To determine the pH of a solution with a given hydronium ion concentration, we use the commonly known formula:
[tex]\[ \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \][/tex]
Here, the hydronium ion concentration ([tex]\[\text{H}_3\text{O}^+\][/tex]) is given as [tex]\(4.7 \times 10^{-11}\)[/tex].
Following the formula step-by-step:
1. Take the logarithm (base 10) of the hydronium ion concentration:
[tex]\[ \log_{10} (4.7 \times 10^{-11}) \][/tex]
2. Then, apply the negative sign as per the pH formula:
[tex]\[ \text{pH} = - \log_{10} (4.7 \times 10^{-11}) \][/tex]
After calculating this, we find that the pH value is approximately 10.33.
Therefore, the pH of the solution is [tex]\( \boxed{10.33} \)[/tex].
