5.1 Ideal gas law and general gas equation

The general gas equation

1. A closed gas system initially has a volume of 8 L and a temperature of 100 ${}^{\circ }$ C. The pressure of the gas is unknown. If the temperature of the gas decreases to 50 ${}^{\circ }$ C, the gas occupies a volume of 5 L. If the pressure of the gas under these conditions is 1.2 atm, what was the initial pressure of the gas?
2. A balloon is filled with helium gas at 27 ${}^{\circ }$ C and a pressure of 1.0 atm. As the balloon rises, the volume of the balloon increases by a factor of 1.6 and the temperature decreases to 15 ${}^{\circ }$ C. What is the final pressure of the gas (assuming none has escaped)?
3. 25 cm ${}^3$ of gas at 1 atm has a temperature of 20 ${}^{\circ }$ C. When the gas is compressed to 20 cm ${}^3$ , the temperature of the gas increases to 28 ${}^{\circ }$ C. Calculate the final pressure of the gas.

The ideal gas equation

In the early 1800's, Amedeo Avogadro hypothesised that if you have samples of different gases, of the same volume, at a fixed temperature and pressure, then the samples must contain the same number of freely moving particles (i.e. atoms or molecules).

Avogadro's Law

Equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.

You will remember from an earlier section, that we combined different gas law equations to get one that included temperature, volume and pressure. In this equation, pV = kT, the value of k is different for different masses of gas. If we were to measure the amount of gas in moles, then k = nR, where n is the number of moles of gas and R is the universal gas constant. The value of R is 8.3143 J.K ${}^{-1}$ .mol ${}^{-1}$ , or for most calculations, 8.3 J.K ${}^{-1}$ .mol ${}^{-1}$ . So, if we replace k in the general gas equation, we get the following ideal gas equation .

The following table may help you when you convert to SI units.