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Question: Boiling point of water at 750 mm Hg is \( {99.63^ \circ } \) C. How much sucrose is to be added to 5...

Boiling point of water at 750 mm Hg is 99.63∘{99.63^ \circ } C. How much sucrose is to be added to 500 g of water such that it boils at 100∘{100^ \circ } C.

Explanation

Solution

Colligative properties are the properties of solution. Colligative properties depend only on the number of solute particles and not on the nature of solute particles. But it depends on the nature of solvent particles. To solve this question, we will use the colligative property of elevation in boiling point.
Formula used: ΔTb=iKb×m\Delta {T_b} = i{K_b} \times m
Where m is the molality, i is the Van’t Hoff Factor, ΔTb\Delta {T_b} is the change in boiling point and Kb{K_b} is the boiling point constant.

Complete step by step solution:
In the given question, the colligative property to be used is elevation in boiling point. Elevation in boiling point is a phenomenon in which the boiling point of a solvent will be higher when compound is added to it as compared to the boiling point of pure solvent. This happens when non-volatile solute is added to pure solvent. The formula to be used here is,
ΔTb=iKb×m\Delta {T_b} = i{K_b} \times m
where ΔTb\Delta {T_b} is the difference in the temperature between solution and pure solvent. 'i' is the van’t Hoff factor. It accounts for the number of ions formed by the compound in the solution. For non-electrolyte the value of i is 1. Here the value of i is 1. Kb{K_b} is the ebullioscopic constant or boiling point elevation constant. 'm' is the molality.
Here, ΔTb=100−99.63=0.37∘\Delta {T_b} = 100 - 99.63 = {0.37^ \circ }
For sucrose, Kb=0.52{K_b} = 0.52
Let x be the amount of sucrose to be added in g. Molality of a solute is defined as number of moles of solute divided by weight of solvent in kg. The number of moles is equal to the given weight divided by the molar mass. The molar mass of sucrose is 342 g/mol. Hence, molality is given as follows,
Molality(m) = x×1000342×500 = x171{\text{Molality(m) = }}\dfrac{{x \times 1000}}{{342 \times 500}}{\text{ = }}\dfrac{x}{{171}}
Now, ΔTb=iKb×m\Delta {T_b} = i{K_b} \times m
Substituting the values,
0.37=0.52×x1710.37 = 0.52 \times \dfrac{x}{{171}}
∴x=121.67 g\therefore x = 121.67{\text{ g}}
Therefore, the amount of sugar to be added is 121.67121.67 g.

Note:
The boiling point can be measured accurately using an ebullioscope.
There are four colligative properties of solution which are as follows,
-Elevation in boiling point
-Depression in freezing point
-Osmotic pressure
-Relative lowering of vapour pressure.