# What is the difference between ideal gas equation and combined gas equation? Thank you

Jun 4, 2017

The ideal gas law is:

$\frac{P V}{T} = n R$

The combined gas law is:

$\frac{P V}{T} = \text{const}$

where the pressure, temperature, volume, mols, and universal gas constant are given by $P$, $T$, $V$, $n$, and $R$, respectively.

The only difference is that the mols of gas are constant (this tends to be the case in a closed nonrigid container, where $\Delta n = 0$ but $\Delta V \ne 0$), or the initial and final states of $n$ are identical (even if the mols of gas change in between). Of course, this assumes ${P}_{i} \ne {P}_{f}$, ${V}_{i} \ne {V}_{f}$, and ${T}_{i} \ne {T}_{f}$.

In a more general scenario where $\Delta n \ne 0$, i.e. the mols of gas do change, the ideal gas law is more applicable.

In fact, in most cases, the ideal gas law is more appropriate BECAUSE it is more general, and relevant conditions with constant variables can be derived.

Jun 4, 2017

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$ versus $P V = n R T$?
Clearly, the Ideal Gas Law includes the amount of gaseous particles, represented by the molar quantity, whereas the combined gas equation requires a constant molar quantity. And thus the Ideal Gas Law includes Avogadro's experimental gas law, $V \propto n$.