Ideal Gas Equation

Combining the three laws

Boyle's, Charles' and Avogadro's laws each hold one pair of variables fixed while relating the other two:

• at constant $T$ and $n$: $V \propto \dfrac{1}{p}$ — Boyle's Law
• at constant $p$ and $n$: $V \propto T$ — Charles' Law
• at constant $p$ and $T$: $V \propto n$ — Avogadro's Law

Putting all three together:

where $R$ is a proportionality constant common to all gases, called the gas constant — or, since it applies universally, the Universal Gas Constant. Equation $pV=nRT$ is the ideal gas equation; rearranged, $R = \dfrac{pV}{nT}$.

The value of R

Because $R = pV/(nT)$, its numeric value depends on the units chosen for $p$, $V$ and $T$. Using the modern STP values ($273.15\,\text{K}$, $1\,\text{bar}$, molar volume $22.710981\,\text{L}\,\text{mol}^{-1}$):

Under the older STP convention ($0\,^{\circ}\text{C}$, $1\,\text{atm}$), $R = 8.20578\times10^{-2}\ \text{L atm K}^{-1}\text{mol}^{-1}$.

Because the ideal gas equation relates all four state variables ($p$, $V$, $n$, $T$), it is also called the equation of state — knowing any three lets you calculate the fourth, and at fixed $T$ and $p$, $n$ moles of any gas occupy the same volume ($V = nRT/p$).

The combined gas law …