A gas mixture in a container at temperature T consists of 3 moles of oxygen gas and an unknown mass m of helium gas. If the total internal energy of the mixture is 15RT (where R is the universal gas constant) and all vibrational modes are neglected, the value of m is: (Take the molar mass of helium as 4 g/mol)

Step-by-step solution

The internal energy of an ideal gas is given by U = f 2 nRT , where f is the number of degrees of freedom. For oxygen (a diatomic gas), f = 5 . The internal energy of 3 moles of oxygen is: U_ O₂ = 5 2 3 RT = 7.5RT The total internal energy of the mixture is given as 15RT . Let the internal energy of helium be U_ He . U_ total = U_ O₂ + U_ He 15RT = 7.5RT + U_ He U_ He = 7.5RT Helium is a monoatomic gas, so its degrees of freedom f = 3 . If there are n moles of helium, its internal energy is: 3 2 nRT = 7.5RT 1.5n =