In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf or water as 1.85, the freezing point of the solution will be nearest to

To find the freezing point of a 0.2 molal aqueous solution of a weak acid HX with a degree of ionization of 0.3, we can use the concept of freezing point depression. This phenomenon occurs when a solute is added to a solvent, lowering the freezing point of the solvent. The formula to calculate the freezing point depression is:

Freezing Point Depression Formula

The formula is given by:

ΔTf = i × Kf × m

• ΔTf = change in freezing point
• i = van 't Hoff factor (number of particles the solute breaks into)
• Kf = freezing point depression constant of the solvent (for water, Kf = 1.85 °C kg/mol)
• m = molality of the solution

Calculating the Van 't Hoff Factor

For a weak acid like HX, it partially ionizes in solution. The degree of ionization (α) is given as 0.3, meaning that 30% of the acid dissociates into ions. The dissociation can be represented as:

HX ⇌ H⁺ + X^-

In a 0.2 molal solution, the concentration of HX is 0.2 mol/kg. The degree of ionization tells us how many moles of HX dissociate:

Ionized moles = 0.2 mol × 0.3 = 0.06 mol

This means that 0.06 moles of HX dissociate into 0.06 moles of H⁺ and 0.06 moles of X^-. Therefore, the total number of moles of particles in solution is:

Total moles = moles of undissociated HX + moles of ions = (0.2 - 0.06) + 0.06 + 0.06 = 0.2 mol

Thus, the van 't Hoff factor (i) is:

i = 1 + α = 1 + 0.3 = 1.3

Calculating Freezing Point Depression

Now that we have the values needed, we can substitute them into the freezing point depression formula:

ΔTf = i × Kf × m

Substituting the values:

ΔTf = 1.3 × 1.85 °C kg/mol × 0.2 mol/kg

ΔTf = 1.3 × 1.85 × 0.2 = 0.481 °C

Finding the New Freezing Point

The normal freezing point of pure water is 0 °C. To find the new freezing point of the solution, we subtract the freezing point depression from the normal freezing point:

New Freezing Point = 0 °C - ΔTf

New Freezing Point = 0 °C - 0.481 °C = -0.481 °C

Therefore, the freezing point of the 0.2 molal aqueous solution of the weak acid HX will be approximately -0.48 °C. This means the solution will freeze at a temperature slightly below the freezing point of pure water, demonstrating the effect of solute on the freezing point of a solvent.