Carbon tetrachloride (CCl4) and benzene (C6H6) form ideal solutions. Consider an equimolar solution of CCl4 and C6H6 at 25°C. The vapor above this solutionis collected and condensed. Using the following data, determine the composition in mole fraction of the condensed vapor.

Substance ∆Gf°
C6H6 (l) 124.50 kJ/mol
C6H6 (g) 129.66 kJ/mol
CCl4 (l) -65.21 kJ/mol
CCl4 (g) -60.59 kJ/mol

How do I go about solving this?

To solve this problem, we need to use the Gibbs free energy change (∆G) associated with the phase transition between liquid and gas. The difference in ∆G between the liquid and gaseous states of a substance is related to its vapor pressure. The substance with a higher vapor pressure will have a larger ∆G.

First, let's calculate the ∆G for each substance:

∆G = ∆Gf(g) - ∆Gf(l)

∆G for C6H6 = 129.66 kJ/mol - 124.50 kJ/mol = 5.16 kJ/mol
∆G for CCl4 = -60.59 kJ/mol - (-65.21 kJ/mol) = 4.62 kJ/mol

Since C6H6 has a higher ∆G, it means it has a higher vapor pressure compared to CCl4. Therefore, more C6H6 will evaporate and condense in the collected vapor.

To determine the composition in mole fraction of the condensed vapor, follow these steps:

1. Calculate the total ∆G of the system:
Total ∆G = ∆G for C6H6 + ∆G for CCl4

2. Calculate the mole fractions of C6H6 (x6H6) and CCl4 (xCCl4):
x6H6 = (∆G for C6H6) / (Total ∆G)
xCCl4 = (∆G for CCl4) / (Total ∆G)

3. Calculate the mole fraction of the condensed vapor:
Mole fraction of vapor = x6H6 / (x6H6 + xCCl4)

Substitute the calculated values into the equations above to find the composition in mole fraction of the condensed vapor.