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At $300 K$ , a one litre solution of sucrose (molecular weight: $342$ ) was prepared by dissolving $40 g$ of sucrose. What is the approximate osmotic pressure (in $kPa$ ) of the solution at the same temperature? $(R = 8.314 \times 10^{6} {cm}^{3} Pa K^{- 1} {mol}^{- 1})$

A $292$
B $500$
C $292000$
D $600$

Verified Solution

Answer & Solution

Correct Answer

(A) $292$

Step-by-step Solution

Detailed explanation

Osmotic pressure, π=CRT. Putting the values: 401000×342×8.314×106×300 ∴ π=291.71≅292 kPa

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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At 300 K, a one litre solution of sucrose (molecular weight: 342) was prepared by dissolving 40 g of sucrose. What is the approximate osmotic pressure (in kPa) of the solution at the same temperature? R=8.314×106 cm3 Pa K-1 mol-1

Step-by-step Solution

At $300 K$ , a one litre solution of sucrose (molecular weight: $342$ ) was prepared by dissolving $40 g$ of sucrose. What is the approximate osmotic pressure (in $kPa$ ) of the solution at the same temperature? $(R = 8.314 \times 10^{6} {cm}^{3} Pa K^{- 1} {mol}^{- 1})$