Question

\(5\) g urea is dissolved in \(100\) g water. Find the amount of glucose to be dissolved in \(120\) g of water so that the boiling points of both solutions will be the same.
[Molar mass of urea \(= 60\) g \(\text{mol}^{-1}\) & Molar mass of glucose \(= 180\) g \(\text{mol}^{-1}\)]

• A. \(17\) g
• B. \(19\) g
• C. \(18\) g
• D. \(20\) g

Hint:

Set the two molalities equal and solve for the glucose mass.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Elevation in boiling point is \(\Delta T_b = K_b m\). Both solutes are non-electrolytes, so the boiling points are equal when the molalities are equal.

Step 2: Molality of urea solution:
Moles of urea \(= 5/60 = 0.0833\). Mass of water \(= 100\) g \(= 0.1\) kg.
\[ m = \frac{0.0833}{0.1} = 0.833\ \text{mol/kg} \]

Step 3: Glucose solution:
Let the mass of glucose be \(w\) g. Moles \(= w/180\), and water is \(0.12\) kg.
\[ \frac{w/180}{0.12} = 0.833 \]

Step 4: Solve:
\[ w = 0.833\times 0.12\times 180 = 18\ \text{g} \]

Step 5: Choose:
The answer is 18 g, option (C).

Final Answer:
Equal molality gives 18 g of glucose. \[ \boxed{18\ \text{g}} \]