Chemistry Q55 – JEE-MAIN 2026

Home Chemistry Basic ChemistryQuestion #35

19.5 g of fluoro acetic acid (molar mass = 78 g mol

^{- 1}

) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1°C. What is

K_{a}

of fluoro acetic acid ? (For water,

K_{f}

=1.86 K kg mol

^{- 1}

). Assume molarity and molality to have same values.

Clue 1 of 3: Colligative Properties and Dissociation

The depression in freezing point depends on the total number of particles in the solution, which is affected by the dissociation of the weak acid.

🧠 Full Solution Path

Step 1: Calculate Molality and Van't Hoff Factor✦ Active

First, calculate the moles of fluoro acetic acid and the molality of the solution. Then, use the freezing point depression formula to find the Van't Hoff factor ( $i$ ). Moles of fluoro acetic acid ( $n_{2}$ ) = $\frac{Mass}{Molar Mass} = \frac{19.5 g}{78 g/mol} = 0.25 mol$ . Mass of water ( $w_{1}$ ) = $500 g = 0.5 kg$ . Molality ( $m$ ) = $\frac{n_{2}}{w_{1} (kg)} = \frac{0.25 mol}{0.5 kg} = 0.5 mol/kg$ . Using the freezing point depression formula: $Δ T_{f} = i K_{f} m$ .

1 = i \times 1.86 {K kg mol}^{- 1} \times 0.5 mol/kg

1 = i \times 0.93

i = \frac{1}{0.93} \approx 1.07526

Step 2: Determine the Degree of Dissociation (

α

)○ Expand

For a weak acid (HFA) that dissociates into two ions (H $^{+}$ and FA $^{-}$ ), the Van't Hoff factor ( $i$ ) is related to the degree of dissociation ( $α$ ) by the formula $i = 1 + α$ .

α = i - 1

α = 1.07526 - 1 = 0.07526

Step 3: Calculate the Acid Dissociation Constant (

K_{a}

)○ Expand

The acid dissociation constant ( $K_{a}$ ) for a weak acid is given by the expression $K_{a} = \frac{C α^{2}}{1 - α}$ , where $C$ is the initial concentration (molality in this case, as molarity and molality are assumed to be same).

K_{a} = \frac{0.5 \times (0.07526)^{2}}{1 - 0.07526}

K_{a} = \frac{0.5 \times 0.005664}{0.92474}

K_{a} = \frac{0.002832}{0.92474} \approx 0.003062

Rounding this value, $K_{a} \approx 3 \times 10^{- 3}$ .

💡 Teacher's Secret Hint

Ensure to use the correct formula for $K_{a}$ in terms of $C$ and $α$ for a weak acid.

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Chemistry Question 55 – JEE-MAIN 2026

Clue 1 of 3: Colligative Properties and Dissociation

🧠 Full Solution Path