91Ó°ÊÓ

Osmotic pressure can be defined as the minimum pressure that must be applied to a solution to halt the flow of solvent molecules through a semipermeable membrane (osmosis).

Molar Mass may be defined as the ratio of Mass and Molar Mass.

First, since the ideal gas constant is in units of (L atm mol^–1 ·°­^–1), convert the osmotic pressure to atmospheres. For the same reason, convert the temperature from °C to kelvin.

\(\begin{aligned}{\rm{1}}\;{\rm{atm}} &= \;{\rm{760}}\;{\rm{torr}}\\\dfrac{{{\rm{23}}\;{\rm{torr}}\;{\rm{ \times 1}}\;{\rm{atm}}}}{{{\rm{760}}}} &= \;{\rm{0}}{\rm{.030}}\;{\rm{atm}}\end{aligned}\)

\(\begin{aligned}{\rm{M}} &= \;\dfrac{{\rm{\Pi }}}{{{\rm{RT}}}}\\{\rm{M}} &= \;\dfrac{{{\rm{0}}{\rm{.030}}\;{\rm{atm}}}}{{\left( {{\rm{0}}{\rm{.08206}}\;{\rm{L}}\;{\rm{atm}}\;{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\;{{\rm{K}}^{{\rm{ - 1}}}}} \right){\rm{ \times }}\left( {{\rm{298}}{\rm{.15}}\;{\rm{K}}} \right)}}\\{\rm{M}} &= \;{\rm{1}}{\rm{.23 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{M}}\end{aligned}\)

\(\begin{aligned}{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} &= \;{\rm{mass \times volume}}\;{\rm{(in}}\;{\rm{liters)}}\\{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} &= \;\left( {{\rm{1}}{\rm{.23 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{M}}} \right)\left( {{\rm{1L}}} \right)\\{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} &= \;{\rm{1}}{\rm{.23 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{M}}\end{aligned}\)

\(\begin{aligned}{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} &= \;\dfrac{{{\rm{Mass}}}}{{{\rm{Molar}}\;{\rm{Mass}}}}\\{\rm{1}}{\rm{.23 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{M}} &= \;\dfrac{{{\rm{7}}\;{\rm{g}}}}{{{\rm{Molar}}\;{\rm{Mass}}}}\\{\rm{Molar}}\;{\rm{mass}} &= \;{\rm{5}}{\rm{.7 \times 1}}{{\rm{0}}^{\rm{3}}}\;{\rm{g}}\;{\rm{mol}}{{\rm{e}}^{{\rm{ - 1}}}}\end{aligned}\)

The Molar Mass of Insulin \({\rm{ = }}\;{\rm{5}}{\rm{.7 \times 1}}{{\rm{0}}^{\rm{3}}}{\rm{g mo}}{{\rm{l}}^{{\rm{-1}}}}\) .