20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is ______ $\times 10^{-3}$ $^{\circ}\mathrm{C}$. Atomic mass of C, H and O are 12, 1 and 16 a.m.u. respectively. [Given: Molal depression constant and density of water are $1.86~\mathrm{K~kg~mol}^{-1}$ and $1~\mathrm{g~cm}^{-3}$ respectively.]

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Solutions

20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is ______

\times 1 0^{- 3}

^{\circ} C

. Atomic mass of C, H and O are 12, 1 and 16 a.m.u. respectively.
[Given: Molal depression constant and density of water are

1.86 K kg mol^{- 1}

and

1 g cm^{- 3}

respectively.]

Answer: 372

Solution

Acetic acid has molar mass

60

g mol

^{- 1}

, so

5

g is

\frac{5}{60}

mol dissolved in

500

g, that is

0.5

kg, of water, giving a molality of

\frac{1}{6}

mol kg

^{- 1}

. With one-fifth of the acid dissociating into two ions, the van't Hoff factor is

i = 1 + α = 1.2

. The depression of freezing point is

Δ T_{f} = i K_{f} m = 1.2 \times 1.86 \times \frac{1}{6} = 0.372

K, which equals

372 \times 1 0^{- 3}^{\circ} C

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Solutions →

More JEE Main questions on Solutions

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $PQ_{2}$ . When 1 g of PQ is dissolved in 50 g of solvent 'A', $Δ T_{b}$ was 1.176 K while when 1 g of $PQ_{2}$ is dissolved in 50 g of solvent 'A', …
JEE Main 2026View solution →
Consider a solution of $CO_{2} (g)$ dissolved in water in a closed container.

Which one of the following plots correctly represents variation of log (partial pressure of CO2 in vapour phase above water) [y-axis] with log (mole fraction of $CO_{2}$ …
JEE Main 2026View solution →
Given below are two statements:

Statement I: The Henry's law constant $K_{H}$ is constant with respect to variations in solution's concentration over the range for which the solutions is ideally dilute.
Statement II : $K_{H}$ does not diff …
JEE Main 2026View solution →
The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is $____$ $g L^{- 1}$ . (Nearest integer)

Given: …
JEE Main 2026View solution →
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass $= 300 g mol^{- 1}$ ) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____$ $\times 1 0^{- 2}$ . (Nearest integer)
[Giv …
JEE Main 2026View solution →
Which one of the following graphs accurately represents the plot of partial pressure of $CS_{2}$ vs its mole fraction in a mixture of acetone and $CS_{2}$ at constant temperature ?
JEE Main 2026View solution →