Chapter 13, Problem 70QP

Interpretation Introduction

Interpretation:

The osmotic pressure of thesaline solution at $37°\text{C}$ temperature with given density is to be calculated.

Concept introduction:

The properties of a solution that depends on the number of solute particles present in solution but do not depend on the nature of solute particles are called as colligative properties.

The four colligative properties of solution are vapor-pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

The word, colligative, means binding of particles together.

The osmotic pressure of a solution is given by the expression as follows:

$\pi =iMRT$

Here, $\pi$ denotes osmotic pressure, $i$ denotes Van’t Hoff factor, $M$ denotes the molarity of solute, $R$ denotes the universal gas constant $\left(0.0821\text{ L}\cdot \text{atm/mol}\cdot \text{K}\right)$, and $T$ denotes the temperature.

The conversion of temperature from degree Celsius $\left[T\left(°\text{C}\right)\right]$ into Kelvin $\left(T\right)$ is done by the expression as follows:

$T=T\left(°\text{C}\right)+273$

The molality of the solution is calculated by the expression as:

$m=\frac{\text{moles of solute}}{\text{mass of solvent }\left(\text{kg}\right)}$

Moles of compound can be calculated by the expression:

$\text{moles = }\frac{\text{mass of compound}}{\text{molar mass of compound}}$

So, molality can also be calculated by:

$m=\left(\frac{\text{mass of solute}}{\text{molar mass of}\text{solute}}\right)\left(\frac{\text{1}}{\text{mass of solvent }\left(\text{kg}\right)}\right)$