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A $3 ml$ of solution was made by dissolving $20 mg$ of protein at $0 ° C .$ The osmotic pressure of the resulting solution is $3.8$ torr. The molecular weight of the protein is approximately (in $g / mol$ )

A $300$
B $3 \times 10^{5}$
C $3 \times 10^{4}$
D $3 \times 10^{3}$

Verified Solution

Answer & Solution

Correct Answer

(C) $3 \times 10^{4}$

Step-by-step Solution

Detailed explanation

This question is based on osmosis and osmotic pressure. The excess pressure which must be applied to a solution to prevent the passage of solvent into it through a semi-permeable membrane.…

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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A 3ml of solution was made by dissolving 20mg of protein at 0°C. The osmotic pressure of the resulting solution is 3.8 torr. The molecular weight of the protein is approximately (in g/mol)

Step-by-step Solution

A $3 ml$ of solution was made by dissolving $20 mg$ of protein at $0 ° C .$ The osmotic pressure of the resulting solution is $3.8$ torr. The molecular weight of the protein is approximately (in $g / mol$ )