An aqueous solution of 0.01 m KCl cause the same elevation in boiling point as an aqueous solution of urea. The concentration of urea solution is :

Options

A. (a) 0.01 m
B. (b) 0.005 m
C. (c) 0.02 m
D. (d) 0.04 m

Answer

To solve the problem, we need to determine the concentration of urea solution that causes the same elevation in boiling point as a 0.01 m KCl solution. We will use the formula for boiling point elevation, which is given by:

\[ \Delta T_b = i \cdot K_b \cdot m \]

where:
- \(\Delta T_b\) is the elevation in boiling point,
- \(i\) is the Van't Hoff factor,
- \(K_b\) is the molal elevation constant of the solvent,
- \(m\) is the molality of the solution.

### Step 1: Identify the Van't Hoff factor for KCl
KCl dissociates into two ions in solution: K\(^+\) and Cl\(^-\). Therefore, the Van't Hoff factor \(i\) for KCl is:

\[ i_{KCl} = 2 \]

### Step 2: Identify the Van't Hoff factor for urea
Urea is a non-electrolyte, which means it does not dissociate into ions in solution. Thus, the Van't Hoff factor \(i\) for urea is:

\[ i_{urea} = 1 \]

### Step 3: Set up the equation for boiling point elevation
Since the elevation in boiling point for both solutions is the same, we can set up the equation:

\[ i_{KCl} \cdot K_b \cdot m_{KCl} = i_{urea} \cdot K_b \cdot m_{urea} \]

### Step 4: Substitute known values into the equation
Substituting the known values into the equation:

\[ 2 \cdot K_b \cdot 0.01 = 1 \cdot K_b \cdot m_{urea} \]

### Step 5: Cancel out \(K_b\)
Since \(K_b\) is the same for both solutions (as they are both aqueous), we can cancel it out from both sides:

\[ 2 \cdot 0.01 = m_{urea} \]

### Step 6: Calculate the molality of urea
Now, we can calculate the molality of the urea solution:

\[ m_{urea} = 0.02 \]

### Conclusion
The concentration of the urea solution is:

\[ \text{Concentration of urea solution} = 0.02 \, m \]