Chapter 5, Problem 5.86P

Interpretation Introduction

Interpretation:

The ${\text{N}}_{\text{2}}$ gas behaves more ideally at $1\text{ atm}$ or at $500\text{atm}$ is to be explained.

Concept introduction:

Gases that obey the ideal gas equation at all temperature and pressure are known as ideal gas.

The ideal gas equation can be expressed as follows,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas and $R$ is the gas constant.

The expression of van der Waals equation is as follows:

$\left(P+\frac{n^{2}a}{V^2}\right)\left(V-nb\right)=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas, $R$ is the gas constant, $a$ and $b$ are van der Waals constants.

The van der waals constants are depends upon the nature of gas, The value of $a$ is greater than $b$.

At low pressure and high temperature, real gas will obey the gas laws.

The compressibility factor equation can be given as follows:

$Z=\frac{PV}{RT}$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $Z$ is the compressibility factor, $n$ is the mole of the gas and $R$ is the gas constant.

$Z=1$, that means gas shows ideal behaviour at all temperature and pressure.

At high pressure, $Z>1$, the gas has less compressibility and more replusive force between the gas molecule. It shows positive deviation from ideal behaviour.

At low pressure, $Z<1$, the gas has high compressibility and more attractive force between the gas molecules. It shows negative deviation from ideal behaviour.