To determine the pH of a solution with a given hydronium ion concentration, we use the formula for pH, which is defined as:
[tex]\[ \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \][/tex]
Given the concentration of hydronium ions [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] is [tex]\(5.45 \times 10^{-5}\)[/tex] M, we follow these steps to calculate the pH:
1. Identify the hydronium ion concentration:
[tex]\[
[\text{H}_3\text{O}^+] = 5.45 \times 10^{-5} \text{ M}
\][/tex]
2. Calculate the pH:
[tex]\[
\text{pH} = -\log_{10} (5.45 \times 10^{-5})
\][/tex]
After applying the logarithm function, we obtain a pH value of approximately 4.2636.
3. Round the pH to the nearest hundredth:
[tex]\[
\text{pH} \approx 4.26
\][/tex]
Therefore, the pH of the solution is 4.26 when rounded to the nearest hundredth.
