Chapter 13, Problem 22A

Interpretation Introduction

Interpretation:

The fact that Boyle’s law can be derived from the ideal gas law have to be shown.

Concept Introduction:

Boyle’s law: The pressure of a gas is inversely proportional to the volume of the gas at constant temperature.

The relationship between pressure and volume of a gas is expressed as-

  $\begin{array}{l}\mathrm{P}\propto \frac{1}{V}\\ \mathrm{or},PV=Constant\end{array}$ When T is constant.

The ideal gas law can be expressed as-

  $\mathrm{PV}=nRT$ Where, R is universal gas constant.

The ideal gas law consists of all the variables of a gas such as pressure (P), volume (V), number of moles (n) and temperature (T).

Answer to Problem 22A

Boyle’s law can be derived from the ideal gas law by keeping number of moles and temperature constant.

Explanation of Solution

The ideal gas law consists of all the variables of a gas such as pressure (P), volume (V), number of moles (n) and temperature (T).

  $\mathrm{PV}=nRT$

Keeping both n and T constant, the ideal gas equation can be written as-

  $\mathrm{PV}=nRT$ Where ‘nRT’ is constant while P and V are changing.

Or, $\mathrm{PV}=Constant$

  $\begin{array}{l}\mathrm{P}=\frac{Constant}{V}\\ \mathrm{or},\mathrm{P}\propto \frac{1}{V}\end{array}$

This is an expression of Boyle’s law.

So, the pressure of a gas is inversely proportional to the volume of the gas at constant temperature and fixed number of moles.

So by keeping n and T constant, the Boyle’s law equation is obtained from the ideal gas equation.