Mass of methane required to produce $22 \mathrm{~g}$ of $\mathrm{CO}_2$ after complete combustion is _______ g.

(Given Molar mass in g mol-1 $\mathrm{C}=12.0$, $\mathrm{H}=1.0$, $\mathrm{O}=16.0)$

<p>To solve this problem, we can use stoichiometry. First, we need to write down the balanced chemical equation for the complete combustion of methane ($\mathrm{CH}_4$).</p> <p>The balanced equation for combustion of methane is:</p> <p>$\mathrm{CH}_4+2 \mathrm{O}_2 \rightarrow \mathrm{CO}_2+2 \mathrm{H}_2 \mathrm{O}$</p> <p>This equation tells us that one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water.</p> <p>Next, we should find the molar mass of methane ($\mathrm{CH}_4$) using the given molar masses:</p> <p>Molar mass of $\mathrm{CH}_4$ = molar mass of C + 4 * molar mass of H</p> <p>Molar mass of $\mathrm{CH}_4$ = $12.0\ \mathrm{g/mol}$ (for C) + $4 * 1.0\ \mathrm{g/mol}$ (for H)</p> <p>Molar mass of $\mathrm{CH}_4$ = $12.0\ \mathrm{g/mol} + 4.0\ \mathrm{g/mol}$</p> <p>Molar mass of $\mathrm{CH}_4$ = $16.0\ \mathrm{g/mol}$</p> <p>Now, to determine the mass of methane required to produce $22\ \mathrm{g}$ of $\mathrm{CO}_2$, we should find out how many moles of $\mathrm{CO}_2$ there are in $22\ \mathrm{g}$ and use the mole ratio from the balanced equation to find the moles of methane required.</p> <p>Moles of $\mathrm{CO}_2$ = mass of $\mathrm{CO}_2$ / molar mass of $\mathrm{CO}_2$</p> <p>Molar mass of $\mathrm{CO}_2$ = molar mass of C + 2 * molar mass of O</p> <p>Molar mass of $\mathrm{CO}_2$ = $12.0\ \mathrm{g/mol}$ + $2 * 16.0\ \mathrm{g/mol}$</p> <p>Molar mass of $\mathrm{CO}_2$ = $12.0\ \mathrm{g/mol} + 32.0\ \mathrm{g/mol}$</p> <p>Molar mass of $\mathrm{CO}_2$ = $44.0\ \mathrm{g/mol}$</p> <p>Moles of $\mathrm{CO}_2$ = $\frac{22\ \mathrm{g}}{44.0\ \mathrm{g/mol}}$</p> <p>Moles of $\mathrm{CO}_2$ = $0.5\ \mathrm{moles}$</p> <p>We will use the stoichiometric ratio from the balanced chemical equation to find the moles of $\mathrm{CH}_4$ required to produce $0.5\ \mathrm{moles}$ of $\mathrm{CO}_2$:</p> $1\ \mathrm{mole\ of\ CH}_4 : 1\ \mathrm{mole\ of\ CO}_2$ <p>This means that we also require $0.5\ \mathrm{moles}$ of $\mathrm{CH}_4$.</p> <p>Finally, we need to convert moles of methane to grams to find the mass:</p> <p>Mass of $\mathrm{CH}_4$ = moles of $\mathrm{CH}_4$ * molar mass of $\mathrm{CH}_4$</p> <p>Mass of $\mathrm{CH}_4$ = $0.5\ \mathrm{moles} * 16.0\ \mathrm{g/mol}$</p> <p>Mass of $\mathrm{CH}_4$ = $8.0\ \mathrm{g}$</p> <p>Therefore, $8.0\ \mathrm{g}$ of methane is required to produce $22\ \mathrm{g}$ of carbon dioxide after complete combustion.</p>