Identify the correct statement :

Options

A. 0.1 M NaCl and 0.1 M glucose solution are isotonic
B. 0.1 M NaCl and 0.3 M glucose solution are isotonic.
C. The boiling point of 0.1 m aqueous urea solution is less than 0.1 m aqueous KCl solution.
D. The freezing point of 0.1 m glucose solution is less than 0.1 m KCl solution.

Answer

To solve the question of identifying the correct statement among the given options, we will analyze each statement step by step.

### Step 1: Understanding Isotonic Solutions
Isotonic solutions have the same osmotic pressure. The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iCRT \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution
- \( R \) = gas constant
- \( T \) = temperature (in Kelvin)

### Step 2: Analyzing the First Statement
**Statement 1:** "0.1 molar NaCl solution and 0.1 molar glucose solution are isotonic."

- For NaCl:
- \( i = 2 \) (Na⁺ and Cl⁻)
- \( C = 0.1 \)
- \( \pi_{NaCl} = 2 \times 0.1 \times R \times T = 0.2RT \)

- For glucose:
- \( i = 1 \) (does not dissociate)
- \( C = 0.1 \)
- \( \pi_{glucose} = 1 \times 0.1 \times R \times T = 0.1RT \)

Since \( \pi_{NaCl} \neq \pi_{glucose} \), they are not isotonic. **This statement is incorrect.**

### Step 3: Analyzing the Second Statement
**Statement 2:** "0.1 molar NaCl and 0.3 molar glucose solution is isotonic."

- For NaCl:
- \( \pi_{NaCl} = 2 \times 0.1 \times R \times T = 0.2RT \)

- For glucose:
- \( i = 1 \)
- \( C = 0.3 \)
- \( \pi_{glucose} = 1 \times 0.3 \times R \times T = 0.3RT \)

Since \( \pi_{NaCl} \neq \pi_{glucose} \), they are not isotonic. **This statement is incorrect.**

### Step 4: Analyzing the Third Statement
**Statement 3:** "The boiling point of 0.1 molal aqueous urea solution is less than 0.1 molal aqueous KCl solution."

- For urea:
- \( i = 1 \)
- \( \Delta T_b = i \cdot K_b \cdot m = 1 \cdot K_b \cdot 0.1 = 0.1K_b \)

- For KCl:
- \( i = 2 \)
- \( \Delta T_b = 2 \cdot K_b \cdot 0.1 = 0.2K_b \)

Since \( \Delta T_b(KCl) > \Delta T_b(Urea) \), the boiling point of urea is indeed less than that of KCl. **This statement is correct.**

### Step 5: Analyzing the Fourth Statement
**Statement 4:** "The freezing point of 0.1 molar glucose solution is less than 0.1 molar KCl solution."

- For glucose:
- \( i = 1 \)
- \( \Delta T_f = i \cdot K_f \cdot m = 1 \cdot K_f \cdot 0.1 = 0.1K_f \)

- For KCl:
- \( i = 2 \)
- \( \Delta T_f = 2 \cdot K_f \cdot 0.1 = 0.2K_f \)

Since \( \Delta T_f(KCl) > \Delta T_f(glucose) \), the freezing point of glucose is actually greater than that of KCl. **This statement is incorrect.**

### Conclusion
The only correct statement among the options provided is:
**The boiling point of 0.1 molal aqueous urea solution is less than 0.1 molal aqueous KCl solution.**

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