If a "62.4 g/L" solution of bovine insulin in an appropriate solvent achieves an osmotic pressure of "0.305 atm" at "298 K", estimate the molar mass?

a) "10000 g/mol"
b) "5000 g/mol"
c) "506887 g/mol"
d) "5069 g/mol"

1 Answer
Doc048 ยท Truong-Son N.
Jun 3, 2017

Formula Wt Insulin ~ 5000 g/mole*

Explanation:

Using the Osmotic Pressure Equation*

Pi = MRT = ("moles"/"Vol"_L)*R*T

=> "moles" = (Pi*"Vol"_L)/("R"cdot"T") = "mass(g)"/"f.wt."

=> f.wt. = ("mass(g)"cdot"R"cdot"T")/(Picdot"Vol"_L)

=> f.wt. = (("62.4 g")("0.08206 L"cdot"atm"cdot"mol"^(-1)cdotK^(-1))("298 K"))/(("0.305 atm")("1.00 L")

=> f.wt. = "5000 g"/"mol"

Note: the method of mole weight analysis is not specified. That is, the 5808 mole wt. value is perhaps a weight average mole weight (mass fraction analysis), whereas the 5000 mole wt. calculation is based upon Pi, which is a colligative property and defines 'number average' mole weight values (size/chain length fraction analysis).

The calculation using the osmotic pressure equation is correctly done but is a colligative property dependent relationship which will typically give lower values than other methods defining weight average mole weights.

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