To determine the number of moles of steam (H₂O) produced by the complete combustion of 12.50 liters of methane gas (CH₄) at 2.00 atm and 202.0°C, we'll follow these steps:
1. Convert the given temperature from Celsius to Kelvin:
- The given temperature is 202.0°C. To convert Celsius to Kelvin, we add 273.15.
- Temperature in Kelvin (K) = 202.0°C + 273.15 = 475.15 K.
2. Use the Ideal Gas Law to find the number of moles of methane (CH₄):
- The Ideal Gas Law is [tex]\( PV = nRT \)[/tex], where:
- [tex]\( P \)[/tex] is the pressure in atm (2.00 atm),
- [tex]\( V \)[/tex] is the volume in liters (12.50 L),
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the ideal gas constant (0.0821 L·atm/(K·mol)),
- [tex]\( T \)[/tex] is the temperature in Kelvin (475.15 K).
- Rearrange the Ideal Gas Law to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{PV}{RT}
\][/tex]
- Substituting the values:
[tex]\[
n = \frac{2.00 \, \text{atm} \times 12.50 \, \text{L}}{0.0821 \, \text{L·atm/(K·mol)} \times 475.15 \, \text{K}} \approx 0.6408643568291723 \, \text{mol}
\][/tex]
3. Determine the moles of steam (H₂O) produced:
- The balanced chemical equation for the complete combustion of methane is:
[tex]\[
\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}
\][/tex]
- According to the equation, 1 mole of CH₄ produces 2 moles of H₂O.
- Thus, the number of moles of H₂O produced from 0.6408643568291723 moles of CH₄ is:
[tex]\[
n_{\text{H}_2\text{O}} = 0.6408643568291723 \, \text{mol} \times 2 \approx 1.2817287136583446 \, \text{mol}
\][/tex]
4. Final Answer:
- The number of moles of steam (H₂O) produced is approximately 1.2817287136583446 moles, which can be rounded to 1.28 moles.
Therefore, the correct answer is:
1.28 mol
