(a) Define the following terms:
(i) Mole fraction (ii) Van't Hoff factor
(b) `100mg` of a protein is dissolved in enough water to make `10.0 mL` of a solution. If this solution has an osmotic pressure of `13.3 mm Hg` at `25^(@)C`, what is the molar mass of protein?
`(R=0.821 L "atom mol"^(-1)K^(-1) "and" 760mm Hg=1` atm.)

Answer

(a) (i) Mole fraction: Mole fraction is the ratio of any one component of the solution with respect to total mole of solution.
(ii) Van't Hoff factor: Van't Hoff factor is the ratio of calculated molar mass with respect of normal molar mass
`i=(MC)/(MO)=("Calculated molar mass")/("Observed molar mass")`
(b) `W=100xx10^(-3)gm`.
`V=10 ml "or" 10cm^(3)`
`1` atm `=760mm`
`1mm=(1)/(760)` atm
`13.3mm=(13.3)/(760)` atm `=0.0175atm
`T=273+25=298K`
`PV=nRT`
`PV=(W)/(M)RT`
`PVm=WRT`
`m=(100xx10^(-3)xx0.0821xx298)/(0.0175xx10)`
`m=(0.0275xx10^(-3))/)0.0175)=0.157xx10^(-3)gm`