To determine the pH of a solution with a given hydronium ion concentration, we use the formula:
[tex]\[ \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \][/tex]
Given:
[tex]\[ [\text{H}_3\text{O}^+] = 5.6 \times 10^{-9} \, \text{M} \][/tex]
Step-by-Step Solution:
1. Identify the hydronium ion concentration:
[tex]\[ [\text{H}_3\text{O}^+] = 5.6 \times 10^{-9} \, \text{M} \][/tex]
2. Apply the pH formula:
[tex]\[ \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \][/tex]
[tex]\[ \text{pH} = -\log_{10} (5.6 \times 10^{-9}) \][/tex]
3. Calculate the logarithm:
[tex]\[ \log_{10} (5.6 \times 10^{-9}) \][/tex]
This calculation yields:
[tex]\[ \log_{10} (5.6 \times 10^{-9}) \approx -8.2518119729938 \][/tex]
4. Apply the negative sign to obtain the pH:
[tex]\[ \text{pH} = -(-8.2518119729938) \][/tex]
[tex]\[ \text{pH} = 8.2518119729938 \][/tex]
Given the options:
A. 7.00
B. 8.25
C. 9.00
D. 9.76
The pH value closest to our calculated result is B. 8.25.
Therefore, the correct answer is B. 8.25.
