b) decomposition of one mole of NO at 300∘C300^\circ\mathrm{C} for the reaction 2 NO(g)⟶N2(g)+O2\mathrm{2\,NO(g) \longrightarrow N_2(g) + O_2}
  15. Ex Q.4 (xv)
    When 6.0 g of O2\mathrm{O_2} reacts with CIF as per 2Cl F(g)+O2(g)⟶Cl2O(g)+OF2(g)\mathrm{2Cl\,F(g) + O_2(g) \longrightarrow Cl_2O(g) + OF_2(g)} The enthalpy change is 38.55 kJ. What is standard enthalpy of the reaction ?
  16. Ex Q.4 (xvi)
    Calculate the standard enthalpy of formation of CH3OH(l)\mathrm{CH_3OH(\mathit{l})} from the following data i. CH3OH(l)+32 O2(g)⟶CO2(g)+2H2O(l)\mathrm{CH_3OH(\mathit{l}) + \tfrac{3}{2}\,O_2(g) \longrightarrow CO_2(g) + 2H_2O(\mathit{l})}, ΔH0=−726 kJ mol−1\Delta H^0 = -726\ \mathrm{kJ\ mol^{-1}} ii. C (Graphite)+O2(g)⟶CO2(g)\mathrm{C\,(Graphite) + O_2(g) \longrightarrow CO_2(g)}, ΔcH0=−393 kJ mol−1\Delta_c H^0 = -393\ \mathrm{kJ\ mol^{-1}} iii. H2(g)+12 O2(g)⟶H2O(l)\mathrm{H_2(g) + \tfrac{1}{2}\,O_2(g) \longrightarrow H_2O(\mathit{l})}, ΔfH0=−286 kJ mol−1\Delta_f H^0 = -286\ \mathrm{kJ\ mol^{-1}}
  17. Ex Q.4 (xvii)
    Calculate ΔH0\Delta H^0 for the following reaction at 298 K H2B4O7(s)+H2O(l)⟶4HBO2 (aq)\mathrm{H_2B_4O_7(s) + H_2O(\mathit{l}) \longrightarrow 4HBO_2\,(aq)} i. 2H3BO3(aq)⟶B2O3(s)+3H2O(l)\mathrm{2H_3BO_3(aq) \longrightarrow B_2O_3(s) + 3H_2O(\mathit{l})}, ΔH0=14.4 kJ mol−1\Delta H^0 = 14.4\ \mathrm{kJ\ mol^{-1}} ii. H3BO3(aq)⟶HBO2(aq)+H2O,(l)\mathrm{H_3BO_3(aq) \longrightarrow HBO_2(aq) + H_2O,(\mathit{l})}, ΔH0=−0.02 kJ mol−1\Delta H^0 = -0.02\ \mathrm{kJ\ mol^{-1}} iii. H2B4O7(s)⟶2P2O3(s)+H2O(l)\mathrm{H_2B_4O_7(s) \longrightarrow 2P_2O_3(s) + H_2O(\mathit{l})}, ΔH0=17.3 kJ mol−1\Delta H^0 = 17.3\ \mathrm{kJ\ mol^{-1}}
  18. Ex Q.4 (xviii)
    Calculate the total heat required (a) to melt 180 g of ice at 0∘C0^\circ\mathrm{C}, (b) heat it to 100∘C100^\circ\mathrm{C} and then (c) vapourise it at that temperature. Given ΔfusH0(ice)=6.01 kJ mol−1\Delta_{fus}H^0(\mathrm{ice}) = 6.01\ \mathrm{kJ\ mol^{-1}} at 0∘C0^\circ\mathrm{C}, ΔvapH0(H2O)=40.7 kJ mol−1\Delta_{vap}H^0(\mathrm{H_2O}) = 40.7\ \mathrm{kJ\ mol^{-1}} at 100∘C100^\circ\mathrm{C} specific heat of water is 4.18 J g−1 K−14.18\ \mathrm{J\ g^{-1}\ K^{-1}}
  19. Ex Q.4 (xix)
    The enthalpy change for the reaction, C2H4(g)+H2(g)⟶C2H6(g)\mathrm{C_2H_4(g) + H_2(g) \longrightarrow C_2H_6(g)} is −620-620 J when 100 ml of ethylene and 100 mL of H2\mathrm{H_2} react at 1 bar pressure. Calculate the pressure volume type of work and ΔU\Delta U for the reaction.
  20. Ex Q.4 (xx)
    Calculate the work done and comment on whether work is done on or by the system for the decomposition of 2 moles of NH4NO3\mathrm{NH_4NO_3} at 100∘C100^\circ\mathrm{C} NH4NO3(s)⟶N2O(g)+2H2O(g)\mathrm{NH_4NO_3(s) \longrightarrow N_2O(g) + 2H_2O(g)}