Question
Sea water is $$3.5\% $$ by mass of common salt and has a density $$1.04\,g\,c{m^{ - 3}}$$ at $$293\,K.$$ Assuming the salt to be sodium chloride, then osmotic pressure of sea water will be ( assume complete ionisation of the salt )
A.
$$25.45\,atm$$
B.
$$11.56\,atm$$
C.
$$29.98\,atm$$
D.
$$30.20\,atm$$
Answer :
$$29.98\,atm$$
Solution :
$$\eqalign{
& {\rm{Let}}\,\,{\rm{mass}}\,\,{\rm{of}}\,\,{\rm{solution}}\,\,{\rm{be}}\,\,{\rm{100 g}}{\rm{.}} \cr
& {\rm{Volume}}\,\,{\rm{of}}\,\,{\rm{solution}} \cr
& = {{{\rm{Mass}}} \over {{\rm{Density}}}} \cr
& = {{100} \over {1.04}} \cr
& = 96.154\,mL \cr
& = 0.096\,L \cr} $$
$${w_B} = 3.5\,g;{M_B} = 58.5\,g\,mo{l^{ - 1}}$$ ( molar mass of $$NaCl$$ )
For complete ionisation of $$NaCl,$$ van't Hoff factor will be $$'2'.$$
$$\eqalign{
& i = 2, \cr
& {\rm{we}}\,\,{\rm{know,}} \cr
& \pi = iCRT \cr
& \,\,\,\, = i{n \over V}RT \cr
& \,\,\, = 2 \times {{3.5 \times 0.0821 \times 293} \over {58.5 \times 0.096}} \cr
& \,\,\, = 29.98\,atm \cr} $$