To find the pH of a solution, you use the formula:
[tex]\[ \text{pH} = -\log_{10} [H^+] \][/tex]
where [tex]\([H^+]\)[/tex] is the concentration of hydrogen ions in moles per liter (M).
Given [tex]\([H^+] = 7.0 \times 10^{-12}\)[/tex] M, we can plug this value into the pH formula:
1. Write the formula for pH:
[tex]\[ \text{pH} = -\log_{10} [H^+] \][/tex]
2. Substitute the given hydrogen ion concentration:
[tex]\[ \text{pH} = -\log_{10} (7.0 \times 10^{-12}) \][/tex]
3. Calculate the logarithm:
By using logarithmic properties, log base 10 of the product can be separated into:
[tex]\[ \log_{10} (7.0 \times 10^{-12}) = \log_{10} 7.0 + \log_{10} 10^{-12} \][/tex]
4. Using known logs and properties:
[tex]\[ \log_{10} 7.0 \approx 0.845 \][/tex]
[tex]\[ \log_{10} 10^{-12} = -12 \][/tex]
Adding these together:
[tex]\[ \log_{10} (7.0 \times 10^{-12}) \approx 0.845 - 12 = -11.1549 \][/tex]
5. Apply the negative sign from the pH formula:
[tex]\[ \text{pH} = -(-11.1549) = 11.1549 \][/tex]
So, the correct answer is:
C. 11.15
