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

Answer:

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.