Chapter 13, Problem 13.139P

(a)

Interpretation Introduction

Interpretation:

The molar mass of the fragment is to be calculated.

Concept introduction:

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:

$\prod =MRT$ (1)

Here, $\prod$ is the osmotic pressure.

$M$ is the molarity of the solution.

$R$ is universal gas constant.

$T$ is the absolute temperature.

Molarity is defined as the number of moles of solute that are dissolved in one litre of solution. It is represented by $M$ and its unit is $\text{mol/L}$.

The formula to calculate the molarity of the solution is as follows:

$\text{Molarity}=\frac{\text{amount}\left(\text{mol}\right)\text{of}\text{solute}}{\text{volume }\left(\text{L}\right)\text{of}\text{}\text{solution}}$ (2)

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

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

(b)

Interpretation Introduction

Interpretation:

The depression in freezing point is 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:

$\Delta T_{\text{f}}=i{k}_{\text{f}}m$ (6)

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.

Molality is the measure of the concentration of solute in the solution. It is the amount of solute that is dissolved in one kilogram of the solvent. It is represented by $m$ and its unit is moles per kilograms. The solute is the substance that is present in a smaller amount and solvent is the substance that is present in a larger amount.

The formula to calculate the density of the solution is as follows:

$\text{Density of solution}=\frac{\text{Mass of solution}}{\text{Volume of solution}}$ (7)