Answer
$ C_V = 65.5J/mol.K $
$ C_p = 73.8 J /mol.K $
Work Step by Step
We know that $\frac{C_p}{C_V} = \gamma = 1.127$ and $R = 8.314 J/mol.K$
The molar heat capacity at constant volume
$C_V = C_p - R$
$C_V = \gamma C_V - R$
$C_V - \gamma C_V = - R$
$C_V - 1.127 C_V = - 8.314 J/mol.K$
Now we solve for $C_V$
$-0.127 C_V = - 8.314 J/mol.K$
$C_V = \frac{- 8.314 J/mol.K}{-0.127 } $
$ C_V = 65.5J/mol.K $
The molar heat capacity at constant pressure is $C_p$
$ C_p = C_V + R$
$ C_p = 65.5J/mol.K + 8.314 J/mol.K $
$ C_p = 73.8 J /mol.K $
