Lesson 2 - Gas Laws

If we take the three previously discussed gas laws of Boyle, Charles, and Gay-Lussac, we can combine them as follows:

In this combined form, if we eliminate a constant temperature, pressure, or volume, we get the laws of Boyle, Charles, and Gay-Lussac. As in the expression of the three original laws, the combined gas law assumes a constant mass of gas.

If we consider the combined gas law more closely, it suggests that for any gas, the combination of pressure, volume, and temperature is a constant for whatever gas and values of P, V and T, thus:

So, if we think about any value of P, V and T, rather than an initial 1 or final 2 value, we can express the combined gas law equation as a universally applicable (irrespective of which gas we are using) gas law:

We normally express the constant in the above equation by taking account of the quantity of gas. We then separately introduce another constant which, as this is a universally applicable gas law, we term ‘the universal gas constant’ R, and it has units of J/g mol or J/kg kmol.

The origin of the abbreviation R for the universal gas constant is slightly mysterious. There is some suggestion that it was named after Henri Regnault (1810-1878), a French chemist and physicist who did some of the early work on such a gas constant, but it seems there is no agreed view of this.

The value of R, the universal gas constant is 8,314.5 J/kmol K (or 8.3145 kJ/kmol K).

The unit of the quantity of gas would be the kmol. We use the letter n, for the number of kmols. Hence the universal gas law reduces to:

• P is the absolute pressure of the gas

• V is the gas volume in m³

• n is the number of kmols

• R is the universal gas constant

• T is the absolute temperature in Kelvin

Below is a worked example of the universal gas law in action.

Example:

In the previous worked example, we determined the number of kmols equivalent to 4 kg of CO₂ produced from a fermentation.

If this gas was trapped in a balloon with a pressure of 1 bar g and a temperature of 15 °C, what would the balloon volume be? What would the density of the gas be? Assume atmospheric pressure is 101.325 kPa.

From the previous example, we know that the number of kmol equivalent to 4 kg is given by the following:

The universal gas law is:

And rearranging for the required parameter volume gives us:

We must remember to use the correct units for pressure and temperature: absolute pressure (Pa) and absolute temperature (K):

We know that the density ρ of a substance is the mass of the substance divided by its volume:

If we were to do any further reading on the universal gas law and the universal gas constant R, we might come across a different symbol and value of R. This might confuse us, but all will be explained in the next section.