Insulin `(C_(2)H_(10)O_(5))_(n)` is dissolved in a suitable solvent and the osmotic pressure `(pi)` of solutions of various concentrations `(g//cm^(3))C` is measured at `20^(@)C`. The slope of a plot of `pi` against `C` is found to be `4.65 xx 10^(-3)`. The molecular weight of insulin is:

Options

A. `4.8 xx 10^(5)`
B. `9 xx 10^(5)`
C. `3 xx 10^(5)`
D. `5.16 xx 10^(6)`

Answer

D

Explanation

`pi V = W/M RT, :. pi = W/V (RT)/M`
`pi = C(RT)/M (C is in g/litre)`
`"The plots of" pi vs C (g//cm^(3)) "have slope" = (RT xx 1000)/M`
`:. (RT xx 1000)/M = 4.65 xx 10^(-3)`
`M= (0.0821 xx 293 xx 1000)/(4.65 xx 10^(-3))=5.17 xx 10^(6) g`