Question

At $300K,36g$ of glucose present in a litre of its solution has an osmotic pressure of $4.98bar$. If the osmotic pressure of the solution is $1.52$ bars at the same temperature, what would be its concentration?

Answer 1

As per the van't Hoff equation, the relationship between the osmotic pressure and the molar concentration is $\Pi =CRT$. Here, $R$ is the ideal gas constant and $T$ is absolute temperature.

$C_1=\frac{36}{180}$ M

(Note: Molar mass of glucose is $180$ g/mol and molar concentration is the ratio of number of moles of glucose to the volume of solution in L. Number of moles is the ratio of mass to molar mass).

${\Pi }_1=4.98$ bar
$C_2=$ ?
${\Pi }_2=1.52$ bar

$4.98=\frac{36}{180}$ RT ......(i)

$1.52=C_2$ RT ......(ii)

Divide equation (ii) with equation (i),

$\frac{C_2}{36}\times 180=\frac{1.52}{4.98}$

$C_2=0.061M$

Hence, second solution has concentration of $0.061M$.