An electrolyte A gives 3 ions &B is a noon n electrolyte . if 0.1M solution of B produces an osmotic pressure P, then 0.05M solution of A will produce an osmotic pressure assuming that the electrolyte is completely ionized

To tackle this question, we need to understand the relationship between osmotic pressure and the concentration of solute particles in a solution. Osmotic pressure is influenced by the number of particles in solution, which is determined by the degree of ionization of electrolytes.

Understanding Osmotic Pressure

Osmotic pressure (\( \Pi \)) can be calculated using the formula:

\( \Pi = iCRT \)

• i = van 't Hoff factor (number of particles the solute dissociates into)
• C = molarity of the solution
• R = universal gas constant (0.0821 L·atm/(K·mol))
• T = absolute temperature in Kelvin

Analyzing Electrolyte A and B

In this scenario:

• Electrolyte A dissociates into 3 ions, so its van 't Hoff factor \( i \) is 3.
• Electrolyte B is a non-electrolyte, meaning it does not dissociate, so its \( i \) is 1.

Calculating Osmotic Pressure for B

For the 0.1 M solution of B, the osmotic pressure \( P \) can be expressed as:

\( P = (1)(0.1)RT \)

This simplifies to:

\( P = 0.1RT \)

Finding Osmotic Pressure for A

Now, let’s calculate the osmotic pressure for the 0.05 M solution of A. Since A completely ionizes into 3 ions, we have:

\( \Pi_A = (3)(0.05)RT \)

This simplifies to:

\( \Pi_A = 0.15RT \)

Comparing the Two Pressures

Now, we can compare the osmotic pressures:

• For B: \( P = 0.1RT \)
• For A: \( \Pi_A = 0.15RT \)

From this, we can see that the osmotic pressure produced by the 0.05 M solution of A is greater than that produced by the 0.1 M solution of B. Specifically, the osmotic pressure of A is 1.5 times that of B.

Final Thoughts

In summary, the 0.05 M solution of electrolyte A, which produces 3 ions upon dissociation, results in a higher osmotic pressure compared to the 0.1 M non-electrolyte solution B. This illustrates the significant impact of ionization on osmotic pressure in solutions.