To find the pH of a solution given its hydronium ion concentration, we use the 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 [tex]\(4.7 \times 10^{-11}\)[/tex].
Now, let's calculate the pH:
1. First, take the common logarithm (base 10) of the hydronium ion concentration:
[tex]\[ \log_{10} (4.7 \times 10^{-11}) \approx -10.327902142064282 \][/tex]
2. Then, multiply this value by -1 to find the pH:
[tex]\[ \text{pH} = -(-10.327902142064282) = 10.327902142064282 \][/tex]
3. Lastly, round this value to the nearest hundredth:
[tex]\[ \text{pH} \approx 10.33 \][/tex]
Therefore, the pH of the solution is approximately:
[tex]\[ \boxed{10.33} \][/tex]
