Question

A saline solution begins to freeze at -1.13°C. Express the concentration of NaCl in this solution in mass %. Kf for water is 1.86°C m-1.

A)0.870%

B)8.90%

C)3.48%

D)17.8%

E)1.74%

Answer 1

We know that ΔT _f = iK_f x m
Where

ΔT _f = depression in freezing point

        = freezing point of pure solvent – freezing point of solution

        = 0 - ( -1.13 )

= 1.13 oC

K _f = depression in freezing constant of water = 1.86 oC / m

i= vanthoff’s factor = 2 ( NaCl ---> Na+ + Cl- )

m = molality of the solution

    = ( mass / Molar mass ) / weight of the solvent in Kg

Plug the values we get m = 0.0304 m

molality is the number of moles of solute present in 1 kg of the solvent

0.0304 m menas 0.0304 moles of NaCl present in 1000 g of solvent water

0.0304 moles x ( 58.5 g/mol) = 17.4 g of NaCl present in 1000 kg of solvent

OR 1.78 g of NaCl present in 100 g of water

So mass percent of NaCl is 1.74 %

So option (E) is correct