Consider the following date
Heat of combustion of H2(g) = -241.8 kJ mol-1
Heat of combustion of C(s) = -393.5 kJ mol-1
Heat of combustion of C2H5OH(1) = -1234.7 kJ mol-1
The heat of formation of C2H5OH(1) is (-) ____ kJ mol-1 (Nearest integer)
Heat of combustion of H2(g) = -241.8 kJ mol-1
Heat of combustion of C(s) = -393.5 kJ mol-1
Heat of combustion of C2H5OH(1) = -1234.7 kJ mol-1
The heat of formation of C2H5OH(1) is (-) ____ kJ mol-1 (Nearest integer)
Correct Answer: 278
Approach Solution - 1
Hess's Law Enthalpy Calculation
Given Reactions and Enthalpy Changes:
\( 2\text{C(s)} + \text{O}_2 \rightarrow 2\text{CO}_2 \qquad \Delta H = -393.5 \times 2 = -787 \text{ kJ} \qquad (1) \)
\( 3\text{H}_2 + \frac{3}{2}\text{O}_2 \rightarrow 3\text{H}_2\text{O} \qquad \Delta H = -241.5 \times 3 = -725.4 \text{ kJ} \qquad (2) \)
\( \text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O} \qquad \Delta H = -1234.7 \text{ kJ} \qquad (3) \)
\( 3\text{H}_2\text{O} + 2\text{CO}_2 \rightarrow \text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \qquad \Delta H = +1234.7 \text{ kJ} \qquad (4) \)
Target Reaction:
\( 2\text{C(s)} + 3\text{H}_2\text{(g)} + \frac{1}{2}\text{O}_2 \rightarrow \text{C}_2\text{H}_5\text{OH} \qquad (5) \)
Calculation:
Equation (5) is derived as:
\( (5) = (1) + (2) + (4) \)
\( \Delta H = (-787) + (-725.4) + (1234.7) \)
\( \Delta H = -277.7 \text{ kJ} \implies \Delta H \approx -278 \text{ kJ} \)
Approach Solution -2
\( \Delta H_{\text{f}} \) = \( -393.5 \times 2 \) - \( 241.5 \times 8 \times 3 \) + 1234.7 = -277.7 kJ mol\(^{-1}\)
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