The empirical gas laws can be combined into one relation connecting the pressure, volume, amount and absolute temperature of a gas:

$$\boxed{pV=nR_uT},$$

where

• $p$ is absolute pressure,
• $V$ is volume,
• $n$ is amount of gas in moles,
• $T$ is absolute temperature in kelvins,
• $R_u$ is the universal gas constant.

For example, when pressure is measured in kilopascals and volume in liters,

$$R_u\approx8.314,\mathrm{kPa,L,mol^{-1},K^{-1}}.$$

Because $1,\mathrm{kPa,L}=1,\mathrm J$, the SI form is also

$$R_u\approx8.314,\mathrm{J,mol^{-1},K^{-1}}.$$

Example

What volume is occupied by $0.500,\mathrm{mol}$ of an ideal gas at $300,\mathrm K$ and $100,\mathrm{kPa}$?

$$V=\frac{nR_uT}{p} =\frac{(0.500)(8.314)(300)}{100} \approx12.5,\mathrm L.$$

The familiar individual gas laws follow by holding variables fixed:

• fixed $n,T$: $pV=\text{constant}$;
• fixed $n,p$: $V/T=\text{constant}$;
• fixed $n,V$: $p/T=\text{constant}$;
• fixed $p,T$: $V/n=\text{constant}$.

For a fixed amount of gas, two equilibrium states therefore satisfy

$$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}.$$

Mass-based form

If $m$ is the gas mass and $M$ its molar mass, then $n=m/M$. Defining the specific gas constant

$$R_s=\frac{R_u}{M}$$

gives the engineering form

$$pV=mR_sT,$$

or, using specific volume $v=V/m$,

$$pv=R_sT.$$

An ideal gas is a model whose state obeys this relation. Real gases approach ideal behavior most closely at low density, commonly at relatively low pressure and temperatures well above condensation. The equation relates equilibrium state variables; it does not by itself determine reaction rate, heat transfer or work.