Question

The solubility of $O_2$ at a certain pressure P and temperature $298Kis0.08g{L}^{-1}.$ If $K_{H}of{O}_{2}is35k$ bar, the value of pressure P is _____________.

• A. 1.0 bar
• B. 1.58 bar
• C. 3.5 bar
• D. 35,0 bar

Answer 1

The correct option is B 1.58 bar

$\begin{array}{c}\text{Mass of}1L\text{solution}=1000ml\times 1\frac{g}{ml}=1000g\\ \text{Mass of solution water}=(1000-0.08)\approx .1000g\end{array}$

$\begin{array}{cc}& \text{No of moles of water}=\frac{1000}{18}=55.5mol\\ & \begin{array}{cc}\text{No of mole of}{O}_2=\frac{0.08}{32}& =0.0025mol\\ & =2.5\times {10}^{-3}mol\end{array}\end{array}$

$\begin{array}{cc}X{O}_2& =\frac{n{N}_2}{n{N}_2+n{H}_{2}O}=\frac{2.5\times {10}^{-3}}{2.5\times {10}^{-3}+55.5}\\ & =\frac{2.5\times {10}^{-3}}{(2.5+55500)\times {10}^{-3}}\end{array}$

$\begin{array}{cc}{X}_{O_2}& =\frac{2.5}{55502.5}=4.5\times {10}^{-5}\\ P_{O_2}& =K_H\times X_{N_2}\text{Henry law}\\ & =35\times 4.5\times {10}^{-5}\times {10}^3\\ & =157.5\times {10}^{-5}\times {10}^3\\ P_{0_2}& =1.575\times {10}^{-3}\times {10}^3\\ & =1.575\\ P_{0_2}& \approx .1.5\text{bar}\end{array}$