To determine which solution has the lowest freezing point, we need to consider the effect of the solute on the freezing point, known as freezing point depression. The freezing point depression can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( \Delta T_f \) is the change in freezing point,
- \( i \) is the van 't Hoff factor (the number of particles the solute dissociates into),
- \( K_f \) is the freezing point depression constant (specific to the solvent), and
- \( m \) is the molality of the solution.
In the case of NaCl, it dissociates into two ions: Na\(^+\) and Cl\(^-\), so \( i = 2 \).
Now, we can calculate the effective concentration of particles in each solution:
-
0.25 M NaCl: \[ i \cdot m = 2 \times 0.25 = 0.5 \]
-
0.5 M NaCl: \[ i \cdot m = 2 \times 0.5 = 1.0 \]
-
1.0 M NaCl: \[ i \cdot m = 2 \times 1.0 = 2.0 \]
-
1.5 M NaCl: \[ i \cdot m = 2 \times 1.5 = 3.0 \]
-
2.0 M NaCl: \[ i \cdot m = 2 \times 2.0 = 4.0 \]
The more particles present in solution, the greater the freezing point depression. Therefore, the solution with the highest value of \( i \cdot m \) will have the lowest freezing point.
From the calculations:
- 0.25 M NaCl → 0.5
- 0.5 M NaCl → 1.0
- 1.0 M NaCl → 2.0
- 1.5 M NaCl → 3.0
- 2.0 M NaCl → 4.0
The solution with the lowest freezing point is 2.0 M NaCl (Option E).