Calculate the pH of 0.001M  KOH solution.

Analysis

To find the pH of a KOH solution, we must recognize that KOH (Potassium Hydroxide) is a strong base. It dissociates completely in water to produce hydroxide ions ($OH^-$). We need to calculate the concentration of hydroxide ions, find the pOH, and then convert that to pH.

Concept

1. Dissociation: $KOH \rightarrow K^+ + OH^-$. Since it is a strong base, the concentration of $OH^-$ is equal to the concentration of the KOH solution.
2. pOH formula: $pOH = -\log_{10}[OH^-]$
3. pH relationship: $pH + pOH = 14$ (at 25°C)

Step-by-Step Solution

Step 1: Determine the concentration of $[OH^-]$ Since $KOH$ is a strong base, $[OH^-] = 0.001 \, M$. We can write this in scientific notation as: $[OH^-] = 1 \times 10^{-3} \, M$

Step 2: Calculate the pOH Using the formula $pOH = -\log[OH^-]$: $pOH = -\log(1 \times 10^{-3})$ $pOH = -(-3)$ $pOH = 3$

Step 3: Calculate the pH Using the relationship $pH + pOH = 14$: $pH + 3 = 14$ $pH = 14 - 3$ $pH = 11$

Conclusion

The pH of the 0.001M KOH solution is 11.

Exam Tip

Always check if the substance is an acid or a base before calculating. If you calculate the $-\log$ of a base concentration, you get the pOH, not the pH. Many students stop at 3 and choose option D, which is a common distractor! Always remember to subtract your result from 14 if you started with a base.