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Question

The freezing point of an aqueous solution of NaHSO4 is 0.372 oC. The dissociation constant for the reaction
HSO4H++SO24 is 0.4. Find the concentration of NaHSO4 in mol/kg.

[Kf for H2O=1.86 Kkgmol1]
(Assume dilute solution and take molality = molarity)


Solution

Let the molality of NaHSO4 solution be m, then assuming molarity = molality.
HSO4  H+   +   SO24
m(1α)      mα             mα

i=1+1+α=2+α

Effective molality =[Na+]+i[HSO4]
 =m+m(1+α)=m(2+α)
Tf=Kfim
0.372=1.86×m(2+α)
0.2=m(2+α)

Also, Ka=mα21α=0.4
0.22+α×α21α=0.4
α2=0.2(2+α)(1α)
So,
1.2α2+0.2α0.4=0
6α2+α2=0
α=0.5
So, m=0.22.5=0.08 mol/kg

 

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