Question

A dilute solution of an ionic compound \( A_3B \) has an osmotic pressure which is 6 times that of 0.02 M \( \text{MgCl}_2 \). What is the molar concentration of \( A_3B \), assuming that it undergoes complete dissociation in water?

• A. 0.03 M
• B. 0.26 M
• C. 0.12 M
• D. 0.09 M

Hint:

When dealing with osmotic pressure, remember that the van't Hoff factor represents the number of particles produced by dissociation of the solute. The higher the dissociation, the larger the van't Hoff factor.

Answer 1

The Correct Option is D

Step 1: Use the formula for osmotic pressure.
The osmotic pressure (\( \Pi \)) of a solution is given by the formula:
\[ \Pi = i M R T \]
Where:
- \( i \) is the van't Hoff factor (the number of particles the solute dissociates into),
- \( M \) is the molarity of the solution,
- \( R \) is the gas constant,
- \( T \) is the temperature in Kelvin.

Step 2: Osmotic pressure of \( \text{MgCl}_2 \).
For \( \text{MgCl}_2 \), the dissociation is: \[ \text{MgCl}_2 \rightarrow \text{Mg}^{2+} + 2 \text{Cl}^- \]
Thus, the van't Hoff factor \( i = 3 \). The osmotic pressure for \( \text{MgCl}_2 \) is:
\[ \Pi_{\text{MgCl}_2} = 3 \times 0.02 M \times R \times T \]

Step 3: Osmotic pressure of \( A_3B \).
For \( A_3B \), the dissociation is:
\[ A_3B \rightarrow 3A^{+} + B^{3-} \]
Thus, the van't Hoff factor \( i = 4 \) for \( A_3B \). The osmotic pressure for \( A_3B \) is:
\[ \Pi_{A_3B} = 4 \times M_{A_3B} \times R \times T \]

Step 4: Use the given osmotic pressure ratio.
We are told that the osmotic pressure of \( A_3B \) is 6 times that of \( \text{MgCl}_2 \):
\[ \Pi_{A_3B} = 6 \times \Pi_{\text{MgCl}_2} \]
Substituting the expressions for osmotic pressures: \[ 4 \times M_{A_3B} \times R \times T = 6 \times 3 \times 0.02 M \times R \times T \]

Step 5: Solve for \( M_{A_3B} \).
Canceling \( R \) and \( T \) from both sides: \[ 4 \times M_{A_3B} = 6 \times 3 \times 0.02 \]
\[ M_{A_3B} = \frac{6 \times 3 \times 0.02}{4} = 0.09 M \]

Step 6: Conclusion.
The molar concentration of \( A_3B \) is 0.09 M. Therefore, the correct answer is option (D).