First slide

Colligative properties, Osmotic pressure(OP)

Question

At 10°C, the osmotic pressure of urea solution was formed to be 500 mm. The solution is diluted 'x' times and the temperature raised to 25°C when the osmotic prssure was noticed to be 105.3mm, then 'x' is

Easy

A

3
B

4
C

5
D

12

Solution

I(before dilution)                         II(after dilution)

$π_{1}$ = 500mm                                     $π_{2}$ = 105.3mm
T₁ = (10+273)K                                T₂ = (25+273)K
V₁ = 1 lit                                            V₂ = x lit
$\large \pi =CST\\\\\frac{\pi_1}{\pi_2}=\frac{C_1T_1}{C_2T_2}$
$\large \because$
the amount of urea remains constant , Wt. and GMW of urea remain constant
$\large \therefore \frac{\pi_1}{\pi_2} =\frac{(\frac{w}{GMW}X\frac{1}{1})XT_1}{(\frac{w}{GMW}X\frac{1}{x})XT_2}$
$\large \frac{\pi_1}{\pi_2}=\frac{xT_1}{T_2}\\\frac{500}{105.3}=\frac{x(283)}{298}$
$\large x=\frac{500X298}{105.3X283}$
x=5
$\large \therefore$
the solution is diluted by 5 times

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