Question

Henry's law states that the concentration of a gas dissolved in a liquid is proportional to the pressure of the gas. This law is a consequence of the equilibrium

$\mathit{X}\left(g\right)\stackrel{{\mathbf{K}}_{\mathbf{h}}}{\mathbf{\leftrightharpoons }}\mathit{X}\left(aq\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathit{K}}_{\mathbf{h}}\mathbf{=}\frac{\left[x\right]}{{\mathbf{p}}_{\mathbf{X}}}$

where ${\mathit{K}}_{\mathbf{h}}$is called the Henry's law constant. For the gasoline additive MTBE, ${\mathbf{K}}_{\mathbf{h}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{71}\mathbf{}\mathbf{M}\mathbf{/}\mathbf{bar}$ . Suppose we have a closed container with aqueous solution and air in equilibrium. If the concentration of MTBE in the water is $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{x}{\mathbf{10}}^{\mathbf{2}}\mathbf{ppm}$ $\left(=100\mathrm{\mu g}\mathrm{MTBE}/g\mathrm{solution}\approx 100\mathrm{\mu g}/\mathrm{mL}\right)$, what is the pressure of MTBE in the air?

$\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathbf{-}\mathit{O}\mathbf{-}\mathit{C}{\mathbf{\left(}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{3}}$Methyl- -butyl ether (MTBE, FM 88.15)

Short answer

The pressure of MTBE in the gas phase was calculated as 0.663 mbar .

Step-by-step solution

The concept used.

Henry's law:

This law states that the concentration of a gas dissolved in a liquid is directly proportional to the pressure of the gas. Henry's law is a sign of equilibrium.

$$\begin{gathered} A_{\left(g\right)}\stackrel{K_h}{\leftrightharpoons }{A}_{\left(aq\right)} \\ {K}_h=\frac{\left[A\right]}{P_A} \end{gathered}$$

here,

$K_h$ is Henry's law constant.

The pressure of MTBE in gas phase

Henry's law constant for gasoline = 1.71M/bar

The concentration of gasoline in the water is$1.00\times {10}^2\mathrm{ppm}$

The concentration of gasoline in the solution is $100\mu g/mL=100mg/L$

The molarity of MTBE,

$$\begin{gathered} Molarity=\frac{0.100g/L}{88.15g/mol} \\ =1.134\times {10}^{-3}M \end{gathered}$$

Therefore, the pressure of MTBE present in the gas phase:

$$\begin{gathered} Pressure=\frac{concerntration}{K_h} \\ =\frac{1.134\times {10}^{-3}M}{1.71M/bar} \\ =0.663mbar \end{gathered}$$