A researcher studies a three-component gas mixture consisting of gases A, B
CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance
Problem
A researcher studies a three-component gas mixture consisting of gases A, B, and C in a frictionless, movable-piston cylinder maintained at 350 K. Initially, the piston is locked in place. The mixture occupies a volume of 4.00 L and contains 0.800 mol A, 0.400 mol B, and 0.800 mol C. The total pressure at this point is 5.00 atm.
The piston is then unlocked and allowed to move so that the system undergoes an isothermal expansion until the total pressure falls to 3.00 atm. During the expansion, 0.200 mol of gas B leak out through a semipermeable membrane that is permeable only to B. All gases behave ideally, and no other changes occur.
(a) Derive an algebraic expression for the final volume Vf in terms of the initial volume Vi, the initial total number of moles ni, the number of moles of B that escape (ΔnB), and the ratio of final to initial pressure.
(b) Using the expression from part (a), calculate the numerical value of the final volume.
(c) Determine the final mole fraction and partial pressure of gas C.
(d) The researcher claims, “The partial pressure of gas C is unaffected by the loss of gas B because the gases do not interact.” Evaluate this claim both quantitatively and conceptually.