# Osmotic Pressure

- Page ID
- 1593

## Introduction

Semipermiable membranes do not let the solute pass through (Think of the sugar example). A solvent will move to the side that is more concentrated to try to make each side more similar! Since there is a flow of solvents, the height of each side changes, which is *osmotic pressure*. When we work with aqueous solutions, we use mm of H_{2}O to describe the difference.

Osmosis is the diffusion of a fluid through a semipermeable membrane. When a semipermeable membrane (animal bladders, skins of fruits and vegetables) separates a solution from a solvent, then only solvent molecules are able to pass through the membrane. The osmotic pressure of a solution is the pressure difference needed to stop the flow of solvent across a semipermeable membrane. The osmotic pressure of a solution is proportional to the *molar concentration* of the solute particles in solution.

\[\Pi = i \dfrac{n}{V}RT = i M RT \label{eq1}\]

where

- \(\Pi\) is the osmotic pressure,
- \(R\) is the ideal gas constant (0.0821 L atm / mol K),
- \(T\) is the temperature in Kelvin,
- \(i\) is the van 't Hoff factor
- \(n\) is the number of moles of solute present,
- \(V\) is the volume of the solution, and
- \(M\) is the molar concentration of added solute (the \(i\) factor accounts for how many species in solution are generated)

Exercise \(\PageIndex{1}\)

Calculate molarity of a sugar solution in water (300 K) has osmotic pressure of 3.00 atm.

**Answer**-
Since it is sugar, we know it doesn't dissociate in water, so \(i\) is 1. Then we use Equation \ref{eq1} directly

\[M = \dfrac{\Pi}{RT} = \dfrac{3.00\, atm}{(0.0821\, atm.L/mol.K)(300\,K)} = 0.122\,M \nonumber\]

Exercise \(\PageIndex{2}\)

Calculate osmotic pressure for 0.10 M \(\ce{Na3PO4}\) aqueous solution at 20°C.

**Answer**-
Since \(\ce{Na3PO4}\) ionizes into four particles (3 Na+1 + \(PO_4^{-3}\)), then \(i = 4\). We can then calculate the osmotic pressure via Equation \ref{eq1}

\[\Pi = iMRT = (0.40)(0.0821)(293) = 9.6\, atm \nonumber\]

Exercise \(\PageIndex{3}\)

Hemoglobin is a large molecule that carries oxygen in human blood. A water solution that contains 0.263 g of hemoglobin (Hb) in 10.0 mL of solution has an osmotic pressure of 7.51 torr at \(25 ^oC\). What is the molar mass of the hemoglobin?

**Answer**-
\(6.51 \times 10^4 \; g/mol\)

## Contributors and Attributions

- Jenna Harvey (UCD)