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Difficulty: EasyStandard Enthalpy Changes and Hess's Law
Consider the following thermochemical reactions:
S(s)+O2(g)→SO2(g)ΔH=−297 kJ mol−1\text{S}(s) + \text{O}_2(g) \rightarrow \text{SO}_2(g) \quad \Delta H = -297\text{ kJ mol}^{-1}
2SO2(g)+O2(g)→2SO3(g)ΔH=−198 kJ mol−12\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g) \quad \Delta H = -198\text{ kJ mol}^{-1}
What is the standard enthalpy change for the reaction represented by the equation below?
2S(s)+3O2(g)→2SO3(g)2\text{S}(s) + 3\text{O}_2(g) \rightarrow 2\text{SO}_3(g)
  1. −792 kJ mol−1-792\text{ kJ mol}^{-1}Answer
  2. B
    −495 kJ mol−1-495\text{ kJ mol}^{-1}
  3. C
    −396 kJ mol−1-396\text{ kJ mol}^{-1}
  4. D
    +792 kJ mol−1+792\text{ kJ mol}^{-1}

Answer

−792 kJ mol−1-792\text{ kJ mol}^{-1}
According to Hess's law, the total enthalpy change is the sum of the enthalpy changes for each step. Multiplying the first equation by 2 yields an enthalpy change of −594 kJ mol−1-594\text{ kJ mol}^{-1}. Adding the second equation directly (ΔH=−198 kJ mol−1\Delta H = -198\text{ kJ mol}^{-1}) gives a combined enthalpy change of −594+(−198)=−792 kJ mol−1-594 + (-198) = -792\text{ kJ mol}^{-1}.

Step-by-Step Solution

1
Multiply the first thermochemical equation by 2 to match the 2 moles of sulfur in the target equation.
2S(s)+2O2(g)→2SO2(g)ΔH1=2×(−297 kJ mol−1)=−594 kJ mol−12\text{S}(s) + 2\text{O}_2(g) \rightarrow 2\text{SO}_2(g) \quad \Delta H_1 = 2 \times (-297\text{ kJ mol}^{-1}) = -594\text{ kJ mol}^{-1}
The stoichiometric coefficient of solid sulfur in the target reaction is 2.
2
Add the modified first equation to the second equation.
2S(s)+3O2(g)→2SO3(g)2\text{S}(s) + 3\text{O}_2(g) \rightarrow 2\text{SO}_3(g)
Intermediate sulfur dioxide (2SO22\text{SO}_2) on opposite sides of the combined reaction cancels out.
3
Sum the enthalpy changes for both steps according to Hess's law.
ΔH=−594 kJ mol−1+(−198 kJ mol−1)=−792 kJ mol−1\Delta H = -594\text{ kJ mol}^{-1} + (-198\text{ kJ mol}^{-1}) = -792\text{ kJ mol}^{-1}
Hess's law states that the net enthalpy change of a reaction is the sum of the enthalpy changes of its constituent steps.

Key Concept

Hess's Law of Constant Heat Summation
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Topics

Standard Enthalpy Changes and Hess's Law