The osmotic pressure of a solution is directly proportional to the concentration of the solution. This means that a concentrated solution will have a higher osmotic pressure than a dilute solution. Therefore, the answer (3) is higher than that of the dilute solution.
Osmotic pressure (\(\pi\)) is a colligative property of a solution, meaning it depends solely on the concentration of solute particles in the solution and is independent of the identity of the solute. It plays a crucial role in various biological and chemical processes.
The relationship between osmotic pressure (\(\pi\)), concentration (\(c\)), and temperature (\(T\)) is given by the van't Hoff equation:
\[\pi = iCRT\]
Where:
\(\pi\) is the osmotic pressure.
\(i\) is the van't Hoff factor, which represents the number of particles into which the solute dissociates or associates in the solution. For non-ionic solutes (those that don't dissociate into ions), \(i\) is typically equal to 1. For ionic compounds that dissociate into multiple ions, \(i\) is greater than 1.
\(C\) is the molar concentration of the solute in the solution (measured in mol/L or M).
\(R\) is the ideal gas constant.
\(T\) is the absolute temperature (in Kelvin).
Now, let's compare the osmotic pressure of concentrated and dilute solutions:
1. Dilute Solution:
In a dilute solution, the concentration of the solute is relatively low, which means there are fewer solute particles per unit volume of the solution. As a result, the van't Hoff factor (\(i\)) is close to 1, assuming the solute does not significantly dissociate or associate. Therefore, in a dilute solution, the osmotic pressure is directly proportional to the concentration of the solute.
2. Concentrated Solution:
In a concentrated solution, the concentration of the solute is high, implying there are more solute particles per unit volume compared to the dilute solution. Consequently, the van't Hoff factor (\(i\)) may still be close to 1 for non-ionic solutes, but it can be significantly greater than 1 for ionic solutes due to their dissociation into multiple ions.
Since the osmotic pressure depends on both the concentration (\(C\)) and the van't Hoff factor (\(i\)), a concentrated solution can have a substantially higher osmotic pressure compared to a dilute solution, even if the solute in both solutions is the same. This is because the effect of an increased number of solute particles in a concentrated solution dominates, leading to a higher osmotic pressure.
In summary, the osmotic pressure of a concentrated solution is generally higher than that of a dilute solution due to the higher concentration of solute particles in the former. The relationship between osmotic pressure and concentration is described by the van't Hoff equation, which accounts for the impact of both concentration and the nature of the solute on osmotic pressure. |
