The total internal energy ($U$) of a mixture of ideal gases is the sum of the internal energies of individual gases. The internal energy for $n$ moles of an ideal gas is given by $U = \frac{f}{2}nRT$, where $f$ is the number of degrees of freedom.

1. For Argon (Ar): It is a monatomic gas, so it has 3 degrees of freedom ($f=3$) associated with translational motion . $n_{Ar} = 4$ $U_{Ar} = \frac{3}{2} (4) RT = 6RT$

2. For Oxygen ($O_2$): It is a diatomic gas. Neglecting vibrational modes, it has 5 degrees of freedom ($f=5$; 3 translational + 2 rotational). $n_{O_2} = 2$ $U_{O_2} = \frac{5}{2} (2) RT = 5RT$

Total Internal Energy: $U_{total} = U_{Ar} + U_{O_2} = 6RT + 5RT = 11RT$.