Which one of the following plots correctly describes the variation of osmotic pressure (H) of a fixed amount of a solute against the volume (V) of the solution at a fixed temperature?
Show Hint
Whenever two variables \(y\) and \(x\) satisfy \(y \cdot x = \text{constant}\), their graph is always a rectangular hyperbola asymptotic to the axes.
This is a standard mathematical rule applicable across physics and chemistry.
Osmotic pressure (\( \Pi \)) is given by the formula:
\(\Pi = \cfrac{nRT}{V}\)
Where:
\( n \) = number of moles of solute
\( R \) = ideal gas constant
\( T \) = temperature (in Kelvin)
\( V \) = volume of the solution
From the formula, it is clear that osmotic pressure is inversely proportional to the volume of the solution when the amount of solute and temperature are constant. This means that as the volume increases, the osmotic pressure decreases, forming a hyperbolic relationship.
The correct plot that represents this inverse relationship would show a downward curve starting from a higher value of osmotic pressure at lower volumes and approaching zero as the volume increases. Among the given options, only option A correctly represents this behavior.
Thus, the correct answer is option A, which shows a hyperbolic decrease of osmotic pressure with an increase in volume.
