Final answer:
To find the mass fraction of C2HCl3 in the liquid phase, we start with the given mole fraction of CHCl3 in the vapor phase (0.59), assume ideal behavior, calculate the mole fraction of C2HCl3, and then convert it to mass fraction using molecular weights.
Step-by-step explanation:
To determine the mass fraction of trichloroethene (C2HCl3) in the liquid phase, when we know that the mole fraction of trichloromethane (CHCl3) in the vapor phase is 0.59, we can use Raoult's Law which states that the vapor pressure of each component of an ideal solution is proportional to its mole fraction in the solution.
Using the mole fraction of CHCl3 in the vapor phase, we can find the mole fraction of C2HCl3 in the vapor phase since the mole fractions must sum up to 1. Therefore, the mole fraction of C2HCl3 in the vapor phase would be 1 - 0.59 = 0.41.
Assuming ideal behavior, the mole fraction ratio in the vapor phase will be equal to the volatile ratio in the liquid phase. Thus, if x is the mole fraction of C2HCl3 in the liquid phase, the mole fraction of CHCl3 in the liquid phase would be (1 - x), and the ratio of mole fractions in vapor to liquid for trichloromethane would be:
0.59 / (1 - x) = x / 0.41
Solving this for x gives us the mole fraction of C2HCl3 in the liquid phase. We then convert this mole fraction into mass fraction using molecular weights of C2HCl3 and CHCl3. Let's denote the mass fraction of C2HCl3 in the liquid phase as w. Since the molecular weight of C2HCl3 is 131.4 g/mol and that of CHCl3 is 119.4 g/mol, we can express the mass fraction as:
w = (x × 131.4) / (x × 131.4 + (1 - x) × 119.4)
By substituting the value of x that we found earlier into this equation, we can calculate the mass fraction of C2HCl3 in the liquid phase.