Chapter 13, Problem 13.120P

Interpretation Introduction

Interpretation:

The freezing point, boiling point and osmotic pressure of glucose are to be calculated.

Concept introduction:

The freezing point is the temperature at which both the solid and liquid phases coexist in equilibrium. It is the temperature at which the vapor pressure of the substance in the liquid state becomes equal to the vapor pressure in a solid state.

The formula to calculate the change in freezing point is as follows:

$\Delta T_{\text{f}}=i{k}_{\text{f}}m$        (1)

Here,

$\Delta T_{\text{f}}$ is the change in freezing point.

$i$ is van’t Hoff factor.

$k_{\text{f}}$ is the freezing point depression constant.

$m$ is the molality of the solution.

The boiling point of the substance is the temperature at which the vapor pressure of the liquid becomes equal to the atmospheric pressure and the liquid changes into a vapor. Liquids can change into vapors at temperatures below the boiling point through evaporation. It is the process that occurs on the liquid surface due to which it changes into vapors. Both boiling and freezing points are colligative properties because these depend on the number of moles of solute particles that are present in the substance.

The formula to calculate the change in boiling point is as follows:

$\Delta T_{\text{b}}=i{k}_{\text{b}}m$        (2)

Here,

$\Delta T_{\text{b}}$ is the change in boiling point.

$i$ is van’t Hoff factor.

$k_{\text{b}}$ is the boiling point elevation constant.

$m$ is the molality of the solution.

The osmotic pressure is defined as the measure of the tendency of a solution to take in pure solvent via osmosis. It is defined as the minimum pressure that is to be applied to the solution to prevent the inward flow of the pure solvent across the semipermeable membrane. Osmosis occurs when two solutions have different concentrations of solute and are separated by a semipermeable membrane.

The formula to calculate the osmotic pressure of the solution is as follows:

$\prod =iMRT$        (3)

Here,

$\prod$ is the osmotic pressure.

$i$ is van’t Hoff factor.

$M$ is the molarity of the solution.

$R$ is universal gas constant.

$T$ is the absolute temperature.

The conversion factor to convert $°\text{C}$ to $\text{K}$ is as follows:

$T\left(\text{K}\right)=T\left(°\text{C}\right)+273.15\text{K}$