50 mL of 0.2 molal urea solution (density = 1.012 g mL^–1 at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in torr) of the resulting at 300 K is ____.
[Use : Molar mass of urea = 60 g mol^–1; gas constant, R = 62 L torr K^–1 mol^–1;
Assume, $∆$ _mix H = 0, $∆$ _mix V = 0]

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answer is 682.

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Detailed Solution

solution-I 50ml, 0.2 molal urea solution with density 1.012 g/L of solution wt of solution =50.6 gram Let urea = x gram
Solvent = (50.6-x) gram
Molality = $\frac{x \times 1000}{60 \times (50.6 - x)}$
$0.2 = \frac{1000 x}{60 \times (50.6 - x)}$
X=0.6gram
Solution II- 0.06 gram urea in 250ml. solution
Total wt of urea =0.6+0.06
= 0.66gram
Total volume =50+250 =300ml
$π = C . RT = [\frac{0.66 \times 1000}{60 \times 300}] \times 62 \times 300 = 682 torr$