Question:
The osmotic pressure of a solution is given by the relation
The osmotic pressure of a solution is given by the relation
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Remember that in dilute solutions, the osmotic pressure can be approximated using the ideal gas law modified for concentration.
Updated On: May 31, 2026
- $\pi = CRT$
- $\pi = C/RT$
- $\pi = RT/C$
- $\pi = CR/T$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The osmotic pressure (\(\pi\)) of a solution is the minimum pressure which needs to be applied to prevent the inward flow of water across a semipermeable membrane. It can be related to the ideal gas law, where \(R\) is the universal gas constant, \(T\) is temperature in Kelvin, and \(C\) is the molar concentration of the solute.
Step 2: Meaning
The osmotic pressure equation should correctly represent how these variables interact with each other in a solution. The correct form must match the ideal gas law modified for solutions.
Step 3: Analysis
To analyze this, we start from the relationship between osmotic pressure and the ideal gas law. For an ideal dilute solution, the osmotic pressure \(\pi\) is given by: \[\pi = CRT\] where: \(C\) is the molarity (concentration) of the solute, \(R\) is the universal gas constant, \(T\) is the absolute temperature. This equation directly follows from the ideal gas law, where the pressure (\(P\)) in an ideal gas is given by: \[PV = nRT\] For a solution, if we consider one mole of solute dissolved in a solvent to form 1 liter of solution at concentration \(C\) (in moles per liter), then the number of moles \(n\) can be expressed as \(n = C \times V\). Substituting this into the ideal gas law gives us: \[P \times V = (C \times V)RT\] Simplifying, we get: \[P = CRT\] Since osmotic pressure is essentially a form of pressure in a solution context, it follows the same relationship. Therefore, the correct equation for osmotic pressure is indeed: \[\pi = CRT\]
Step 4: Conclusion
The given options are evaluated against this derived formula. Final Answer: (A)
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