Final answer:
To determine the composition of liquid and vapor phases of a mixture of n-butane, n-pentane, and n-hexane at equilibrium, Raoult's Law and Dalton's Law would be applied. However, without the specific vapor pressures of the components at the given temperature, the calculation cannot be completed.
Step-by-step explanation:
To find the composition of the liquid and vapor in a mixture of n-butane, n-pentane, and n-hexane at 120°F and 20 psia with a known liquid mole fraction of n-butane, we would use Raoult's Law and Dalton's Law of Partial Pressures. These principles state that the partial pressure of a component in a mixture is equal to the vapor pressure of the pure component at that temperature multiplied by its mole fraction in the liquid. Similarly, the vapor composition is determined by the partial pressures as ratios of the total pressure.
Unfortunately, to provide a complete answer, we would need the equilibrium vapor pressures of pure n-butane, n-pentane, and n-hexane at the given temperature. Given those, we could calculate the partial pressures (partial pressure = vapor pressure × liquid mole fraction), and then get the vapor mole fractions by dividing each component's partial pressure by the total pressure.
Since we don't have the vapor pressures, we can't solve this problem fully. Yet, the process would involve setting up a system of equations based on Raoult's Law for each component and solving for the unknowns, which would give us the mole fractions of each component in both the liquid phase and vapor phase.