Question

What is the osmotic pressure (atm) of a solution with a volume of 0.750 L that contains 5.0 g of methanol,\({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH}}\), in water at 37 °C?

Short answer

The osmotic pressure (atm) solution is 5.3 atm.

Step-by-step solution

 Step 1: Osmotic Pressure

Osmotic pressure is defined as the pressure that is exerted on a solvent to prevent it from passing through the osmosis. This is often used to express the concentration of the solution. It is given by

\({\bf{\Pi = iMRT}}\)

where,

π = Osmotic pressure

i= Van't Hoff factor

M = Molarity

R = Ideal gas constant, and

T= Temperature.

Explanation

Mass of Methanol,\({\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{OH}}\)= 5.0 g

Molar Mass of Methanol,\({\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{OH}}\)= 32 g/mole

\({\rm{Number of Moles of Methanol = }}\frac{{{\rm{5 }}}}{{{\rm{32}}}}{\rm{ = 0}}{\rm{.16mole}}\)

Mass of Solute = 0.750 L

\(Molarity{\rm{ }} = {\rm{ }}\frac{{Number{\rm{ }}of{\rm{ }}Moles}}{{Volume{\rm{ }}of{\rm{ }}Solvent{\rm{ }}\left( {Litre} \right)}}{\rm{ }}\)

\({\rm{Molarity = }}\frac{{{\rm{0}}{\rm{.16}}}}{{{\rm{0}}{\rm{.750}}}}{\rm{ = 0}}{\rm{.213M}}\)

Temperature = 37 °C = (273 + 37) K = 310 K

Gas Constant, R = 0.08206 L atm/mol K

\(\begin{aligned}{}{\rm{\Pi = 0}}{\rm{.213 mol/L \times 0}}{\rm{.08206 L atm/mol K \times 310 K}}\\{\rm{\Pi = 5}}{\rm{.3 atm}}\end{aligned}\)