Question

Pressure is dependent on volume, temperature, amount of substance and ideal gas constant of R. Use dimensional analysis to derive the formula of the ideal gas law.

Answer 1

To derive the ideal gas law, we consider the relationship between it's volume, $V$ and pressure, $P$, temperature, $T$, and amount of substance, $n$.

From Boyle's law, $V$ $\propto \frac{1}{P}$ at constant $n$ and $T$

From Charle's law $V \propto T$ at constant $n$ and $P$

From Avogadro's law, $V \propto n$ at constant $T$ and $P$

The three expressions can be combined to give,

$V \propto \frac{nT}{P}$ which can also be written as,

$V = constant(\frac{nT}{P})$

The constant is called the ideal gas constant and, is represented by $R$.

Therefore, $V = \frac{RnT}{P} = \frac{nRT}{P}$

multiply both sides by $P$ to get,

$PV = nRT$ (the ideal gas law equation)