Question

What are the boiling point and freezing point of a 0.625$m$ aqueous solution of any nonvolatile, nonelectrolyte solute?

Short answer

The boiling and freezing points of a 0.625 molal aqueous solution of a nonvolatile, nonelectrolyte solute are 100.320°C and -1.16375°C, respectively.

Step-by-step solution

Identify the molality of the solution

The molality (m) of the solution is given as 0.625 m.

Determine the van't Hoff factor

Since the solute is a nonvolatile, nonelectrolyte, the van't Hoff factor (i) is equal to 1.

Calculate the boiling point elevation

Use the boiling point elevation formula: ΔT_b = i * K_b * m ΔT_b = (1) * (0.512 °C/m) * (0.625 m) = 0.320 °C

Calculate the freezing point depression

Use the freezing point depression formula: ΔT_f = i * K_f * m ΔT_f = (1) * (1.86 °C/m) * (0.625 m) = 1.16375 °C

Determine the boiling and freezing points

Add the boiling point elevation to the normal boiling point of water (100°C) and subtract the freezing point depression from the normal freezing point of water (0°C). Boiling Point = 100°C + 0.320°C = 100.320°C Freezing Point = 0°C - 1.16375°C = -1.16375°C The boiling and freezing points of the 0.625 molal aqueous solution of a nonvolatile, nonelectrolyte solute are 100.320°C and -1.16375°C, respectively.

Key concepts

Boiling Point Elevation

When a solute is added to a solvent, the boiling point of the resulting solution is typically higher than that of the pure solvent. This phenomenon is known as boiling point elevation. It occurs because the presence of solute particles interferes with the ability of solvent molecules to escape into the gas phase. As a result, more energy (in the form of heat) is required to bring the solution to its boiling point.

The boiling point elevation can be calculated using the formula $\mathrm{\Delta }{T}_b=i\times K_b\times m$, where $\mathrm{\Delta }{T}_b$ is the boiling point elevation, $i$ is the Van't Hoff factor representing the number of particles the solute breaks up into or produces in solution, $K_b$ is the ebullioscopic constant of the solvent (a proportionality constant), and $m$ is the molality of the solution. In the case of nonvolatile solutes that do not ionize in solution, such as sugar in water, $i$ is equal to 1.

Freezing Point Depression

Freezing point depression is the process in which the addition of a solute to a solvent decreases the temperature at which the liquid becomes a solid. Just like boiling point elevation, this is a colligative property, meaning that it depends on the number of solute particles, not their identity. By dissolving a solute into a solvent, the solvent's freezing point is lowered because the solute disrupts the formation of the regular crystal lattice necessary for solidification.

The equation to determine the freezing point depression is given by $\mathrm{\Delta }{T}_f=i\times K_f\times m$, with $\mathrm{\Delta }{T}_f$ representing the decrease in freezing point, $i$ as the Van't Hoff factor, $K_f$ the cryoscopic constant (a characteristic of each solvent), and $m$ the molality. For substances that do not dissociate in solution, such as many organic compounds, the Van't Hoff factor $i$ is 1.

Van't Hoff Factor

The Van't Hoff factor, denoted by $i$, is a crucial concept in determining the magnitude of colligative properties such as boiling point elevation and freezing point depression. It represents the number of particles a compound produces when it dissolves in a solvent. For a nonvolatile, nonelectrolyte solute, which does not dissociate in solution, $i$ is equal to 1. This means there is a one-to-one ratio between the moles of solute added to the solution and the moles of particles in the solution.

However, for electrolytes that dissociate into ions in solution, the Van't Hoff factor is greater than 1, depending on the extent of dissociation and the number of ions produced. The accurate measurement of $i$ is essential for precise calculations of colligative properties, as any deviation from the expected $i$ value would affect the results.

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. Its unit is mol/kg and is often denoted by the symbol $m$. Unlike molarity, which is measured in moles of solute per liter of solution, molality is not affected by changes in volume due to temperature fluctuations, making it particularly useful in colligative property calculations where temperature changes are involved.

It's calculated using the formula $m=\frac{\text{moles of solute}}{\text{kilograms of solvent}}$. In the context of calculating colligative properties, molality helps in determining how much the presence of a solute affects the physical properties of the solvent, such as boiling point elevation and freezing point depression, as demonstrated in the earlier examples.