# The Ideal Gas Law

The ideal gas law predicts the state of a gas at a given pressure and temperature. It is expressed mathematically as PV = nRT, where P represents pressure, V represents volume, T represents the absolute temperature in Kelvin degrees, n is the amount of gas expressed in moles, and R is the gas constant, whose value is 0.0821 when standard units of measurement are used. (Kelvin degrees are identical to Celsius degrees, but the count is started from absolute zero.) Since the purpose of n is to represent the actual amount of gas (ie. number of molecules), some variants of the ideal gas law replace molar count with mass (m).

This law actually combines several other gas laws: Boyle’s law, Lussac’s law, and Avogadro’s principle. Boyle’s law states that at a fixed temperature and within a closed system, the volume of a fixed quantity of a gas is inversely proportional to the pressure it exerts: P = kV, where k is a constant. Lussac’s law states that at a fixed pressure, increasing the temperature of a fixed quantity of gas also linearly increases its volume. Avogadro’s principle states that at equal pressure and temperature, equal volumes always contain the same number of molecules, regardless of the type of gas or even whether it is a monoatomic gas, containing only one element (eg. hydrogen gas, H2), or polyatomic gas, whose molecules contain more than one element (eg. carbon dioxide, CO2).

The ideal gas law predicts that as the temperature approaches absolute zero (0 degrees K, -273.2 degrees C, -459.67 degrees F), the volume will decrease but it is important to note that here volume is actually a function of molecular motion, and that it is this molecular motion which approaches zero, not strictly volume in itself. Since in this context there can be no such thing as negative molecular motion motion either exists or it does not exist it is impossible for any system to go below absolute zero, or indeed even to reach it.

The ideal gas law suffers from several of the same limitations as its predecessor laws and principles, in that it takes no account of molecular size, intermolecular chemical interactions, or the effects of extremes upon subatomic structure. Consequently it can also take no account of the tendency of gases to shift into liquid and even solid states at high pressures or low temperatures. Thus the ideal gas law serves best as a real-world approximation for monoatomic gases under relatively low pressures and high temperatures.