# Calculating osmotic pressure

In this page, you will learn how to calculate osmotic pressure using van't hoff equation.

Let's calculate osmotic pressure solving example question. Contents

1. For high school students

H.S. Level

## Osmotic pressure formula

Osmotic pressure Π [Pa] is calculated by following formula (van't hoff equation).

$\Pi V = nRT$

In this formula, each character means as follows.

Π
Osmotic pressure [Pa]
V
Volume of the solution [L]
n
Number of all moles of solutes [mol]
R
Ideal gas constant（8.31×103 [Pa L K-1 mol-1]）
T
Absolute temperature [K]

Be careful of substituting n with the number of "all moles of solutes." If solutes is electrolytic, you should consider it.

For example, when 1 mol of NaCl is dissolved in water, NaCl ionize into Na+ and Cl, so the number of "all moles of solutes" is 2 mol.

NaCl → Na+ + Cl

You will notice that this osmotic pressure formula is the similar form as ideal gas law (pV=nRT).

## Calculating osmotic pressure

Let's calculate osmotic pressure using the previous formula.

Question

In water, 58.5 g of sodium chloride is dissolved, and the volume of solution is 1 L. Calculate osmotic pressure of this solution at 27 ℃.

NaCl = 58.5 [g mol-1], so you can know dissolved NaCl is 1 mol, but the number of "all moles of solutes" in water is 2 mol because NaCl ionize into Na+ and Cl.

V = 1 [L]
n = $\frac{58.5 \, \text{g}}{58.5 \, \text{g}\,\text{mol}^\text{-1}} \times 2$ = 2 [mol]
R = 8.31×103 [Pa L K-1 mol-1]
T = (273 + 27) = 300 [K]

Substituting these values for $\Pi V = nRT$ then \begin{align*} \Pi \cdot 1 &= 2 \cdot (8.31 \times 10^3) \cdot 300 \\ \Pi &= 5.0 \times 10^6 \, \mathrm{[Pa]} \end{align*}

The result of question is 50 times as high as atmospheric pressure (≈ 105 Pa). You will know osmotic pressure is very high.

By the way, NaCl can be all dissolved in this question because the solubility of NaCl is 35.9g/100g(water) at 25 ℃.

You can learn the process of osmosis from the following button (written in Japanese).