Which of the following solution will have the highest boiling point ?

Options

A. 1% solution of glucose in water
B. 1% solution of sucrose in water
C. 1% solution of sodium chloride in water
D. 1% solution of calcium chloride in water

Answer

To determine which solution has the highest boiling point, we can use the concept of boiling point elevation, which is influenced by the number of solute particles in the solution. The formula for boiling point elevation is given by:

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

Where:
- \(\Delta T_b\) = boiling point elevation
- \(i\) = van 't Hoff factor (number of particles the solute breaks into)
- \(K_b\) = ebullioscopic constant of the solvent (which is constant for all solutions in this case)
- \(m\) = molality of the solution

Since we are comparing 1% solutions, we can assume the mass of the solvent (water) is approximately 99 g for each solution. We will calculate the van 't Hoff factor \(i\) and the molality \(m\) for each solute.

### Step 1: Calculate the molar mass of each solute and their respective \(i\) values.

1. **Glucose (C6H12O6)**:
- Molar mass = 6(12) + 12(1) + 6(16) = 180 g/mol
- \(i = 1\) (does not dissociate)
- Molality \(m = \frac{1 \text{ g}}{180 \text{ g/mol}} = 0.00556 \text{ mol/kg}\)

2. **Sucrose (C12H22O11)**:
- Molar mass = 12(12) + 22(1) + 11(16) = 342 g/mol
- \(i = 1\) (does not dissociate)
- Molality \(m = \frac{1 \text{ g}}{342 \text{ g/mol}} = 0.00292 \text{ mol/kg}\)

3. **Sodium Chloride (NaCl)**:
- Molar mass = 23 + 35.5 = 58.5 g/mol
- \(i = 2\) (dissociates into Na⁺ and Cl⁻)
- Molality \(m = \frac{1 \text{ g}}{58.5 \text{ g/mol}} = 0.0171 \text{ mol/kg}\)

4. **Calcium Chloride (CaCl2)**:
- Molar mass = 40 + 2(35.5) = 111 g/mol
- \(i = 3\) (dissociates into Ca²⁺ and 2 Cl⁻)
- Molality \(m = \frac{1 \text{ g}}{111 \text{ g/mol}} = 0.00901 \text{ mol/kg}\)

### Step 2: Calculate the effective concentration for boiling point elevation.

Now we can calculate the product \(i \cdot m\) for each solute:

1. **Glucose**:
\[ i \cdot m = 1 \cdot 0.00556 = 0.00556 \]

2. **Sucrose**:
\[ i \cdot m = 1 \cdot 0.00292 = 0.00292 \]

3. **Sodium Chloride**:
\[ i \cdot m = 2 \cdot 0.0171 = 0.0342 \]

4. **Calcium Chloride**:
\[ i \cdot m = 3 \cdot 0.00901 = 0.02703 \]

### Step 3: Compare the values.

Now we compare the \(i \cdot m\) values:

- Glucose: 0.00556
- Sucrose: 0.00292
- Sodium Chloride: 0.0342
- Calcium Chloride: 0.02703

### Conclusion:

The solution with the highest boiling point will be the one with the highest \(i \cdot m\) value, which is **Sodium Chloride (NaCl)** with a value of 0.0342.

### Final Answer:
**Sodium Chloride (NaCl) solution will have the highest boiling point.**

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