Step 1: Understanding the Concept:
Osmotic pressure (\(\pi\)) is the pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.
It is one of the four main colligative properties, meaning its value is determined solely by the number of solute particles in the solution.
In a biological or chemical context, if two solutions have different particle concentrations, the solvent will naturally move from the region of lower particle concentration (lower osmotic pressure) to the region of higher particle concentration (higher osmotic pressure).
When comparing different solutions, if the molar concentrations are the same, the differences in osmotic pressure arise from how many ions the solute dissociates into.
Step 2: Key Formula or Approach:
The relationship between osmotic pressure and concentration is given by the van't Hoff equation:
\[ \pi = i \cdot C \cdot R \cdot T \]
Where:
\(\pi\) is the osmotic pressure.
\(i\) is the van't Hoff factor (number of ions per formula unit).
\(C\) is the molar concentration (Molarity).
\(R\) is the gas constant ($0.0821 L \cdot atm/K \cdot mol$).
\(T\) is the absolute temperature in Kelvin.
In this problem, the molarity (\(C = 1 M\)), gas constant (\(R\)), and temperature (\(T\)) are assumed to be identical for all solutions.
Therefore, the osmotic pressure is directly proportional to the van't Hoff factor:
\[ \pi \propto i \]
To find the "highest osmotic pressure," we simply need to find the solution with the "highest \(i\) value."
Step 3: Detailed Explanation:
Let us analyze the dissociation of each solute in water:
1. 1 M NaCl: Sodium chloride is a strong binary electrolyte.
Dissociation: \(NaCl \rightarrow Na^{+} + Cl^{-}\).
Total ions = 2. Therefore, \(i = 2\).
The effective concentration of particles is \(1 M \times 2 = 2 M\).
2. 1 M \(MgCl_{2}\): Magnesium chloride is a strong ternary electrolyte.
Dissociation: \(MgCl_{2} \rightarrow Mg^{2+} + 2Cl^{-}\).
Total ions = 3. Therefore, \(i = 3\).
The effective concentration of particles is \(1 M \times 3 = 3 M\).
3. 1 M urea: Urea is an organic molecule that does not ionize in water.
It remains as intact molecules. Therefore, \(i = 1\).
The effective concentration of particles is \(1 M \times 1 = 1 M\).
4. 1 M glucose: Glucose (\(C_{6}H_{12}O_{6}\)) is a carbohydrate and a non-electrolyte.
It does not dissociate. Therefore, \(i = 1\).
The effective concentration of particles is \(1 M \times 1 = 1 M\).
Comparing the particle concentrations: \(3 M>2 M>1 M\).
Because \(MgCl_{2}\) produces the greatest number of solute particles per unit volume, it will exert the highest osmotic pressure against a semipermeable membrane.
Step 4: Final Answer:
1 M \(MgCl_{2}\) has the highest osmotic pressure among the given options because it dissociates into the maximum number of ions ($i=3$).