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. `3.17xx10^(6)`
B. `4.17xx10^(6)`
C. `5.17xx10^(6)`
D. `6.17xx10^(6)`

Answer

C

Explanation

`pi=C'RT`. Hence concentration C' is in `"mol L"^(-1)` To convert `"g cm"^(-3)` into `"mol L"^(-1)`, we have
Thus, C' in the formula should be replaced by this factor, i.e.,
`pi=(Cxx1000)/(M_(2))RT=(1000RT)/(M_(2))C`
Thus, a plot of `pi` vs C will be linear with slope
`=(1000RT)/(M_(2))=4.65xx10^(-3)" (Given)"`
`therefore (1000xx0.0821xx293)/(M_(2))=4.65xx10^(-3)`
`"or "M_(2)=5.17xx10^(6)`