Correct increasing order of freezing point of \(1 M\) solution :

A. \(Na_3(PO_4) > K_2SO_4 > NaCl > K_4[Fe(CN)_6]\)

B. \(K_4[Fe(CN)_6] < Na_3(PO_4) < K_2SO_4 < NaCl\)

C. \(Na_3(PO_4) < K_2SO_4 < NaCl < K_4[Fe(CN)_6]\)

D. \(NaCl > K_2SO_4 > Na_3(PO_4) > K_4[Fe(CN)_6]\)

E. \(K_2SO_4 > NaCl > K_4[Fe(CN)_6] > Na_3(PO_4)\)

Choose the correct answer from the options given below:

B only

The correct answer is option 2. B only.

To determine the correct order of freezing points for the given \(1 M\) solutions, we can use the principle of colligative properties, which states that the freezing point depression of a solvent is directly proportional to the molality (moles of solute per kilogram of solvent) of the solute particles in the solution.

The freezing point depression equation is given by:

\(\Delta T_f = i \cdot K_f \cdot m \)

Where:

\( \Delta T_f \) = Freezing point depression

\( i \) = Van't Hoff factor (number of particles formed in solution)

\( K_f \) = Cryoscopic constant (specific to the solvent)

\( m \) = Molality of the solution

The Van't Hoff factor (\(i\)) for each compound is determined by the number of ions it dissociates into in solution.

Now, let's analyze the given compounds:

1. \(Na_3(PO_4)\): Dissociates into \(4\) ions (\(3 \times Na^+\) and \(1 \times PO_4^{3-}\))

2. \(K_2SO_4\): Dissociates into \(3\) ions (\(2 \times K^+\) and \(1 \times SO_4^{2-}\))

3. \(NaCl\): Dissociates into \(2\) ions (\(1 \times Na^+\) and \(1 \times Cl^-\))

4. \(K_4[Fe(CN)_6]\): Does not dissociate significantly in solution, so it remains as a single entity

Based on this analysis, the compound that dissociates into the most ions will exhibit the greatest freezing point depression and consequently the lowest freezing point.

So, the correct order of increasing freezing point is:

\(K_4[Fe(CN)_6] > Na_3(PO_4) > K_2SO_4 > NaCl \)

Therefore, the correct option is: 2. B only