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Chapter 11: Problem 116

A solution at \(50^{\circ} \mathrm{C}\) containing 2.0 \(\mathrm{mol}\) of liquid \(\mathrm{A}\) and 3.0 \(\mathrm{mol}\) of liquid \(\mathrm{B}\) has a total vapor pressure of \(240 .\) torr. If pure A has a vapor pressure of 150 . torr at \(50^{\circ} \mathrm{C},\) what is the vapor pres- sure of pure \(\mathrm{B}\) at \(50^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The vapor pressure of pure B at \(50^{\circ}\mathrm{C}\) is 300 torr.

Step by step solution

01

Determine the mole fractions of A and B

The first step is to calculate the mole fractions of A and B in the solution. Mole fraction is the ratio of the moles of a substance to the total moles of the solution. Mole fraction of A = moles of A / (moles of A + moles of B) Mole fraction of B = moles of B / (moles of A + moles of B)
02

Calculate the mole fractions of A and B

Using the given values, let's calculate the mole fractions of A and B. Mole fraction of A = 2.0 mol / (2.0 mol + 3.0 mol) = 2.0 / 5.0 = 0.4 Mole fraction of B = 3.0 mol / (2.0 mol + 3.0 mol) = 3.0 / 5.0 = 0.6
03

Apply Raoult's Law

Raoult's Law can be applied to calculate the vapor pressures of A and B. P_solution = P_A * mole_fraction_A + P_B * mole_fraction_B Given, P_solution = 240 torr and P_A = 150 torr, we can solve for P_B.
04

Solve for P_B

Let's plug in the values into the equation from step 3 and solve for P_B. 240 = (150 * 0.4) + P_B * 0.6 240 = 60 + 0.6 * P_B 240 - 60 = 0.6 * P_B 180 = 0.6 * P_B Now, divide by 0.6 to find the vapor pressure of pure B: P_B = 180 / 0.6 = 300 torr
05

State the final answer

The vapor pressure of pure B at \(50^{\circ}\mathrm{C}\) is 300 torr.

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Most popular questions from this chapter

At a certain temperature, the vapor pressure of pure benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is 0.930 \(\mathrm{atm} .\) A solution was prepared by dissolving 10.0 \(\mathrm{g}\) of a nondissociating, nonvolatile solute in 78.11 \(\mathrm{g}\) of benzene at that temperature. The vapor pressure of the solution was found to be 0.900 \(\mathrm{atm}\) . Assuming the solution behaves ideally, determine the molar mass of the solute.

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