What is the pH of a 0.02 M NaOH solution?
Understand the Problem
The question is asking for the pH of a 0.02 M NaOH solution. This involves using the formula pH = -log[H+] and knowing that NaOH is a strong base that fully dissociates in solution.
Answer
The pH of the 0.02 M NaOH solution is approximately 12.3.
Answer for screen readers
The pH of the 0.02 M NaOH solution is approximately 12.3.
Steps to Solve
- Identify the concentration of hydroxide ions
Since NaOH is a strong base, it dissociates completely in solution. Therefore, the concentration of hydroxide ions $[OH^-]$ is the same as the NaOH concentration. $$ [OH^-] = 0.02 , M $$
- Calculate the concentration of hydrogen ions
To find the concentration of hydrogen ions, use the relationship between $[H^+]$, $[OH^-]$, and the ion product of water ($K_w$) at 25°C, which is: $$ K_w = [H^+][OH^-] = 1.0 \times 10^{-14} $$
Rearranging this gives: $$ [H^+] = \frac{K_w}{[OH^-]} $$
Plugging in the values: $$ [H^+] = \frac{1.0 \times 10^{-14}}{0.02} $$ $$ [H^+] = 5.0 \times 10^{-13} , M $$
- Calculate the pH
Now that we have $[H^+]$, we can calculate the pH using the formula: $$ \text{pH} = -\log[H^+] $$
Substituting in our value for $[H^+]$: $$ \text{pH} = -\log(5.0 \times 10^{-13}) $$
Using a calculator: $$ \text{pH} \approx 12.3 $$
The pH of the 0.02 M NaOH solution is approximately 12.3.
More Information
NaOH is a strong base that completely dissociates in solution, leading to a higher concentration of hydroxide ions and thus a higher pH. This example illustrates the relationship between pH, $[H^+]$, and $[OH^-]$ in aqueous solutions.
Tips
- Mistaking the pH calculation by using the wrong concentration for $[H^+]$.
- Forgetting to consider the full dissociation of strong bases or acids, which can lead to incorrect calculations.
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