Only gases remains after 15.0 g of carbon is treated with 20 l of air at 380 K and 8.21 atm pressure — Thermodynamics and Thermochemistry Chemistry Question
Question
Only gases remains after 15.0 g of carbon is treated with 20 l of air at 380 K and 8.21 atm pressure. (Assume 19% by volume oxygen, 80% nitrogen, 1% carbon dioxide). Determine the amount of heat evolved (in kcal) under constant pressure. Enthalpies of formation of $\text{CO}_2\text{(g)}$ and $\text{CO(g)}$ are –96.0 and –26.0 kcal/mol, respectively.
💡 Solution & Explanation
Moles of air = $\frac{PV}{RT} = \frac{8.21 \times 20}{0.0821 \times 380} = \frac{100}{19}\text{ moles}$. Moles of $\text{O}_2$ = $0.19 \times (100/19) = 1.0\text{ mole}$. Moles of C = $15.0/12 = 1.25\text{ moles}$. Let $x$ be moles of $\text{CO}_2$ and $y$ be moles of CO formed. Carbon balance: $x + y = 1.25$. Oxygen balance: $x + 0.5y = 1.0$. Solving gives $y = 0.5\text{ mol (CO)}$ and $x = 0.75\text{ mol (CO}_2\text{)}$. Heat evolved = $0.5(-26.0) + 0.75(-96.0) = -13.0 - 72.0 = -85.0\text{ kcal}$. Magnitude is 85. Format as 0085.