Chapter 14, Problem 97A

(a)

Interpretation Introduction

Interpretation-To identify the gas which behaves as ideal gas.

Introduction-

Ideal Gas:

An ideal gas is a hypothetical gas that has randomly moving particles that collides elastically. These particles do not interact with each other and have negligible volume.

Real gases can behave as ideal in specific situations.

Mathematically, ideal gas equation can be represented as:

  $PV=nRT$

Where, p = pressure, v = volume, n = mole, T = temperature and R = universal gas constant

For any gas, if the ratio of $\frac{PV}{nRT}=1$ , they can behave as ideal gases.

Explanation of Solution

As can be seen from the graph methane, $C{H}_4\text{at}{200}^{\circ }C$ lies near to ideal gas line and the ratio of $\frac{PV}{nRT}\simeq 1$ . Hence, it can behave more like ideal gas than methane, $0^{\circ }C$

(b)

Interpretation Introduction

Interpretation- To explain the characteristics of real gases at low and high pressure.

Introduction-

Ideal Gas:

Ideal gas is hypothetical gas that has randomly moving particles that collides elastically. These particles do not interact with each other and have negligible volume as compared to the container.

Real gases can behave as ideal in specific situations.

Explanation of Solution

At low pressure, the intermolecular distance between particles is large, hence they have negligible volume. If the volume is less, then the ratio of $\frac{PV}{nRT}<1$

At high pressure, the intermolecular distance between particles decreases; hence, they have a comparable volume to the volume of the container. If the volume is more, then the ratio of $\frac{PV}{nRT}>1$