Question

0.1 moles of ethane gas $\left(C_2{H}_6\right)$ and 0.3 moles of oxygen gas are sealed in a flask at 27 °C and 1.0 atm pressure. The flask is heated to 1000 K and the following reaction takes place:
$C_2{H}_6+\frac{5}{2}{O}_2\to 2CO+3H_{2}O$
Calculate the partial pressure of water at the end of the reaction.

• A. 0.4
• B. 1.6
• C. 2.1
• D. 2.5

Answer 1

The correct option is D 2.5

1 mole of ethane needs 2.5 moles of oxygen, hence 0.1 moles will need 0.25 moles. Hence the limiting reagent is ethane. The final composition of the products at 1000 K is:
$C_2{H}_6=0\text{mol}{O}_2=0.05\text{mol}CO=0.20\text{mol}{H}_{2}O=0.30\text{mol}$
Total$=0.55\text{mol}$
Applying gas laws at constant volume, we can compute the total pressure in the flask at 1000 K and hence determine the partial pressures knowing mole fractions.
$P_{1}V=n_{1}R{T}_1{P}_{2}V=n_{2}R{T}_2{P}_2=\frac{n_2{T}_2}{n_1{T}_1}\times P_1=\frac{0.55\times 1000}{0.4\times 300}\times 1=4.58\text{atm}P\left(H_{2}O\right)=\frac{0.3}{0.55}\times 4.58=2.499\approx 2.5\text{atm}$