What is the relationship between the combined gas law and the ideal gas law?

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Answer 1 · 2014-05-18T14:54:09

The Combined Gas Law and the Ideal Gas Law are the same relationships written in different ways.

The Combined Gas Law is a combination of Boyle's, Charles' and Gay-Lussac's laws.

$P V$ $PV$ = constant

$\frac{V}{T}$ $V/T$ = constant

$\frac{P}{T}$ $P/T$ = constant

The Combined Gas Law joins these to make

$\frac{P V}{T}$ $(PV)/T$ = constant or $\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1 = (P_2V_2)/T_2$

The Combined Gas Law should also include Avogadro's Law: "The volume of a gas is directly proportional its number of moles".

$\frac{V}{n}$ $V/n$ = constant

Then the Combined Gas Law becomes

$\frac{P V}{n T}$ $(PV)/(nT)$ = constant

If we call the constant $R$ $R$ , the Combined Gas Law becomes

$\frac{P V}{n T} = R$ $(PV)/(nT) = R$

When we rearrange this equation, it becomes

$P V = n R T$ $PV = nRT$

We call this equation the Ideal Gas Law.