CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance
Problem
Two rigid 2.00 L containers, A and B, are held side-by-side at 400 K. Container A holds 1.00 mol of helium gas, while container B holds 1.00 mol of xenon gas. Both gases can be treated as ideal.
Use kinetic molecular theory to analyze the system.
(a) Using appropriate relationships among temperature, molecular mass, and molecular speed, derive an expression for the ratio of the root-mean-square speeds vrms(He)/vrms(Xe) in terms of the molar masses of helium and xenon. State all assumptions clearly.
(b) Calculate the numerical value of the speed ratio using MHe=4.00g mol−1 and MXe=131.3g mol−1. Show your work.
(c) Despite the large difference in rms speeds, both gases exert the same pressure on the walls of their respective containers. Provide a detailed explanation, grounded in KMT, of how differences in molecular speed and mass combine to yield equal macroscopic pressures.
(d) Suppose the temperature of both containers is doubled to 800 K while the volumes remain constant. Predict quantitatively how the pressure in each container changes. Then comment qualitatively on whether your explanation from part (c) remains valid at the higher temperature.