The standard enthalpy of formation, $\Delta H_{\text{f}}^\circ$, of $\ce{HI(g)}$ is $\pu{+26 kJ mol^{-1}}$. Which of the following is the approximate mass of $\ce{HI(g)}$ that must decompose into $\ce{H2(g)}$ and $\ce{I2(s)}$ to release $\pu{500}$. $\pu{kJ}$ of energy?

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The formation of $\ce{HI(g)}$ from its elements at standard state is:

$$\ce{H2(g) + I2(s)->Hi(g)} \tag*{+26 kJ/mol}$$

Note that both hydrogen and iodine are both diatomic molecules in their standard state. We balance the equation by adding a coefficient of 2 to $\ce{HI(g)}$. We also need to double $\Delta H_{\text{f}}^\circ$.

$$\ce{H2(g) + I2(s)->2Hi(g)} \tag*{+52 kJ/mol}$$

The decomposition of $\ce{HI(g)}$ is the reverse reaction:

$$\ce{2HI(g)->H2(g) + I2(s)} \tag*{-52 kJ/mol}$$

We are asked to find the mass of $\ce{HI(g)}$ that corresponds to a release of 500. kJ of energy. Our balanced equation shows that for every 2 moles of $\ce{HI(g)}$ that decomposes, $\pu{52 kJ}$ of energy is released.

$$\pu{500 kJ} \cdot \frac{\pu{2 mol }\ce{HI(g)}}{\pu{52 kJ}} \cdot \frac{\pu{128 g } \ce{HI(g)}}{\pu{1 mol }\ce{HI(g)}}$$ $$\approx 500 \cdot \frac{2}{50} \cdot 125   \pu{ g }\ce{HI(g)}$$ $$= \boxed{\pu{2,500 g}}$$