Q. Depression of freezing point of 0.01 molal aqueous Acetic Acid solution is 0.0204 degree Celsius. 1 molal urea solution freezes at -1.86 degree Celsius. Assuming molality equal to molarity, pH of Acetic Acid solution.

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Solution

freezing point depression equation:

ΔT = iK_fm
where
ΔT = Change in temperature in °C
i = van 't Hoff factor
K_f =molal freezing point depression constant or cryoscopic constant in °C kg/mol
m = molality of the solute in mol solute/kg solvent
1 molal urea solution freezes at -1.86 degree celsius
1.86=K_{f }1
K_f=1.86
Using value of K_f
Find value of i
ΔT=K_fm*i
ie,0.0204=1.86i.01
{Given m=0.01 K_f=1.86
and ΔT=0.0204}
so i=0.0204/(1.86.01)
=1.1
CH₃CO₂H → CH₃CO₂⁻ + H^{+ {ionization releasing proton}}
(c-α) cα cα
i=1+α
α=1.1-1=0.1
[H+]=cα =0.010.1=0.001
pH=-log[H+]=-log 0.001= 3 Answer

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