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Chapter 13: Problem 109

Using Henry's law and the ideal gas equation to prove the statement that the volume of a gas that dissolves in a given amount of solvent is independent of the pressure of the gas. (Hint: Henry's law can be modified as \(n=k P\), where \(n\) is the number of moles of the gas dissolved in the solvent.)

Short Answer

Expert verified
By substituting Henry's Law into Ideal Gas Law, we can prove that at a given temperature and solvent amount, the volume of the gas dissolved in the solvent is constant, thus demonstrating its independence from the gas's pressure.

Step by step solution

01

Understand Henry's Law

Henry's law states that the concentration of a gas in a liquid is proportional to the partial pressure of that gas over the liquid. This law can be written as \( n = kP \), where \( n \) is the number of moles of gas dissolved in the solvent, \( k \) is Henry's Law constant and \( P \) is the pressure of the gas.
02

Understand Ideal Gas Law

The Ideal Gas Law is given by \( PV = nRT \), where \( P \) is the pressure of the gas, \( V \) is the volume of the gas, \( n \) is the number of moles of the gas, \( R \) is the universal gas constant, and \( T \) is the temperature.
03

Substitute Henry's Law in Ideal Gas Law

Substitute \( n = kP \) from Henry's Law into the Ideal Gas Law. The resulting equation is \( PV = k PR T \). Simplifying this equation gives us \( V = kRT \).
04

Conclude

From \( V = kRT \), we can see that the volume of the gas that dissolves in a given amount of solvent is independent of the pressure of the gas. While volume does vary with \( T \), the question states the amount of solvent is fixed, meaning \( T \) is constant, hence the volume is constant.

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Most popular questions from this chapter

A 0.86 percent by mass solution of \(\mathrm{NaCl}\) is called "physiological saline" because its osmotic pressure is equal to that of the solution in blood cells. Calculate the osmotic pressure of this solution at normal body temperature \(\left(37^{\circ} \mathrm{C}\right)\). Note that the density of the saline solution is \(1.005 \mathrm{~g} / \mathrm{mL}\).

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