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Osmotic Pressure

At 10oC, th...

Question

At $10^{o} C$ , the osmotic pressure of urea solution is 500 mm. The solution is diluted and the temperature is raised to $25^{o} C$ , when the osmotic pressure is found to be 105.3 mm. Determine extent of dilution.

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Solution

We have the equation $π = i C R T$
As urea is non-electrolyte, $i = 1$

$π_{s o l u t i o n} = i C_{s o l u t i o n} R T_{1}$ $- - - - - - - - > 1$
$π_{s o l u t i o n} = i C_{s o l u t i o n} R T_{2}$ $- - - - - - - - > 2$

Dividing Equation 1 and 2,

$\frac{π_{u r e a}}{π_{s o l u t i o n}}$ $=$ $\frac{C_{u r e a} T_{1}}{C_{s o l u t i o n} T_{2}}$

$\frac{500 \times 298}{105 \times 283}$ $=$ $\frac{C_{u r e a}}{C_{s o l u t i o n}}$

We get,
$5 C_{s o l u t i o n} = C_{u r e a}$

This means the solution was dilluted $5$ $t i m e s$ with respect to the urea concentration.

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