Consider the following cases of standard enthalpy of reaction (\( \Delta H_f^\circ \) in kJ mol\(^{-1}\)): \[ \text{C}_2\text{H}_6(g) + 7 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 3 \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = -1550 \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2^\circ = -393.5 \] \[ \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{H}_2\text{O}(g) \quad \Delta H_3^\circ = -286 \] The magnitude of \( \Delta H_f^\circ \) of \( \text{C}_2\text{H}_6(g) \) is \(\_\_\_\_\_\) kJ mol\(^{-1}\) (Nearest integer).
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Correct Answer: 84
Solution and Explanation
We can calculate \( \Delta H_f^\circ \) for \( \text{C}_2\text{H}_6(g) \) using Hess's law.
Using the given reactions: \[ \text{C}_2\text{H}_6(g) + 7 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 3 \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = -1550 \]
Adding the reactions and using the enthalpy values for \( \text{CO}_2 \) and \( \text{H}_2\text{O} \): \[ \Delta H_f^\circ = -1550 + 2 \times 393.5 + 3 \times 286 = -84 \]
Thus, the magnitude of \( \Delta H_f^\circ \) for \( \text{C}_2\text{H}_6(g) \) is \( -84 \) kJ/mol.
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