Ideal gas equation

Ideal gas equation

The gaseous state is described completely using the following four variables T, P, V and n and their relationships were governed by the gas laws studied so far.

Charles law V  Î±  T

Avogadro’s law V  Î±  n

We can combine these equations into the following general equation that describes the physical behaviour of all gases.

where,  R  is  the  proportionality

constant called universal gas constant.

The above equation can be rearranged to give the ideal gas equation

PV = nRT. ------ (6.11)

We already know that pressure is expressed in many different units (Table 6.1) hence it is important to know the values of gas constant R in different units as well.

We can calculate R using the equation,

For Conditions in which P is 1 atm., volume 22.414 dm³. for 1 mole at 273.15 K.

= 0.0821 dm³ atm. mol^–1 K^–1

Under standard conditions (STP) Where P = 1 bar (10⁵ pascal), V= 22.71 × 10^-3 m³ for 1 mole of a gas at 273.15 K

= 8.314 Pa m³ K^–1 mol^–1

= 8.314 × 10^–5  bar m³ K^–1 mol^–1

= 8.314 × 10^–2 bar dm³ K^–1 mol^–1

= 8.314 × 10^–2 bar L K^–1 mol^–1

= 8.314 J K^–1 mol^–1

The ideal gas equation is a relationship between four variables (P, V, T, n). Since it describes the state of any gas, it is referred to as the equation of state of gases.

Let us calculate the pressure exerted by 2 moles of sulphur hexafluoride in a steel vessel of volume 6 dm³ at 70 °C assuming it is an ideal gas.

We will use the ideal gas equation for this calculation as below:

= 9.39 atm.