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Chapter 13: Problem 82

Solutions \(A\) and \(B\) containing the same solute have osmotic pressures of 2.4 atm and 4.6 atm, respectively, at a certain temperature. What is the osmotic pressure of a solution prepared by mixing equal volumes of \(\mathrm{A}\) and \(\mathrm{B}\) at the same temperature?

Short Answer

Expert verified
The osmotic pressure of the solution prepared by mixing equal volumes of solution A and B is 3.5 atm.

Step by step solution

01

Recognize what is given and what needs to be calculated

The osmotic pressures of solutions A and B are 2.4 atm and 4.6 atm, respectively. The task is to find the osmotic pressure after mixing equal volumes of solutions A and B.
02

Infer the relationship between osmotic pressure and concentration

Osmotic pressure is directly proportional to concentration, so more concentrated solution will yield higher osmotic pressure. Since solution A and solution B are mixed equally, the total concentration is the average of the two individual concentrations.
03

Calculate the osmotic pressure of the mixture

The osmotic pressure of the resulting solution, when equal volumes of A and B are combined, is the average of the osmotic pressures of solutions A and B. Mathematically, this can be calculated as follows: \( (2.4~atm + 4.6~atm)/2 = 3.5~atm \)

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Most popular questions from this chapter

Basing your answer on intermolecular force considerations, explain what "like dissolves like" means.

Using Henry's law and the ideal gas equation to prove the statement that the volume of a gas that dissolves in a given amount of solvent is independent of the pressure of the gas. (Hint: Henry's law can be modified as \(n=k P\), where \(n\) is the number of moles of the gas dissolved in the solvent.)

Liquids A (molar mass \(100 \mathrm{~g} / \mathrm{mol}\) ) and \(\mathrm{B}\) (molar mass \(110 \mathrm{~g} / \mathrm{mol}\) ) form an ideal solution. At \(55^{\circ} \mathrm{C}\), A has a vapor pressure of \(95 \mathrm{mmHg}\) and \(\mathrm{B}\) has a vapor pressure of \(42 \mathrm{mmHg}\). A solution is prepared by mixing equal masses of \(\mathrm{A}\) and \(\mathrm{B}\). (a) Calculate the mole fraction of each component in the solution. (b) Calculate the partial pressures of \(\mathrm{A}\) and \(\mathrm{B}\) over the solution at \(55^{\circ} \mathrm{C}\). (c) Suppose that some of the vapor described in (b) is condensed to a liquid. Calculate the mole fraction of each component in this liquid and the vapor pressure of each component above this liquid at \(55^{\circ} \mathrm{C}\).

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