Molar heat capacity is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant pressure. In order to determine the molar heat capacity of the mixture, we need to consider the individual molar heat capacities of the components and their respective amounts.

Given:
- 2 moles of He
- 2 grams of H2

To find the molar heat capacity of the mixture, we can use the following formula:

Cp,mix = (n1Cp1 + n2Cp2) / (n1 + n2)

Where:
Cp,mix is the molar heat capacity of the mixture
n1 and n2 are the number of moles of the components
Cp1 and Cp2 are the molar heat capacities of the components

Step 1: Determine the molar heat capacities of He and H2
The molar heat capacity of an ideal gas at constant pressure is given by the equipartition theorem, which states that each degree of freedom contributes (1/2)R to the molar heat capacity. For monoatomic gases like He, there are 3 degrees of freedom (translational motion in three dimensions), so Cp1 = (3/2)R. For diatomic gases like H2, there are 5 degrees of freedom (3 translational + 2 rotational), so Cp2 = (5/2)R.

Step 2: Calculate the molar heat capacity of the mixture
Plugging in the values into the formula, we get:

Cp,mix = (2 * (3/2)R + 2 * (5/2)R) / (2 + 2)
= (3R + 5R) / 4
= 8R / 4
= 2R

Therefore, the molar heat capacity at constant pressure for the mixture is 2R, which corresponds to option (c).