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Chapter 13: Problem 11

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\(]\)

Short Answer

Expert verified
The final volume of the solution inside the balloon when the system reaches equilibrium through osmosis is \(0.5 L\).

Step by step solution

01

Identify the initial conditions

We are given the following information: - The initial volume of the solution inside the balloon is \(0.25 L\). - The initial concentration (molarity) of the solution inside the balloon is \(0.2 M\). - The initial concentration of the solution outside the balloon is \(0.1 M\). Since both solutions contain the same solute, we can assume their van't Hoff factors (i) are equal.
02

Calculate osmotic pressures

Using the formula \(Π = iMRT\), we'll calculate the osmotic pressures for both the inside and outside solutions. Let's assume the temperature is constant and equal for both solutions, and the van't Hoff factor (i) is equal for both solutions. Hence the difference in osmotic pressure inside and outside the balloon depends only on the difference in molarity. Diff_Π = iRT(M_inside - M_outside)
03

Calculate the equilibrium concentration

When the system reaches equilibrium through osmosis, the osmotic pressures of both the inside and outside solutions will be equal. Thus, the final concentration of both solutions will also be equal. Let's denote the equilibrium concentration as M_eq.
04

Calculate the moles of solute inside the balloon

Before osmosis occurs, we can calculate the moles of solute inside the balloon. moles_solute_inside = M_inside × V_inside = 0.2 M × 0.25 L = 0.05 moles
05

Find the final volume of the solution inside the balloon

As the system reaches equilibrium, the moles of solute inside the balloon stay constant. We can use the equilibrium concentration to find the final volume. moles_solute_inside = M_eq × V_eq We already know M_eq = M_inside = M_outside from Step 3. Therefore, we can solve for the final volume: V_eq = moles_solute_inside / M_eq = 0.05 moles / 0.1 M = 0.5 L The final volume of the solution inside the balloon when the system reaches equilibrium through osmosis is 0.5 L.

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Most popular questions from this chapter

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.

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