# 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

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（8.31×10
^{3}[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.

^{+}+ 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^{－}.

n = $ \frac{58.5 \, \text{g}}{58.5 \, \text{g}\,\text{mol}^\text{-1}} \times 2 $ = 2 [mol]

R = 8.31×10

^{3}[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 (≈ 10^{5} 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).