A rigid container of volume holds a mixture of two ideal gases that do not react with…
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A rigid container of volume V holds a mixture of two ideal gases that do not react with each other. Species A has mass m1, number density n1, and root-mean-square speed vrms,1. Species B has mass m2, number density n2, and root-mean-square speed vrms,2. Interactions between the two species can be neglected except for perfectly elastic collisions.
(a) For species A alone, derive an expression for the partial pressure P1 it exerts on the container walls in terms of n1, m1, and vrms,1.
(b) Repeat part (a) for species B to obtain its partial pressure P2.
(c) Using kinetic arguments, explain why the total pressure Ptot exerted by the mixture equals the sum of the two partial pressures even though atoms of different masses collide with the same walls.
(d) Combine your results to write Ptot explicitly in terms of n1, n2, m1, m2, vrms,1, and vrms,2. Comment on how increasing the heavier species’ number density affects the total pressure when all other quantities remain the same.