Final answer:
To solve part a, we can use Raoult's Law to calculate the pressure at which condensation occurs and the composition of the first liquid droplet. For part b, the minimum pressure required for complete condensation is equal to the pure vapor pressure of the more volatile component. The composition of the first liquid droplet can be calculated using the mole fractions of each component in the solution.
Step-by-step explanation:
In order to solve this problem, we need to use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the mole fraction of that component multiplied by its pure vapor pressure.
a) To find the pressure at which condensation occurs, we need to consider the composition of the vapor mixture. Since the vapor mixture is 60 mol% n-pentane (component 1) and 40% n-hexane (component 2), we can calculate the mole fractions as follows:
Mole fraction of n-pentane (x1) = 0.6, Mole fraction of n-hexane (x2) = 0.4
Using Raoult's Law, we can calculate the partial pressures of each component:
Partial pressure of n-pentane (P1) = x1 * P1°, Partial pressure of n-hexane (P2) = x2 * P2°
where P1° and P2° are the pure vapor pressures of n-pentane and n-hexane, respectively. Given the mole fractions and pure vapor pressures, we can substitute the values into the equation to find the total pressure.
b) The minimum pressure required for complete condensation occurs when the partial pressure of the more volatile component, which is n-pentane in this case, reaches its pure vapor pressure. Since n-pentane has a higher pure vapor pressure than n-hexane, the minimum pressure required for complete condensation is equal to the pure vapor pressure of n-pentane.
The composition of the first liquid droplet can be calculated by finding the mole fractions of each component in the solution at the pressure where condensation occurs. Using the values calculated in part a), we can find the mole fraction of n-pentane (component 1) and n-hexane (component 2) in the first liquid droplet.