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The gas constant (R) relates pressure, volume, temperature, and moles of gas in the ideal gas law (PV = nRT). Ideal gases obey simple gas laws and have a molar volume of 22.4141 L at STP. Real gases deviate from ideal behavior due to intermolecular forces, so the van der Waals equation is used to compensate. The van der Waals equation is only needed at high temperature or low pressure.
The gas constant (represented by the letter R), also known as the ideal gas constant, is a function of pressure (P), volume (V), temperature (T), and moles of a gas (n) in a stoichiometric equation. The equation PV = nRT is known as the ideal gas law. The value of R can be found by rearranging the equation to read R = (PV) / (nT). In other words, the gas constant is the pressure of the gas times its volume, divided by the number of moles of the gas times its temperature in Kelvin.
Ideal gases are hypothetical: they strictly obey all the simple gas laws and have a molar volume of 22.4141 liters at standard temperature and pressure (STP), which is 273 Kelvin, 1 atmosphere. At STP, however, most gases behave like ideal gases, so the value of R is usually 0.0821 L atm/mol K or 8.3145 J/mol K. For example, the ideal gas law and gas constant can be used to find the pressure of 0.508 moles of oxygen in a 15 liter container at 303 Kelvin. The volume, temperature and number of moles are known.
P = (nRT) / V = (0.508 mol x 0.0821 L atm x 303 K) / 15.0 L mol K = 0.842 atm
Things change when a gas is at low temperature or at high pressure. Under these conditions, the gas molecules move closer together and more slowly, so intermolecular forces, called van der Waals forces, cause the measured pressure to be lower than expected. As the molecules are closer together, the volume of the real molecules also becomes a larger fraction of the total volume of the gas.
To compensate for the behavior of real gases, the van der Waals equation comes into play. The (n2a)/V2 expression compensates for intermolecular attractive forces and the nb expression compensates for the volume of gas molecules. Together, these terms make up the van der Waals equation:
(P + (n2a) / V2) x (V-nb) = nRT
The expressions n2a and nb are called van der Waals constants and must be determined experimentally. The van der Waals equation is only needed when the gas is at high temperature or low pressure. If the gas is at or above room temperature and at a pressure of less than a few atmospheres, the ideal gas law applies.
