To determine the pH of a solution with a given concentration of hydrogen ions [tex]\([ \text{H}^+ ] = 7.0 \times 10^{-7}\)[/tex], we can use the formula for pH:
[tex]\[ \text{pH} = -\log_{10}([\text{H}^+]) \][/tex]
Let's break down the calculation step-by-step:
1. Identify the hydrogen ion concentration:
[tex]\[ [\text{H}^+] = 7.0 \times 10^{-7} \][/tex]
2. Substitute this value into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(7.0 \times 10^{-7}) \][/tex]
3. Calculate the logarithm component:
[tex]\[ \log_{10}(7.0 \times 10^{-7}) = \log_{10}(7.0) + \log_{10}(10^{-7}) \][/tex]
4. Logarithm properties:
[tex]\[ \log_{10}(10^{-7}) = -7 \][/tex]
[tex]\[ \log_{10}(7.0) \approx 0.845 \][/tex]
5. Combine the results:
[tex]\[ \log_{10}(7.0 \times 10^{-7}) = 0.845 + (-7) = 0.845 - 7 = -6.1549 \][/tex]
6. Apply the negative sign:
[tex]\[ \text{pH} = -(-6.1549) = 6.1549 \][/tex]
Rounded to two decimal places, the pH value is approximately 6.15.
Therefore, the correct answer is:
D. 6.15
