In the absence of turbulent mixing, the partial pressure of each constituent of air would fall off with height above sea level in the Earth’s atmosphere as P_i = P_i⁰e^-M,g/RT where P_i is the partial pressure at the height z,P_i⁰ is the partial pressure of component i at sea level, g is the acceleration of gravity, R is the gas constant, T is the absolute temperature, and M_i is the molecular mass of the gas. As a result of turbulent mixing, the composition of the Earth’s atmosphere is constant below an altitude of 100 km, but the total pressure decreases with altitude P = P⁰e-M_ave gz/RT where M _ave is the mean molecular weight of air. At sea level, x_N2 = 0.78084, x_He = 0.00000524, and T = 300 K.

a. Calculate the total pressure ;at 8.5 km assuming a mean molecular mass of 28.9 g mol⁻¹ and that T = 300.K throughout this altitude range.

b. Calculate the value that x_N2/ x_He would have at 8.5 km in the absence of turbulent mixing. Compare your answer with the correct value.