# 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) $\text{10000 g/mol}$ b) $\text{5000 g/mol}$ c) $\text{506887 g/mol}$ d) $\text{5069 g/mol}$

Jun 3, 2017

Formula Wt Insulin ~ 5000 g/mole*

#### Explanation:

Using the Osmotic Pressure Equation*

$\Pi = M R T = \left({\text{moles"/"Vol}}_{L}\right) \cdot R \cdot T$

=> $\text{moles" = (Pi*"Vol"_L)/("R"cdot"T") = "mass(g)"/"f.wt.}$

=> $f . w t . = \left({\text{mass(g)"cdot"R"cdot"T")/(Picdot"Vol}}_{L}\right)$

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

=> $f . w t . = \text{5000 g"/"mol}$

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.