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Chapter 13: Problem 64

The vapor pressure of pure water at \(60^{\circ} \mathrm{C}\) is 149 torr. The vapor pressure of water over a solution at \(60^{\circ} \mathrm{C}\) containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law?

Short Answer

Expert verified
The solution is not ideal according to Raoult's law. The mole fraction of water in the solution is 0.5. Applying Raoult's law, the theoretical vapor pressure of water over the solution should be \(74.5 \,\text{torr}\) (0.5 times the vapor pressure of pure water at \(60^{\circ}\mathrm{C}\), which is 149 torr). However, the given vapor pressure of water over the solution is \(67 \,\text{torr}\), which is different from the theoretical vapor pressure. Thus, the solution does not follow Raoult's law exactly.

Step by step solution

01

Calculate the mole fraction of water in the solution

Since there are equal moles of water and ethylene glycol in the solution, we can easily determine the mole fraction of each component. For water: Mole fraction = (moles of water) / (moles of water + moles of ethylene glycol) Mole fraction of water = 1 / (1 + 1) = 1 / 2 = 0.5
02

Apply Raoult's law to calculate the theoretical vapor pressure of water over the solution

According to Raoult's law, the partial vapor pressure of a component in a solution is equal to its mole fraction multiplied by the vapor pressure of the pure substance at the same temperature. Theoretical vapor pressure of water over the solution = mole fraction of water * vapor pressure of pure water = (0.5) * (149 torr) = 74.5 torr
03

Compare the theoretical and given vapor pressures of water over the solution

To determine if the solution is ideal, we need to compare the theoretical vapor pressure of water (74.5 torr) with the given vapor pressure of water over the solution (67 torr).
04

Determine if the solution is ideal

We'll compare the theoretical vapor pressure and the given vapor pressure: Theoretical vapor pressure of water over the solution = 74.5 torr Given vapor pressure of water over the solution = 67 torr Since these two values are different, the solution does not follow Raoult's law exactly. Therefore, the solution is not ideal according to Raoult's law.

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Most popular questions from this chapter

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false. (a) The freezing point of the solution is unchanged by addition of the solvent. (b) The solid that forms as the solution freezes is nearly pure solute. (c) The freezing point of the solution is independent of the concentration of the solute. ( \(\mathbf{d}\) ) The boiling point of the solution increases in proportion to the concentration of the solute. (e) At any temperature, the vapor pressure of the solvent over the solution is lower than what it would be for the pure solvent.

Calculate the molarity of the following aqueous solutions: (a) 0.540 \(\mathrm{g}\) of Mg \(\left(\mathrm{NO}_{3}\right)_{2}\) in 250.0 \(\mathrm{mL}\) of solution, \((\mathbf{b}) 22.4 \mathrm{gof}\) \(\mathrm{LiClO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) in 125 \(\mathrm{mL}\) of solution, \((\mathrm{c}) 25.0 \mathrm{mL}\) of 3.50 \(\mathrm{M}\) \(\mathrm{HNO}_{3}\) diluted to 0.250 \(\mathrm{L}\)

The presence of the radioactive gas radon (Rn) in well water presents a possible health hazard in parts of the United States. (a) Assuming that the solubility of radon in water with 1 atm pressure of the gas over the water at \(30^{\circ} \mathrm{C}\) is \(7.27 \times 10^{-3} \mathrm{M},\) what is the Henry's law constant for radon in water at this temperature? (b) A sample consisting of various gases contains \(3.5 \times 10^{-6}\) mole fraction of radon. This gas at a total pressure of 32 atm is shaken with water at \(30^{\circ} \mathrm{C} .\) Calculate the molar concentration of radon in the water.

A "canned heat" product used to warm buffet dishes consists of a homogeneous mixture of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and paraffin, which has an average formula of \(\mathrm{C}_{24} \mathrm{H}_{50}\). What mass of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) should be added to \(620 \mathrm{~kg}\) of the paraffin to produce 8 torr of ethanol vapor pressure at \(35^{\circ} \mathrm{C}\) ? The vapor pressure of pure ethanol at \(35^{\circ} \mathrm{C}\) is 100 torr.

Suppose you had a balloon made of some highly flexible semipermeable membrane. The balloon is filled completely with a 0.2\(M\) solution of some solute and is submerged in a 0.1 \(\mathrm{M}\) solution of the same solute: Initially, the volume of solution in the balloon is 0.25 L. Assuming the volume outside the semipermeable membrane is large, as the illustration shows, what would you expect for the solution volume inside the balloon once the system has come to equilibrium through osmosis? [Section 13.5\(]\)
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