Question

You make two solutions of a nonvolatile solute with a liquid solvent, \(0.01 \mathrm{M}\) and \(1.00 \mathrm{M}\). Indicate whether each of the following statements is true or false. (a) The vapor pressure of the concentrated solution is higher than that of the diluted solution. (b) The osmotic pressure of the concentrated solution is higher than that of the diluted solution. (c) The boiling point of the concentrated solution is higher than that of the diluted solution. (d) The freezing point of the concentrated solution is higher than that of the diluted solution.

Short answer

(a) False - The vapor pressure of the concentrated (\(1.00 \mathrm{M}\)) solution is lower than that of the diluted (\(0.01 \mathrm{M}\)) solution. (b) True - The osmotic pressure of the concentrated (\(1.00 \mathrm{M}\)) solution is higher than that of the diluted (\(0.01 \mathrm{M}\)) solution. (c) True - The boiling point of the concentrated (\(1.00 \mathrm{M}\)) solution is higher than that of the diluted (\(0.01 \mathrm{M}\)) solution. (d) False - The freezing point of the concentrated (\(1.00 \mathrm{M}\)) solution is lower than that of the diluted (\(0.01 \mathrm{M}\)) solution.

Step-by-step solution

Statement (a) - Vapor Pressure

The vapor pressure of a solution is the pressure exerted by the solvent molecules when they escape from the solution into the gas phase. A higher concentration of solute results in a lower vapor pressure of the solution, as the solute particles disrupt the orderly arrangement of the solvent molecules and reduce their tendency to escape. Therefore, the vapor pressure of the concentrated (\(1.00 \mathrm{M}\)) solution is lower than that of the diluted (\(0.01 \mathrm{M}\)) solution. This statement is False.

Statement (b) - Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent through a semipermeable membrane separating two solutions with different solute concentrations. A higher concentration of solute results in a higher osmotic pressure, as there would be more solute particles causing the solvent to flow from the area of lower solute concentration to that of higher solute concentration. Therefore, the osmotic pressure of the concentrated (\(1.00 \mathrm{M}\)) solution is higher than that of the diluted (\(0.01 \mathrm{M}\)) solution. This statement is True.

Statement (c) - Boiling Point

The boiling point of a solution is when the vapor pressure of the solution equals the atmospheric pressure and the solution starts to boil. When solutes are added to a solvent, their presence increases the boiling point of the solution compared to the pure solvent, called boiling point elevation. Higher solute concentration causes a greater elevation in boiling point. Thus, the boiling point of the concentrated (\(1.00 \mathrm{M}\)) solution is higher than that of the diluted (\(0.01 \mathrm{M}\)) solution. This statement is True.

Statement (d) - Freezing Point

The freezing point of a solution is the temperature at which the solution begins to solidify. Adding solutes to a solvent lowers the freezing point of the solution compared to the pure solvent, called freezing point depression. A higher solute concentration increases the freezing point depression. Therefore, the freezing point of the concentrated (\(1.00 \mathrm{M}\)) solution is lower than that of the diluted (\(0.01 \mathrm{M}\)) solution. This statement is False.

Key concepts

Vapor Pressure

Vapor pressure is the pressure exerted by the molecules of a liquid as they escape into the gas phase. When a nonvolatile solute is added to a solvent, it interferes with the ability of solvent molecules to escape. This results in a lower vapor pressure for the solution compared to the pure solvent. In solutions with higher solute concentrations, there are more solute particles. These particles disrupt the surface of the liquid more effectively, reducing the number of solvent molecules that can escape to form vapor. Hence, a concentrated solution will have a lower vapor pressure than a diluted one. This is why, in the exercise, the statement that a concentrated solution has higher vapor pressure is false.

Osmotic Pressure

Osmotic pressure is the pressure needed to stop the flow of solvent molecules through a semipermeable membrane, from a region of low solute concentration to high solute concentration. It is directly related to the concentration of solute particles in a solution. In the exercise, it is noted that a more concentrated solution ( 1.00 ext{M} ) has higher osmotic pressure than a more diluted solution ( 0.01 ext{M} ). This is true because greater concentrations create a larger difference in solute concentration between the two sides of the membrane, thereby requiring more pressure to stop the solvent flow.

Boiling Point Elevation

Boiling point elevation occurs when the boiling point of a solution is higher than that of the pure solvent. When solute particles are added to a solvent, they lower the solvent's vapor pressure. This means that a higher temperature is needed for the vapor pressure to equal the atmospheric pressure, resulting in a higher boiling point. In the exercise, the statement regarding the concentrated solution having a higher boiling point than the diluted one is true. This is because the presence of more solute particles in the concentrated solution causes a greater elevation in boiling point.

Freezing Point Depression

Freezing point depression refers to the lowering of a solution's freezing point compared to the pure solvent. As solute particles are introduced into the solvent, they disrupt the formation of the solid structure that occurs during freezing. The more solute particles present, the greater the disruption, leading to a bigger decrease in the freezing point. Therefore, a concentrated solution has a lower freezing point than a diluted one. In the exercise, the statement that a concentrated solution has a higher freezing point is false because increased solute concentration actually results in a lower freezing point.