i) 0.5g of KCl was dissolved in 100g of water and the solution originally at 20 0C froze at -0.24 0C. Calculate the percentageionization of the salt. Kf for water is 1.86 KKgmol-1

To calculate the percentage ionization of the salt, we first need to calculate the molality and then the theoretical freezing point depression.

Step 1: Calculate the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent.

First, we need to convert the mass of KCl to moles. The molar mass of KCl is approximately 74.55 g/mol.

Number of moles = mass/molar mass = 0.5g / 74.55 g/mol = 0.0067 mol

The mass of water needs to be converted to kilograms: 100g = 0.1 kg

So, molality (m) = number of moles / mass of solvent in kg = 0.0067 mol / 0.1 kg = 0.067 mol/kg

Step 2: Calculate the theoretical freezing point depression (ΔTf). The freezing point depression can be calculated using the formula ΔTf = Kf * m * i, where Kf is the cryoscopic constant for water (1.86 K kg/mol), m is the molality, and i is the van't Hoff factor (number of particles the solute splits into in solution). For KCl, i is 2 because it dissociates into two ions (K+ and Cl-).

Theoretical ΔTf = 1.86 K kg/mol * 0.067 mol/kg * 2 = 0.2492 K

Step 3: Calculate the experimental freezing point depression (ΔTf). The experimental ΔTf is the difference between the freezing point of the pure solvent and the freezing point of the solution. For water, the freezing point is 0°C.

Experimental ΔTf = 0°C - (-0.24°C) = 0.24 K

Step 4: Calculate the percentage ionization. The percentage ionization can be calculated by dividing the experimental ΔTf by the theoretical ΔTf and multiplying by 100%.

Percentage ionization = (Experimental ΔTf / Theoretical ΔTf) * 100% = (0.24 K / 0.2492 K) * 100% = 96.3%

So, the percentage ionization of the salt is approximately 96.3%.