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