Question

How do you find the ideal gas law formula?

Answer 1

Hint: Ideal gas law formula is the relation between the pressure, volume, temperature, number of moles of the gas, and gas constant. For finding the ideal gas law, we use Boyle’s law, Charles law, Gay-Lussac’s law, and Avogadro’s law.

Complete step-by-step answer:The ideal gas law formula is the relation between the pressure, volume, temperature, number of moles of the gas, and gas constant. For finding the ideal gas law, we use Boyle's law, Charles law, Gay-Lussac’s law, and Avogadro’s law.
Let us discuss Boyle's law first, it is the relation between the pressure and volume of the gas at a constant temperature. The formula given by him was:
$P\propto \dfrac{1}{V}$
PV = constant.
Now, we will discuss the Charles law, which is the relation between the volume of the gas and the temperature of the gas at constant pressure. The formula is:
$V\propto T$
$\dfrac{V}{T}=\text{constant}$
Now, we will discuss Gay-Lussac's law, which is the relation between the pressure of the gas and the temperature of the gas at constant volume. The formula is:
$P\propto T$
$\dfrac{P}{T}=\text{constant}$
Now, we will discuss Avogadro's law, which is the relation between the volume of the gas and the number of moles of the gas. The formula is:
$V\propto n$
$\dfrac{V}{n}=\text{constant}$
When we combine all the law’s mentioned above, then we can write:
$PV\propto nT$
Removing the proportionality constant we introduce a constant called gas constant (R).
PV = nRT
This is the ideal gas law formula.

Note: The formula is only applicable if the gas mentioned in the question is ideal but for the real gas, this equation will change to:
$\left( P+\dfrac{a}{{{V}^{2}}} \right)\left( V-b \right)=nRT$
In which a and b are constants.