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Question 53

Consider the following data
Heat of combustion of H$$_2$$(g) = -241.8 kJ mol$$^{-1}$$
Heat of combustion of C(s) = -393.5 kJ mol$$^{-1}$$
Heat of combustion of C$$_2$$H$$_5$$OH(l) = -1234.7 kJ mol$$^{-1}$$
The heat of formation of C$$_2$$H$$_5$$OH(l) is (-) ______ kJ mol$$^{-1}$$ (Nearest integer)


Correct Answer: 1

We need to find the heat of formation of C$$_2$$H$$_5$$OH(l) using Hess's Law.

Write the relevant combustion reactions.

$$\text{H}_2(g) + \dfrac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l)$$, $$\Delta H_1 = -241.8$$ kJ/mol

$$\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)$$, $$\Delta H_2 = -393.5$$ kJ/mol

$$\text{C}_2\text{H}_5\text{OH}(l) + 3\text{O}_2(g) \rightarrow 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l)$$, $$\Delta H_3 = -1234.7$$ kJ/mol

Write the formation reaction for ethanol.

$$2\text{C}(s) + 3\text{H}_2(g) + \dfrac{1}{2}\text{O}_2(g) \rightarrow \text{C}_2\text{H}_5\text{OH}(l)$$

Apply Hess's Law.

$$\Delta H_f = 2\Delta H_2 + 3\Delta H_1 - \Delta H_3$$

$$= 2(-393.5) + 3(-241.8) - (-1234.7)$$

$$= -787.0 - 725.4 + 1234.7$$

$$= -1512.4 + 1234.7$$

$$= -277.7$$ kJ/mol

The heat of formation is $$-277.7$$ kJ/mol. The question asks for (-) ______ kJ/mol, so the answer is $$278$$ (nearest integer).

But the stored answer is 1. This likely means the stored answer represents something different or there's a parsing issue. My calculation gives 278.

The answer is $$\boxed{278}$$ kJ/mol.

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