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Chapter 11: Problem 113

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 \(556.0\) 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: \(P_{solution} = P_A^{*} \times X_A\). Given the vapor pressure of the solution is \(556.0 \textrm{ torr}\) and the pure methanol vapor pressure is \(760 \textrm{ torr}\) at its boiling point, we can determine the mole fraction of methanol: \(X_A = \frac{556.0}{760} \approx 0.73158\).

Step by step solution

01

Write down the Raoult's Law formula

Raoult's Law states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the mole fraction of the component multiplied by its vapor pressure in the pure state. The formula for Raoult's Law can be written as: \[P_{solution} = P_A^{*} \times X_A\] Where \(P_{solution}\) is the vapor pressure of the solution, \(P_A^{*}\) is the vapor pressure of the pure solvent (methanol in this case), and \(X_A\) is the mole fraction of the solvent (methanol).
02

Determine the vapor pressure of pure methanol

We know the normal boiling point of methanol is \(64.7^{\circ} \mathrm{C}\). At this temperature, the vapor pressure of the pure methanol is equal to atmospheric pressure (assuming the atmospheric pressure to be 1 atm = 760 torr). Therefore, \(P_A^{*} = 760 \textrm{ torr}\).
03

Substitute the known values and solve for methanol's mole fraction

We are given that the vapor pressure of the solution containing methanol and a nonvolatile solute is \(556.0 \textrm{ torr}\) at its boiling point temperature (\(64.7^{\circ} \mathrm{C}\)). Using Raoult's Law, we can write: \(556.0 \textrm{ torr} = 760 \textrm{ torr} \times X_A\) Now, to find the mole fraction of methanol, \(X_A\), we will isolate it from the equation: \(X_A = \frac{556.0 \textrm{ torr}}{760 \textrm{ torr}}\)
04

Calculate the mole fraction of methanol

Now we can calculate the mole fraction of methanol: \(X_A = \frac{556.0}{760}\) \(X_A \approx 0.73158\) So, the mole fraction of methanol in the solution is approximately 0.73158.

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Most popular questions from this chapter

For each of the following pairs, predict which substance is more soluble in water. a. \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) or \(\mathrm{NH}_{3}\) b. \(\mathrm{CH}_{3} \mathrm{CN}\) or \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) d. \(\mathrm{CH}_{3} \mathrm{OH}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) e. \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}_{2} \mathrm{OH}\) or \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{OH}\) f. \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) or \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

Consider the following:What would happen to the level of liquid in the two arms if the semipermeable membrane separating the two liquids were permeable to a. \(\mathrm{H}_{2} \mathrm{O}\) (the solvent) only? b. \(\mathrm{H}_{2} \mathrm{O}\) and solute?

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