Question

How can I calculate the gas law equations?

Answer 1

An ideal gas has the following properties:-
1. The gas is composed of small indivisible particles called molecules. The individual properties of each molecule are the same as that of the gas as a whole.
2. The distance between the molecules is large compared to that of solid or liquid and hence the forces of intermolecular attraction are negligible.
3. The size of the molecules is infinitesimally small as compared to the average distance traversed by the molecule.
4. The molecules are perfectly hard elastic spheres and collisions between ideal gases are “elastic”. This means that the attractive or repulsive forces are involved during collisions is negligible. Also, the kinetic energy of the gas molecules will remain constant as the intermolecular forces are lacking.

Complete step by step answer:
Boyle’s Law
According to this law, for a given mass of a gas, the volume of a gas at constant temperature (called isothermal process) is inversely proportional to its pressure, i.e.
$V \propto \dfrac{1}{P}$ (T = Constant )
or $PV = {\text{Constant}}$…………………………. (i)
or ${P_i}{V_i} = {P_f}{V_f}$
Thus, the p-V graph in an isothermal process is a rectangular hyperbola. Or the p or V graph is a straight line parallel to the p or V axis.
Charles’ Law
According to this law, for a given mass of a gas volume at constant pressure (called isobar process) is directly proportional to its absolute temperature.
i.e. $V \propto T$ (P = constant)
or $\dfrac{V}{T} = {\text{constant}}$…………………………….(ii)
$\dfrac{{{V_i}}}{{{T_i}}} = \dfrac{{{V_f}}}{{{T_f}}}$
Thus, a V-T graph in an isobaric process is a straight line passing through origin.
Gay Lussa’s Law or Pressure law
According to this law, a given mass of a gas pressure at constant volume (called isochoric process) is directly proportional to its absolute temperature. i.e.
i.e. $P \propto T$ (V = constant)
or $\dfrac{P}{T} = {\text{constant}}$…………………………….(iii)
$\dfrac{{{P_i}}}{{{T_i}}} = \dfrac{{{P_f}}}{{{T_f}}}$
Thus, P-T graph in an isochoric process is a straight line passing through origin.

Ideal Gas equation
All the above four laws can be written in one single equation known as the ideal gas equation. According to this equation.
$PV = {\text{Constant}}$
$\dfrac{V}{T} = {\text{constant}}$
$\dfrac{P}{T} = {\text{constant}}$
Combining all these equations, we get
$PV = nRT$
Where n is the number of moles of the gas
M = molecular mass of the gas
R = Universal gas constant

Note:
Gases, unlike solids and liquids having indefinite volume. As a result, they are subjected to pressure changes, volume changes and temperature changes. The behavior of real gases is simple and it can behave like ideal gas at low pressure and high temperature conditions.