Chapter 16.1, Problem 2SP

Interpretation Introduction

Interpretation: To calculate the pressure needed to produce an aqueous solution containing gas.

Concept introduction: Henry's law is a law that is used to determine the solubility of gases in a liquid. According to this law, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of the gas.
At constant temperature, Henry's law describes the relationship between pressure and solubility as below:

  $\frac{S\text{1}}{P\text{1}}=\frac{S\text{2}}{P\text{2}}$

Answer to Problem 2SP

The pressure needed to produce an aqueous solution is $2.64$ atm.

Explanation of Solution

Calculate the pressure produced by Henry's law. The equation given by Henry's law to determine pressure is as follows:

  $\frac{S\text{1}}{P\text{1}}=\frac{S\text{2}}{P\text{2}}$

Where:

• S₁ is the solubility of gas at pressure P₁ .
• S₂ is the solubility of gas at pressure P₂ .
• P₁ is the initial pressure.
• P₂ is the final pressure.

The data given in the question is as follows:

• Solubility of gas in water ( S₁ ) is $3.6\frac{g}{L}$ .
• Initial Pressure( P₁ ) is $1$ atm.
• New solubility of the gas in water( S₂ ) is $9.5\frac{g}{L}$ .

Substitute all the values in the above formula to get the value of pressure( P₂ ).

  $\frac{3.6\frac{g}{L}}{1\text{ atm}}=\frac{9.5\frac{g}{L}}{P\text{2}}$

  $P\text{2}=\frac{9.5\frac{g}{L}}{3.6\frac{g}{L}}\times 1\text{ atm}$

  $P\text{2}=2.64\text{ atm}$

Therefore, the pressure is found to be $2.64\text{ atm}$ .

Conclusion

The pressure needed to produce an aqueous solution is $2.64\text{ atm}$ .