Final answer:
To find the average molar mass of the atmospheric gas mixture of hydrogen and helium, the ideal gas law is used with given conditions of temperature and density. The molar mass aids in calculating the percentages of hydrogen and helium in the mixture by establishing their ratios and matching to the molar mass found.
Step-by-step explanation:
To calculate the average molar mass of the atmospheric gas mixture, we'll use the ideal gas law in the form of the equation PV = mRT/M. Since the composition of the atmosphere in question consists of hydrogen and helium, and given the conditions of 1 bar pressure and -108°C, we first need to convert the temperature to Kelvin by adding 273.15, resulting in 165.15 K. The ideal gas constant (R) is 8.314 J/(mol·K), and we rearrange the equation to solve for the molar mass
Given the density (ρ = 0.16 kg/m³) and that 1 bar is equal to 100 kPa, we can substitute ρ for m/V, giving us M = ρRT/P. Plugging in the numbers, we get M = (0.16 kg/m³)(8.314 J/(mol·K))(165.15 K) / (100,000 N/m²) which results in the average molar mass of the mixture.
Once the molar mass is found, we can then proceed to calculate the percentage of hydrogen and helium by assuming a variety of ratios until the calculated molar mass matches the one that was found from above calculations. Because hydrogen has a molar mass of approximately 2 g/mol and helium has a molar mass of approximately 4 g/mol, we will use these figures to establish the proportions of each gas in the mixture to match the average molar mass that we calculated.