At $T(\mathrm{~K})$ the molarity of $\mathrm{CO}_2$ (in $\mathrm{mol} \mathrm{L}^{-1}$ ) in 200…
At $T(\mathrm{~K})$ the molarity of $\mathrm{CO}_2$ (in $\mathrm{mol} \mathrm{L}^{-1}$ ) in 200 $\mathrm{mL}$ of soda water packed under a pressure of 3.4 bar is $\left(K_{\mathrm{H}}\right.$ of $\mathrm{CO}_2$ in water is $1.7 \times 10^3$ bar at $T(\mathrm{~K}))$
$2.0 \times 10^{-2}$
$1.11 \times 10^{-1}$
$2.22 \times 10^{-1}$
$5.1 \times 10^{-2}$
Solution
Given, volume $=200 \mathrm{~mL}$
pressure, $p=3.4 \mathrm{bar}$
$K_{\mathrm{H}}$ of $\mathrm{CO}_2$ in water $=1.7 \times 10^3$ bar
According to Henry's law, $p_{\mathrm{CO}_2}=K_{\mathrm{H}} \cdot \chi$
$\chi=\frac{p_{\mathrm{CO}_2}}{K_{\mathrm{H}}}$
$\frac{n_{\mathrm{CO}_2} \times 18}{200}=\frac{3.4}{1.7 \times 10^3}$
$n_{\mathrm{CO}_2}=\frac{2 \times 10^{-3} \times 200}{18}=22.22 \times 10^{-3}$
Molarity $=\frac{\text { Number of mole of solute }}{\text { Volume }}$
$\begin{aligned} & =\frac{22.22 \times 10^{-3}}{200 \times 10^{-3}}=0.1111 \\ & =1.11 \times 10^{-1} \mathrm{~mol} \mathrm{~L}^{-1}\end{aligned}$