Question

A solution containing 0.5 g of naphthalene in 50 g $CC{l_4}$ yields a boiling point elevation of 0.4 K, while a solution of 0.6 g of unknown solute in the same mass of the solvent gives a boiling point elevation of 0.65 K. Find the molar mass of unknown solute.

Answer 1

Hint: To solve the given question 1st we need to find out the molality of different substances given in the question, after finding that we will equate it with the formula which contains terms of temperature and molality in order to calculate the molar mass of unknown solute.

Complete step by step solution:
As we all know the chemical formula of Naphthalene is \[{C_{10}}{H_8}\], having molecular mass of 128g,
Now, Molality (m) of Naphthalene in given $CC{l_4}$is \[m = \dfrac{{0.5 \times 1000}}{{128 \times 50}}\],
As per the given question we need relationship between temperature and molality which is stated below
$\Delta {T_b} = {K_B} \times m$ ​
$ \Rightarrow 0.4 = {K_b} \times \dfrac{{0.5 \times 1000}}{{128 \times 50}}$​ ... (i)
Let us assume the molar mass of unknown solute as M.
Therefore, The molality of unknown solute in $CC{l_4}$​, \[m = \dfrac{{0.6 \times 1000}}{{M \times 50}}\] ​
Substituting this value in the below formula, we get
$\Delta {T_b} = {K_B} \times m$
$ \Rightarrow 0.65 = {K_b} \times \dfrac{{0.6 \times 1000}}{{M \times 50}}$​ ... (ii)
Now divide equation (i) by (ii) we get,
$\dfrac{{0.4}}{{0.65}} = \dfrac{{0.5 \times M}}{{0.65 \times 128}}$​
$ \Rightarrow M = 94.523$
Therefore the molar mass of unknown solute is 94.523 g.

Additional information:
There are different methods for the determination of atomic mass, as there are various properties that can be studied with the help of atomic mass of the element.
- Dulong and Petit’s law
- Cannizzaro method
- The law of isomorphism
- Atomic mass from vapour density of a chloride

Note:
Molality is also known as molal concentration. It is a measure of solute concentration in a solution. The solution is composed of two components; solute and solvent. It is the favoured concentration transmission approach because the solution’s mass of solute and solvent does not change. There are many different ways to express the concentration of solutions like molarity, molality, normality, formality, volume percentage, weight percentage and part per million.