Question

methane, the principal component of natural gas, is used for heating and cooking. the combustion process is \\(\ce{ch_{4}(g) + 2o_{2}(g) -> co_{2}(g) + 2h_{2}o(l)}\\) if 17.5 moles of \\(\ce{ch_{4}}\\) react with oxygen, what is the volume of \\(\ce{co_{2}}\\) produced at 25.1 °c and 0.977 atm? round your answer to 3 significant digits. note: reference the fundamental constants table for additional information.

Explanation:

Step1: Find moles of CO₂

From balanced equation: 1 mol CH₄ → 1 mol CO₂. So 17.5 mol CH₄ → 17.5 mol CO₂.

Step2: Convert to volume (Ideal Gas Law)

$PV = nRT$ → $V = \frac{nRT}{P}$. $T=25.1^\circ C=298.25\ K$, $R=0.0821\ L·atm/(mol·K)$, $P=0.977\ atm$.
$V = \frac{17.5×0.0821×298.25}{0.977} ≈ 438\ L$

Answer:

438