A

Step 1: Identify the molar specific heat capacities of the gases involved. For a monoatomic ideal gas, the molar specific heat at constant volume is given by:
C_v (monoatomic) = \frac{3}{2} R
For a diatomic ideal gas, the molar specific heat at constant volume is:
C_v (diatomic) = \frac{5}{2} R

Step 2: Calculate the specific heat capacity of the mixture.
When two moles of gases are mixed, the total molar specific heat at constant volume can be calculated as a weighted average:
C_v (mixture) = \frac{C_v (monoatomic) + C_v (diatomic)}{2}
= \frac{\frac{3}{2} R + \frac{5}{2} R}{2}
= \frac{8R}{4} = 2R

Therefore, the molar specific heat of the mixture at constant volume is: 2R.