Question

Boiling point of water at 750mmHg is 96.63$^{\circ }C$ . How much sucrose is added to 500g of water such that it boils at ${{100}^{\circ }}C$ . Molal elevation constant (${{K}_{b}}$ ) of ${{H}_{2}}O$ is $0.52K.kg.mo{{l}^{-1}}$

Answer 1

Hint: elevation in boiling point of the solvent occurs when a non-volatile solute is added to the solvent. This question can be solved by using the relationship between elevation in boiling point and molality which is $\Delta {{T}_{b}}={{K}_{b}}\times \dfrac{{{w}_{solute}}}{{{M}_{solute}}}\times \dfrac{1000}{{{w}_{solvent}}}$.

Complete step by step solution:
The boiling point of solvent increases in a solution when a solute is added to the solvent and this change in boiling point is directly proportional to the molal concentration (molality) of the solution formed. Mathematically it can be represented as
$\Delta {{T}_{b}}={{K}_{b}}\times molality$
$\Delta {{T}_{b}}={{K}_{b}}\times \dfrac{{{w}_{solute}}}{{{M}_{solute}}}\times \dfrac{1000}{{{w}_{solvent}}}$ …(i)
Where, $\Delta {{T}_{b}}=$ elevation in boiling point $=100-96.63={{3.37}^{\circ }}C=3.37K$ (given in the question)
${{K}_{b}}=$ Molal elevation constant$=0.52K.kg.mo{{l}^{-1}}$
${{w}_{solute}}=$ given mass of solute (sucrose in this case)
${{M}_{solute}}=$ molar mass of solute(sucrose)
${{M}_{solute}}=$ molar mass of sucrose (${{C}_{12}}{{H}_{22}}{{O}_{11}}$ )$=12\times 12+22\times 1+11\times 16=342g/mol$
${{w}_{solvent}}=$ given mass of water$=500g$
On rearranging equation (i), we get,
${{w}_{solute}}=\Delta {{T}_{b}}\times \dfrac{{{w}_{solvent}}}{{{K}_{b}}}\times \dfrac{{{M}_{solute}}}{1000}$
\[\begin{align}
& {{w}_{sucrose}}=3.37\times \dfrac{500\times 342}{0.52\times 1000} \\
& {{w}_{sucrose}}=1108.21g \\
\end{align}\]
Therefore, 1108.21g of sucrose is added to 500g of water such that it boils at ${{100}^{\circ }}C$ .

Additional information:
Boiling point elevation is one of the four colligative properties of a solution.
A colligative property is a property of a solution that is dependent on the ratio between the number of solute particles to the total number of solvent particles and independent of the nature of or type of solute being added in the solution. The other three colligative properties are freezing point depression, relative lowering of vapour pressure, and osmotic pressure.
The change in boiling point of solution depends upon the concentration of solute added and not on the kind, size or charge of particles of solute added.

Note: Molal elevation constant ${{K}_{b}}$ is different for different solvents. Molal elevation constants are also called Ebullioscopic constants.