The Ideal Gas Law
To derive the ideal gas law, we can extend the argument we used to derive the combined gas law. According to Boyle's law V = k1/P and according to Charles's law V = k2T, while Avogadro's law leads to V = k3n, where n is the number of moles of gas. If we combine the three equations, we obtain the equation V = k'T/P. For one mole of gas the constant k' is called the molar gas constant and is given the symbol R.
According to Avogadro's law, the molar volume at a specific value of T and P is a constant, independent of the nature of the gas. For n moles of gas the ideal gas law is represented by the equation PV = nRT.
The value of the molar gas constant, R, depends on the units used for pressure and volume. In all cases T is kelvins. Values of R in various units are shown in the table below.
Value of R
0.082058 L · atm/(K · mol)
8.3145 J/(K · mol)
8.3145 kg · m2/(s2 · K · mol)
8.3145 kPa · dm3/(K · mol)
1.9872 cal/(K · mol)