Calculating osmotic pressure

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.

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.

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^－.

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 ℃.