Chapter U3.65, Problem 2E

Interpretation Introduction

Interpretation: The use of ideal gas law needs to be explained.

Concept Introduction: An ideal gas law can be explained using a general gas equation known as ideal gas equation. In this equation P, V, n, R and T are related to each other. Here, R is Universal gas constant which is same for all type of ideal gases. The value of R is $0.082\text{ L atm/K mol}$ .

Explanation of Solution

The ideal gas equation is represented as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature.

In the above equation, there are 4 variables and 1 constant. If values of 3 variables are known, the value of unknown variable can be calculated.

For example, if P, V and T is given for a gas, the number of moles of gas can be calculated by rearranging the above equation as follows:

  $n=\frac{PV}{RT}$

Here, R is Universal gas constant with value $0.082\text{ L atm/K mol}$ .

Also, the relation between two variables can be explained by keeping other two variables constant.

For example, the ideal gas law can be used to show the relation between P and T when number of moles and Volume of the gas are kept constant.

  $\frac{P}{T}=\frac{nR}{V}$

Or,

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Here, 1 and 2 represents initial and final values.