Consider the two sequential thermochemical processes:\ (1) $2\mathrm{C}_{( ext{graphite})} + 2\mat

Question

Consider the two sequential thermochemical processes:\ (1) $2\mathrm{C}_{(	ext{graphite})} + 2\mathrm{O}_{2(g)} ightarrow 2\mathrm{CO}_{2(g)} \quad \Delta H = -2X 	ext{ kJ}$, and\ (2) $2\mathrm{CO}_{(g)} + \mathrm{O}_{2(g)} ightarrow 2\mathrm{CO}_{2(g)} \quad \Delta H = -2Y 	ext{ kJ}$.\ Based on this given data, the standard heat of formation of a single mole of Carbon Monoxide ($\mathrm{CO}_{(g)}$) is correctly given by

Professor PC Thomas Classes · Answer

(a) : The target chemical equation defining the standard heat of formation for exactly one mole of $\mathrm{CO}_{(g)}$ is: $\mathrm{C}_{(	ext{graphite})} + \frac{1}{2}\mathrm{O}_{2(g)} ightarrow \mathrm{CO}_{(g)}$. We must logically manipulate the provided equations using Hess's Law to construct this target. First, divide both given equations perfectly by 2: (1') $\mathrm{C} + \mathrm{O}_2 ightarrow \mathrm{CO}_2 \quad \Delta H = -X$. (2') $\mathrm{CO} + \frac{1}{2}\mathrm{O}_2 ightarrow \mathrm{CO}_2 \quad \Delta H = -Y$. Now, subtract equation (2') from equation (1') to isolate CO on the product side: $\Delta H_{target} = (-X) - (-Y) = -X + Y = -(X - Y) 	ext{ kJ/mol}$.