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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)

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