Question

Which from following formulae is used to find the \([OH^-]\) ion concentration of a weak monoacidic base?

• A. \(K_b \cdot c\)
• B. \( \sqrt{K_b \cdot c} \)
• C. \( \sqrt{\frac{K_b}{c}} \)
• D. \( \frac{K_b}{c} \)

Hint:

For weak monoacidic bases, the concentration of hydroxide ions can be found by approximating the dissociation as small and solving the equilibrium equation.

Answer 1

The Correct Option is B

Step 1: Define the concept.
For weak monoacidic bases, the concentration of hydroxide ions \([OH^-]\) can be determined using the equilibrium constant \(K_b\) and the concentration of the base \(c\).

Step 2: Write the equation for a weak base.
For a base \(B\), dissociating in water:
\[ B + H_2O \rightleftharpoons BH^+ + OH^- \] The equilibrium constant expression for this is: \[ K_b = \frac{[BH^+][OH^-]}{[B]} \]

Step 3: Simplify for weak base approximation.
Assuming that the dissociation is small, we can approximate that \([B] \approx c\), and the concentrations of \(OH^-\) and \(BH^+\) are equal at equilibrium. Therefore:
\[ K_b = \frac{x^2}{c} \] Solving for \(x\) (which represents \([OH^-]\)): \[ x = \sqrt{K_b \cdot c} \]

Step 4: Final Answer.
Thus, the formula used to find the hydroxide ion concentration is \( \sqrt{K_b \cdot c} \), corresponding to option \((2)\).