The average osmotic pressure of human blood is 7.7 atm at `40^(@)C`. (a) What would be the total concentration of the various solutes in the blood ? (b) Assuming the concentration to be essentially the same as the molality, find the freezing point of blood `(K_(f)" for water = "1.86^(@)C).`

Explanation

(a) We are given that `"P = 7.7 atm, T"=40^(@)=C=40+273=313K`
`"R = 0.0821 litre atm/degree/mole"`
`"According to van't Hoff equation, "pi=CRT therefore C=(pi)/(RT)=("7.7 atm")/("0.0821 L atm K"^(-1)"mol"^(-1)xx313K)="0.30 mole/litre"`
(b) Taking the molar concentration as equal to molality (Given), we have
`"m = 0.30, "K_(f)=1.86^(@)C" (Given)"`
`therefore" "DeltaT_(f)=K_(f)xxm=1.86xx0.30=0.558^(@)C`
`therefore" Freezing point of blood "=0^(@)C-0.558^(@)=-0.558^(@)C`