Question

Calculate the pH of centimolar solution of monoacidic weak base. Which is 10% dissociated in its aqueous solution?

• A. 9
• B. 10
• C. 11
• D. 12

Hint:

Always pay close attention to terminology. "Decimolar" is 0.1 M, "Centimolar" is 0.01 M, and "Millimolar" is 0.001 M. Also, remember to convert pOH to pH when dealing with bases!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are tasked with finding the pH of a basic solution. We are given the concentration (centimolar) and the percentage dissociation of a weak monoacidic base (like $NH_4OH$).

Step 2: Key Formula or Approach:
For a weak monoacidic base ($BOH \rightleftharpoons B^+ + OH^-$), the concentration of hydroxide ions is:
$$[OH^-] = C \times \alpha$$
Where $C$ is the molar concentration and $\alpha$ is the fractional degree of dissociation.
From $[OH^-]$, we calculate $pOH = -\log_{10}[OH^-]$.
Finally, at standard temperature, $pH + pOH = 14$.

Step 3: Detailed Explanation:
1. Determine the values given:
- "Centimolar" means a concentration ($C$) of $\frac{1}{100} \text{ M} = 0.01 \text{ M} = 10^{-2} \text{ M}$.
- The base is 10% dissociated, so $\alpha = \frac{10}{100} = 0.1 = 10^{-1}$.
2. Calculate the hydroxide ion concentration:
$$[OH^-] = (10^{-2}) \times (10^{-1}) = 10^{-3} \text{ M}$$
3. Calculate the $pOH$:
$$pOH = -\log_{10}(10^{-3}) = 3$$
4. Calculate the $pH$:
$$pH = 14 - pOH$$
$$pH = 14 - 3 = 11$$

Step 4: Final Answer:
The pH of the solution is 11, which corresponds to option (c).