5.6dm^(3) of an unknown gas at S.T.P. requires 52.25 J of heat to raise itstemperature by 10^(@)C at constant volume. Calculate volume. Calculate C_(v) , C_(p) and atomicity of the gas.

5.6dm^(3) of an unknown gas at S.T.P. requires 52.25 J of heat to rais

1.	5.6dm^(3) of an unknown gas at S.T.P. requires 52.25 J of heat to raise itstemperature by 10^(@)C at constant volume. Calculate volume. Calculate C_(v) , C_(p) and atomicity of the gas.
Answer» Solution :`22.4dm(3)` of a gas at S.T.P. `=1` mol `:. 5.6 dm^(3)`of the gas at S.T.P. `= (1)/(22.4) xx 5.6 =0.25 mol` Thus, for `10^(@)` rise , `0.25` mol of the gas at constant volume require heat `= 52.25 J` `:. `For `1^(@)` rise, 1 mol of the gas at constant volume will require heat `= (52.25)/(10 xx 0.25) J = 20.9 J` `:. C_(V) = 20.9 J K^(-1) mol^(-1)` Now, `C_(p) = C_(v) + R= 20. 9 J K^(-1) mol^(-1) + 8. 314 J K^(1) mol^(-1)= 29.214 J K^(-1) mol^(-1)` `:. gamma = (C_(p))/( C_(v))= (29.214)/(20.9) = 1.4`. Hence, the gas is diatomic