Question

The partial pressure of ethane over a saturated solution containing $6.56\times {10}^{-2}g$ of ethane in water is 1 bar. If the solution contains $5\times {10}^{-2}g$ of ethane, then what shall be the partial pressure of the gas ?

Assume: $n_{H_{2}O}>>n_{ethane}$

• A. $0.2bar$
• B. $1.55bar$
• C. $0.76bar$
• D. $2bar$

Answer 1

The correct option is C $0.76bar$

According to Henry's Law
$P_{gas}=K_H\times {\chi }_{gas}$

Case 1:
$1=K_H\times \frac{n_{ethane}}{n_{ethane}+n_{H_{2}O}}$

Since, $n_{H_{2}O}>>n_{ethane}$

$1=K_H\times \frac{n_{ethane}}{n_{H_{2}O}}1=K_H\times \left(\frac{\frac{6.56\times {10}^{-2}}{30}}{n_{H_{2}O}}\right)$

$1=K_H\times \frac{6.56\times {10}^{-2}}{30\times n_{H_{2}O}}eqn\left(i\right)$

Case 2:
$P_{gas}=K_H\times \frac{n_{ethane}}{n_{ethane}+n_{H_{2}O}}$

Since, $n_{H_{2}O}>>n_{ethane}$

$P_{gas}=K_H\times \frac{n_{ethane}}{n_{H_{2}O}}{P}_{gas}=K_H\times \left(\frac{\frac{5\times {10}^{-2}}{30}}{n_{H_{2}O}}\right)$

$P_{gas}=K_H\times \frac{5\times {10}^{-2}}{30\times n_{H_{2}O}}eqn\left(ii\right)$

$\text{Dividing}eqn\left(ii\right)byeqn\left(i\right)$
$\frac{P_{gas}}{1}=\frac{K_H}{K_H}\times \frac{5\times {10}^{-2}\times n_{H_{2}O}\times 30}{6.56\times {10}^{-2}\times n_{H_{2}O}\times 30}{P}_{gas}=\frac{5}{6.56}=0.76bar$