Question

The freezing point of a \(0.21 m\) aqueous solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(-0.796^{\circ} \mathrm{C}\) (a) What is i? (b) Is the solution made up primarily of (i) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) molecules only? (ii) \(\mathrm{H}^{+}\) and \(\mathrm{HSO}_{4}^{-}\) ions? (iii) \(2 \mathrm{H}^{+}\) and \(1 \mathrm{SO}_{4}^{2-}\) ions?

Short answer

Question: Determine the van't Hoff factor (i) and which type of ions primarily constitute a 0.21 m aqueous solution of H2SO4, given that its freezing point is -0.796°C. Answer: The van't Hoff factor (i) is 2, and the solution primarily consists of H+ and HSO4- ions.

Step-by-step solution

Recall the freezing point depression formula for finding i

The formula for the freezing point depression is given by: \(\Delta T_{f} = i * K_{f} * m\) Where: \(\Delta T_{f} = T_{f}(\textrm{solvent}) - T_{f}(\textrm{solution})\) \(i\) is the van't Hoff factor (we want to find this) \(K_{f}\) is the molal freezing point depression constant (1.86 °C/mol for water) \(m\) is the molality of the solution, which is 0.21 mol/kg in this case. But in this exercise, we've given a modified freezing point depression formula, which is already expressed as: \(\Delta T_{f} = -0.796^{\circ} \mathrm{C}\)

Rearrange the formula to find i

Since we have the freezing point depression and molality of the solution, we can solve for i: \(i = \frac{\Delta T_{f}}{K_{f} * m}\)

Calculate i

Let's substitute the given values in the equation: \(i = \frac{-0.796\, \mathrm{°C}}{(1.86\, \mathrm{°C/mol})\, * (0.21\, \mathrm{mol/kg})} = 2\) So the calculated i is 2.

Determine which ions predominate in the solution

From the calculated van't Hoff factor (i) of 2, we can now determine which of the given options primarily make up the solution: (i) H2SO4 molecules only: This would result in an i value of 1 (no dissociation). This option contradicts with the calculated i of 2. (ii) H+ and HSO4- ions: This dissociation would lead to an i value of 2, consistent with the calculated i. (iii) 2H+ and SO4^(2-): This dissociation would result in an i value of 3 (three ions in total). This option contradicts with the calculated i of 2. Therefore, based on the calculated i value, the solution primarily consists of H+ and HSO4- ions (option ii).