To determine the total internal energy of the gas mixture using the grand canonical ensemble model, we need to consider the following:1. The number of particles N in the system.2. The volume V of the container.3. The temperature T of the system, which is given as 300 K.Since we have a mixture of hydrogen and helium gases, we need to consider the degrees of freedom for each gas. Hydrogen and helium are both diatomic gases, so they have 5 degrees of freedom each 3 translational and 2 rotational .Now, we can use the equipartition theorem to determine the internal energy of each gas. The equipartition theorem states that the average energy per degree of freedom is 1/2 kT, where k is the Boltzmann constant 1.38 10^-23 J/K .For hydrogen gas, with 5 degrees of freedom, the average energy per molecule is:E_H2 = 5/2 kTFor helium gas, with 5 degrees of freedom, the average energy per molecule is:E_He = 5/2 kTSince the gas mixture contains equal parts of hydrogen and helium, the total internal energy U of the gas mixture can be calculated as:U = N_H2 * E_H2 + N_He * E_HeSince N_H2 = N_He, we can simplify the equation as:U = N_H2 * E_H2 + E_He Now, we can substitute the expressions for E_H2 and E_He:U = N_H2 * 5/2 kT + 5/2 kT U = N_H2 * 5kT Now, we need the number of particles N_H2 in the system to calculate the total internal energy. However, this information is not provided in the problem. If you can provide the number of particles or the moles of the gases, we can proceed with the calculation.