Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant pressure. In this question, we are given a mixture of 2 moles of He and 2 grams of H2 gas. We need to calculate the molar heat capacity of this mixture at constant pressure.

To solve this problem, we can follow these steps:

1. Calculate the number of moles of H2:
- The molar mass of H2 is 2 grams/mol.
- We are given 2 grams of H2, so the number of moles of H2 can be calculated as:
moles of H2 = mass of H2 / molar mass of H2
= 2 g / 2 g/mol
= 1 mol

2. Calculate the molar heat capacity of He:
- The molar heat capacity of He at constant pressure is given as 5R/2, where R is the gas constant.
- Therefore, the molar heat capacity of 2 moles of He can be calculated as:
molar heat capacity of He = (5R/2) * 2
= 5R

3. Calculate the molar heat capacity of H2:
- The molar heat capacity of H2 at constant pressure is given as 7R/2.
- Therefore, the molar heat capacity of 1 mole of H2 can be calculated as:
molar heat capacity of H2 = (7R/2) * 1
= 7R/2

4. Calculate the molar heat capacity of the mixture:
- Since the molar heat capacities of He and H2 are additive, we can calculate the molar heat capacity of the mixture by summing the molar heat capacities of He and H2.
- molar heat capacity of mixture = molar heat capacity of He + molar heat capacity of H2
= 5R + 7R/2
= 10R/2 + 7R/2
= 17R/2

5. Convert the molar heat capacity to a multiple of R:
- The molar heat capacity is given in terms of R, so we need to express the result as a multiple of R.
- Dividing the molar heat capacity by R gives:
molar heat capacity of mixture in terms of R = (17R/2) / R
= 17/2
= 8.5

Since the question asks for the molar heat capacity rounded up to two decimal places, the answer is 2.85, which falls within the range of 2.80 to 2.85.