## 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.

At constant T and n;          V ∝ 1/p          Boyle’s Law
At constant p and n;          V ∝ T             Charles’ Law
At constant p and T;          V ∝ n             Avogadro Law

Thus,
Where R is proportionality constant. On rearranging the equation we obtained
R is called gas constant. It is same for all gases. Therefore it is also called Universal Gas Constant. Equation is called ideal gas equation.

Above Equation 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

and n, R, T and p are constant. This equation will be applicable to any gas, under those conditions when behavior of the gas approaches ideal behavior. Volume of one mole of an ideal gas under STP conditions (273.15 K and 1 bar pressure) is 22.710981 L mol-1.

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
The above said equation 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 above equation. This equation is also known as Combined gas law.