Question

The compressibility factor of an ideal gas is _______

Answer 1

Hint: We must need to know that the ideal gas is the theoretical concept in gases state of matter. No gas behaves ideal in all conditions. In nature gas molecules are classified as two types. There are real gases and ideal gases.

Complete step by step answer:
We must have to know that the ideal gas means one gas behaves in an ideal character in certain conditions. In that condition of parameter, that real gas is called ideal gas.
We need to know that the temperature of the gas, pressure of the gas molecule, molar volume of the gases, the number of moles in gas molecules are the parameters to determine if one gas acts as ideal or not in that condition.
Ideal gas equation is combined with Boyle's law, Charles law and Avogadro’s hypothesis.
Here, V is the volume or molar volume of the gases
P is the pressure of the gases molecules
T is the temperature of the gas
n is the number of moles of the gas.
Boyle’s law means molar volume of the gas is inversely proportional to the pressure of the gas at constant temperature. If pressure increases, volume decreases and pressure decreases, volume increases.
$V \propto \dfrac{1}{P}$
We need to know that the Charles law means molar volume of the gas is directly proportional to the temperature of the gas at constant pressure. If temperature increases volume of the gas also increases and temperature decreases volume of the gas also decreases.
$V \propto T$
Avogadro’s hypothesis means molar volume of the gas is directly proportional to the number of moles of the gas molecules at constant temperature and pressure. If the number of moles increases, volume also increases and the number of moles decreases, volume of the gas decreases.
$V \propto {\text{n}}$
These three equation are combined to form ideal gas equation,
$V \propto \dfrac{{Tn}}{P}$
$PV \propto {\text{nT}}$
$PV = R{\text{nT}}$
$R$ is the gases constant, the value of $R$ is $8.314J{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$.
The compressibility factor of an ideal gas means the product of pressure and volume is divided by temperature, number of moles and gas constant of the gas is equal always to one. $Z$ is represented as the symbol of compressibility factor.
$Z = \dfrac{{PV}}{{nRT}}{\text{ = 1}}$
The compressibility factor of an ideal equation is $1$

Note: We need to know that the compressibility factor of any gas calculated by using its molar volume. The compressibility factor is the ratio of the molar volume of that gases molecule to the molar volume of an ideal gas. $Z$ value of ideal gas is always unity. In real gases, pressure increases, $Z < {\text{1}}$ . In real gases, pressure decreases, $Z > {\text{1}}$ .