To determine how many grams of [tex]\( CH_4 \)[/tex] are consumed when [tex]\( 1.03 \, \text{g} \)[/tex] of [tex]\( H_2 \)[/tex] is produced in the reaction:
[tex]\[ CH_4 + 2 H_2O \rightarrow 4 H_2 + CO_2 \][/tex]
we follow these steps:
1. Calculate the moles of [tex]\( H_2 \)[/tex] produced:
- The given mass of [tex]\( H_2 \)[/tex] produced is [tex]\( 1.03 \, \text{g} \)[/tex].
- The molar mass of [tex]\( H_2 \)[/tex] (hydrogen gas) is approximately [tex]\( 2.016 \, \text{g/mol} \)[/tex].
[tex]\[
\text{Moles of } H_2 = \frac{\text{mass of } H_2}{\text{molar mass of } H_2} = \frac{1.03 \, \text{g}}{2.016 \, \text{g/mol}} \approx 0.5109 \, \text{mol}
\][/tex]
2. Determine the moles of [tex]\( CH_4 \)[/tex] consumed:
According to the balanced chemical equation, 1 mole of [tex]\( CH_4 \)[/tex] produces 4 moles of [tex]\( H_2 \)[/tex]. Therefore, the moles of [tex]\( CH_4 \)[/tex] consumed can be calculated by:
[tex]\[
\text{Moles of } CH_4 = \frac{\text{moles of } H_2}{4} \approx \frac{0.5109 \, \text{mol}}{4} \approx 0.1277 \, \text{mol}
\][/tex]
3. Calculate the mass of [tex]\( CH_4 \)[/tex] consumed:
- The molar mass of [tex]\( CH_4 \)[/tex] (methane) is approximately [tex]\( 16.04 \, \text{g/mol} \)[/tex].
[tex]\[
\text{Mass of } CH_4 = \text{moles of } CH_4 \times \text{molar mass of } CH_4 \approx 0.1277 \, \text{mol} \times 16.04 \, \text{g/mol} \approx 2.0488 \, \text{g}
\][/tex]
Thus, the mass of [tex]\( CH_4 \)[/tex] consumed is approximately [tex]\( 2.0488 \, \text{g} \)[/tex].
The correct answer is:
a. [tex]\( 2.04 \, \text{g} \, CH_4 \)[/tex]
