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Thermodynamics question

2016 · Shift 0 · Q9
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Thermodynamics question

2016 · Shift 0 · Q9

JEE MainChemistryThermodynamicsMCQ+4 / −1
The heats of combustion of carbon and carbon monoxide are –393.5 and –283.5 kJ mol–1, respectively. The heat of formation (in kJ) of carbon monoxide per mole is :
  1. A
    676.5
  2. B
    -676.5
  3. C
    –110
  4. D
    110.5
View written solutionFree

Correct answer: C

  1. Write the given combustion reactions

    • Combustion of carbon: C(s)+O2(g)→CO2(g)ΔH1=−393.5 kJ mol−1\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)} \qquad \Delta H_1 = -393.5\ \text{kJ mol}^{-1}C(s)+O2​(g)→CO2​(g)ΔH1​=−393.5 kJ mol−1

    • Combustion of carbon monoxide: CO(g)+12O2(g)→CO2(g)ΔH2=−283.5 kJ mol−1\mathrm{CO(g) + \tfrac{1}{2}O_2(g) \rightarrow CO_2(g)} \qquad \Delta H_2 = -283.5\ \text{kJ mol}^{-1}CO(g)+21​O2​(g)→CO2​(g)ΔH2​=−283.5 kJ mol−1

  2. Required reaction

    We need the heat of formation of carbon monoxide: C(s)+12O2(g)→CO(g)ΔHf=?\mathrm{C(s) + \tfrac{1}{2}O_2(g) \rightarrow CO(g)} \qquad \Delta H_f = ?C(s)+21​O2​(g)→CO(g)ΔHf​=?

  3. Apply Hess's law

    If we add the formation of CO and then combust CO, we should get direct combustion of carbon:

    C(s)+12O2(g)→CO(g)ΔHf\mathrm{C(s) + \tfrac{1}{2}O_2(g) \rightarrow CO(g)} \qquad \Delta H_fC(s)+21​O2​(g)→CO(g)ΔHf​ CO(g)+12O2(g)→CO2(g)−283.5\mathrm{CO(g) + \tfrac{1}{2}O_2(g) \rightarrow CO_2(g)} \qquad -283.5CO(g)+21​O2​(g)→CO2​(g)−283.5

    C(s)+O2(g)→CO2(g)−393.5\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)} \qquad -393.5C(s)+O2​(g)→CO2​(g)−393.5

    Therefore, ΔHf+(−283.5)=−393.5\Delta H_f + (-283.5) = -393.5ΔHf​+(−283.5)=−393.5

  4. Solve for ΔHf\Delta H_fΔHf​

    ΔHf=−393.5+283.5\Delta H_f = -393.5 + 283.5ΔHf​=−393.5+283.5 ΔHf=−110.0 kJ mol−1\Delta H_f = -110.0\ \text{kJ mol}^{-1}ΔHf​=−110.0 kJ mol−1

  5. Match with options

    −110 kJ mol−1-110\ \text{kJ mol}^{-1}−110 kJ mol−1 corresponds to Option C.

  6. Comparison with stored correct answer

    Stored correct answer: C

    Derived answer: C

    So, the derived answer agrees with the stored correct answer.

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