5.6 Ideal Gas Equation

The three laws which we have learnt till now can be combined together in a single equation which is known as ideal gas equation.

R is called gas constant. It is same for all gases. Therefore it is also called Universal Gas Constant. Equation (5.17) is called ideal gas equation.

Equation (5.18) shows that the value of R depends upon units in which p, V and T are measured.

If three variables in this equation are known, fourth can be calculated. From this equation we can see that at constant temperature and pressure n moles of any gas will have the same volume because

V = nRT/p and  n,R,T  and  p  are constant. This equation will be applicable to any gas, under those conditions when behaviour of the gas approaches ideal behaviour.

Volume of one mole of an ideal gas under STP conditions (273.15 K and 1 bar pressure) is 22.710981 L mol–1.

Value of R for one mole of an ideal gas can be calculated under these conditions as follows :

At     STP     conditions         used      earlier (0 °C and 1 atm pressure), value of R is 8.20578 × 10–2 L atm K–1 mol–1.

Ideal gas equation is a relation between four variables and it describes the state of any gas, therefore, it is also called equation of state.

Let us now go back to the ideal gas equation. This is the relationship for the simultaneous variation of the variables. If temperature, volume and pressure of a fixed amount of gas vary from T1, V1 and p1 to T2, V2 and p2 then we can write

Equation (5.19) is a very useful equation. If out of six, values of five variables are known, the value of unknown variable can be calculated from the equation (5.19). This equation is also known as Combined gas law.

 

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