What is the pH of a 0.01 M NaOH solution?

Steps to Solve

1. Determine the concentration of hydroxide ions
   Since sodium hydroxide (NaOH) is a strong base, it completely dissociates in water.
   The dissociation of NaOH can be represented as:
   $$ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- $$
   This means that the concentration of $\text{OH}^-$ ions in the solution is the same as the concentration of the NaOH solution, which is 0.01 M. Therefore, the concentration of hydroxide ions $\text{[OH]}^-$ is 0.01 M.

2. Calculate the pOH of the solution
   The pOH can be calculated using the formula:
   $$ \text{pOH} = -\log[\text{OH}^-] $$
   Substituting the concentration we found:
   $$ \text{pOH} = -\log(0.01) $$

3. Evaluate the pOH
   Calculating the logarithm:
   $$ \text{pOH} = -\log(10^{-2}) = 2 $$

4. Calculate the pH of the solution
   The relationship between pH and pOH is given by:
   $$ \text{pH} + \text{pOH} = 14 $$
   Therefore, we can find the pH:
   $$ \text{pH} = 14 - \text{pOH} $$
   Substituting the pOH we found:
   $$ \text{pH} = 14 - 2 $$

5. Final calculation and answer
   Calculating the final value:
   $$ \text{pH} = 12 $$