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Chapter 11: Problem 21

The following pairs of aqueous solutions are separated by a semipermeable membrane. In which direction will the solvent flow? a. \(A=1.25 M N_{a} C l ; B=1.50 M K C 1\) b. \(A=3.45 M C_{a} C l_{2} ; B=3.45 M N_{a B r}\) c. \(A=4.68 M\) glucose; \(B=3.00 M N_{a} C 1\)

Short Answer

Expert verified
Answer: (a) The solvent will flow from the 1.25 M NaCl solution to the 1.50 M KCl solution. (b) There will be no net solvent flow between the 3.45 M CaCl2 solution and the 3.45 M NaBr solution. (c) The solvent will flow from the 3.00 M NaCl solution to the 4.68 M glucose solution.

Step by step solution

01

1. Analyzing the concentrations for part a

For part a, we have the following solutions on either side of the membrane: \(A = 1.25\,\text{M}\, N_{a} C l\), and \(B = 1.50\,\text{M}\, K C l\).
02

2. Comparing the concentrations for part a

Since \(1.50\,\text{M}\, K C l > 1.25\,\text{M}\, N_{a} C l\), the solvent will flow from solution A (\(1.25\,\text{M}\, N_{a} C l\)) to solution B (\(1.50\,\text{M}\, K C l\)).
03

3. Analyzing the concentrations for part b

For part b, we have the following solutions on either side of the membrane: \(A = 3.45\,\text{M}\, C_{a} C l_{2}\) and \(B = 3.45\,\text{M}\, N_{a} B r\).
04

4. Comparing the concentrations for part b

Since both solution A and solution B have equal concentrations (\(3.45\,\text{M}\)), there will be no net solvent flow as the osmotic pressure is equal across the semipermeable membrane.
05

5. Analyzing the concentrations for part c

For part c, we have the following solutions on either side of the membrane: \(A = 4.68\,\text{M}\) glucose, and \(B = 3.00\,\text{M}\, N_{a} C 1\).
06

6. Comparing the concentrations for part c

Since \(4.68\,\text{M}\) glucose \(> 3.00\,\text{M}\, N_{a} C 1\), the solvent will flow from solution B (\(3.00\,\text{M}\, N_{a} C 1\)) to solution A (\(4.68\,\text{M}\) glucose).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Semipermeable Membrane
A semipermeable membrane is like a special filter that allows certain molecules to pass while blocking others. It's essential in processes like osmosis. This type of membrane is selective, meaning:
  • Allows solvent molecules (like water) to move through
  • Blocks larger solute molecules (like salts or sugars)
In our exercise, solutions are separated by a semipermeable membrane. Due to its selective nature, only the solvent is able to move, typically driven from regions of lower solute concentration to regions of higher solute concentration. This movement balances the concentration on both sides of the membrane, maintaining the equilibrium.
Solute Concentration
Solute concentration refers to the amount of solute, such as salt or sugar, dissolved in a solution. It is usually expressed in molarity (M), which is moles of solute per liter of solution. In osmosis, the concentration gradient between two solutions separated by a semipermeable membrane is crucial:
  • The solvent naturally moves from an area of low solute concentration to an area of high solute concentration.
  • This movement aims to equalize concentrations across the membrane.
  • The greater the difference in concentration, the more significant the movement of solvents.
In the exercise, solutions with different solute concentrations experience osmotic flow due to this difference, highlighting the importance of understanding solute concentration dynamics in osmotic processes.
Osmotic Pressure
Osmotic pressure is the force that drives the solvent through a semipermeable membrane due to differences in solute concentration. It's a pressure created by the tendency of water to move into a solution with higher solute concentration. Key points about osmotic pressure include:
  • Higher solute concentrations result in higher osmotic pressure.
  • Osmotic pressure is what causes the net flow of solvent toward the more concentrated solution.
  • If two solutions are of equal concentration, their osmotic pressures are balanced, and there will be no net solvent flow.
In the exercise provided, comparing osmotic pressures helps determine the direction of solvent flow, significantly affecting the solutions' balance over time.

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Most popular questions from this chapter

A bottle is half-filled with a 50: 50 (by moles) mixture of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) at \(25^{\circ} \mathrm{C} .\) What is the mole ratio of heptane vapor to octane vapor in the air space above the liquid in the bottle? The vapor pressures of heptane and octane at \(25^{\circ} \mathrm{C}\) are 31 torr and 11 torr, respectively.

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