The vapor pressure of a solution prepared by mixing two liquids, R, p*=80mmHg, and S, p*=120mmHg is found to be 86 mmHg when X_r=0.4. Which of the following is correct about these solutions?
A) exhibit favorable interactions
B) are partially miscible ******
C) boil more readily then ideal solutions
D)display ideal behavior
I know it's not D but I'm thinkin it's B.
To determine the correct answer, we need to analyze the given information and consider the properties of ideal and non-ideal solutions.
First, let's understand what each answer choice means:
A) Favorable interactions: This implies that the two liquids in the solution attract each other, leading to a decrease in vapor pressure compared to ideal solutions.
B) Partially miscible: Partial miscibility suggests that the two liquids do not mix completely but form two distinct phases in the solution.
C) Boil more readily than ideal solutions: This means that the solution has a lower boiling point compared to an ideal solution.
D) Display ideal behavior: In an ideal solution, the vapor pressure of the solution can be calculated using Raoult's law, which states that the vapor pressure of the solution is directly proportional to the mole fraction of each component in the solution.
Now, let's analyze the given information. The vapor pressure of the solution is 86 mmHg, and the mole fraction of liquid R, X_r, is 0.4.
According to Raoult's law, the vapor pressure of the solution can be calculated as follows:
p_solution = X_r * p*_r + X_s * p*_s,
where p_solution is the vapor pressure of the solution, X_r and X_s are the mole fractions of liquids R and S, and p*_r and p*_s are the vapor pressures of liquids R and S, respectively.
Given p_solution = 86 mmHg and X_r = 0.4, we can rearrange the equation and substitute the given values:
86 mmHg = 0.4 * 80 mmHg + X_s * 120 mmHg.
Simplifying the equation gives:
86 mmHg = 32 mmHg + X_s * 120 mmHg,
54 mmHg = X_s * 120 mmHg,
X_s = 0.45.
The mole fraction of liquid S, X_s, is 0.45.
Since the mole fractions of both components (X_r and X_s) are not equal to 1, it means that these liquids are not completely miscible and will form two distinct phases. Hence, the correct answer is B) are partially miscible.