Question

A gas has a solubility in water at 0 degrees Celsius of 3.5 g/L at a pressure of 0.8 atm. What pressure is needed to produce an aqueous solution containing 8.9 g/L of the same gas at 0 degrees Celsius? Answer choices: .32 atm .5 atm .65 atm 2.0 atm

Answer 1

2.0atm

Explanations:

According to Henry's law, the solubility of a gas in a liquid is directly proportional to its partial pressure of the gas above the liquid. Mathematically;

`\begin{gathered} S\alpha P \\ S=kP \\ k=(S_1)/(P_1)=(S_2)/(P_2) \end{gathered}`

Given the following parameters

`\begin{gathered} S_1=3.5g\text{/L} \\ P_1=0.8atm \\ S_2=8.9g\text{/L} \\ \end{gathered}`

Substitute the given parameters into the formula to have:

`\begin{gathered} P_2=(P_1S_2)/(S_1) \\ P_2=\frac{0.8atm*8.9g\text{/L}}{3.5g\text{/L}} \\ P_2=(7.12atm)/(3.5) \\ P_2=2.0atm \end{gathered}`

Hence the pressure needed to produce an aqueous solution containing 8.9 g/L of the same gas at 0 degrees Celsius is 2.0atm