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Chapter 11: Problem 121

The normal boiling point of methanol is \(64.7^{\circ} \mathrm{C} .\) A solution containing a nonvolatile solute dissolved in methanol has a vapor pressure of 556 torr at \(64.7^{\circ} \mathrm{C} .\) What is the mole fraction of methanol in this solution?

Short Answer

Expert verified
The mole fraction of methanol in the solution can be found using Raoult's Law, which states that the vapor pressure of the solution equals the mole fraction of the solvent times the vapor pressure of pure solvent. At the normal boiling point (64.7°C), the vapor pressure of pure methanol is assumed to be 760 torr. Given the vapor pressure of the solution (556 torr) and the vapor pressure of pure methanol (760 torr), the mole fraction of methanol in the solution can be calculated as follows: \(X_{methanol} = \frac{556}{760} \approx 0.732\). Thus, the mole fraction of methanol in this solution is approximately 0.732.

Step by step solution

01

Find the vapor pressure of pure methanol at its normal boiling point

At the normal boiling point of a liquid, its vapor pressure is equal to the atmospheric pressure. As we are not given the actual atmospheric pressure, we will assume it to be 760 torr. Thus, at 64.7°C, the vapor pressure of pure methanol is 760 torr.
02

Apply Raoult's Law to relate the components' properties

Raoult's Law states that the vapor pressure of a solution is equal to the mole fraction of the solvent times the vapor pressure of pure solvent. In this case, solvent is methanol, and solute is a nonvolatile substance. Let \(P_{solution}\) be the vapor pressure of the solution, \(P_{methanol}\) be the vapor pressure of pure methanol, and \(X_{methanol}\) be the mole fraction of methanol in the solution. According to Raoult's Law, we have: \[P_{solution} = X_{methanol} \times P_{methanol}\]
03

Solve for the mole fraction of methanol in the solution

We are given the vapor pressure of the solution, \(P_{solution} = 556 \, \text{torr}\), and we found the vapor pressure of pure methanol, \(P_{methanol} = 760\, \text{torr}\). We can now solve for the mole fraction of methanol (\(X_{methanol}\)) using the Raoult's Law equation: \(556 = X_{methanol} \times 760\) Now, to find \(X_{methanol}\), we will divide both sides of the equation by 760: \[X_{methanol} = \frac{556}{760}\] By calculating the result, we find the mole fraction of methanol in the solution: \[X_{methanol} \approx 0.732 \] So, the mole fraction of methanol in this solution is approximately 0.732.

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Most popular questions from this chapter

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