Problem 58 - Chemistry: The Central Science

Question

How does increasing the concentration of a nonvolatile solute in water affect the following properties: (a) vapor pressure, (b) freezing point, (c) boiling point; (d) osmotic pressure?

Step-by-Step Solution

Answer

Increasing the concentration of a nonvolatile solute in water affects the following properties: (a) Vapor pressure decreases due to the solute molecules occupying some of the surface area, preventing solvent molecules from escaping to the vapor phase. (b) Freezing point decreases, as solute particles interfere with the formation of the solid solvent's ordered crystal lattice structure. (c) Boiling point increases, since solute particles reduce the vapor pressure of the solution, requiring a higher temperature to reach atmospheric pressure for boiling. (d) Osmotic pressure increases, as solute particles create a concentration difference across a semipermeable membrane, driving solvent molecules to equalize concentrations.

Step 1: (a) Vapor Pressure

When a nonvolatile solute is dissolved in water, there is a decrease in the vapor pressure of the solution compared to the pure solvent. This is due to the fact that the solute molecules occupy some of the surface area of the solvent, reducing the number of solvent molecules that can escape into the vapor phase. The vapor pressure decreases with the increase in concentration of the solute. This phenomenon can be explained using Raoult's Law.

Step 2: (b) Freezing Point

When a nonvolatile solute is dissolved in water, the freezing point of the solution is lower than that of the pure solvent. This occurs because the solute particles interfere with the formation of the ordered crystal lattice structure of the solid solvent, which requires more energy to overcome. As a result, the freezing point decreases with the increase in concentration of the solute. This can be described using the freezing point depression equation: ΔT_f = K_f * molality where ΔT_f is the freezing point depression, K_f is the freezing point depression constant, and molality is the concentration of the solute.

Step 3: (c) Boiling Point

The presence of a nonvolatile solute in water causes the boiling point of the solution to be higher than that of the pure solvent. This is because the solute particles reduce the vapor pressure of the solution, so a higher temperature is required to reach the atmospheric pressure for the solution to boil. The boiling point elevation can be described using the equation: ΔT_b = K_b * molality where ΔT_b is the boiling point elevation, K_b is the boiling point elevation constant, and molality is the concentration of the solute. The boiling point increases with the increase in concentration of the solute.

Step 4: (d) Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent through a semipermeable membrane. When a nonvolatile solute is dissolved in water, the osmotic pressure of the solution increases compared to that of the pure solvent. This is because the solute particles cause a difference in concentration between the two sides of the membrane, driving the movement of the solvent molecules to equalize the concentration. The osmotic pressure can be calculated using the equation: π = cRT where π is the osmotic pressure, c is the concentration of the solute, R is the ideal gas constant, and T is the absolute temperature. The osmotic pressure increases with the increase in concentration of the solute.