To determine the pH of a solution when you are given the concentration of hydronium ions [tex]\([H_3O^+]\)[/tex], you use the following formula:
[tex]\[ \text{pH} = -\log_{10}([H_3O^+]) \][/tex]
Here, the given concentration of hydronium ions is [tex]\([H_3O^+] = 1 \times 10^{-9} \text{ M}\)[/tex].
Follow these steps to calculate the pH:
1. Identify the given concentration of hydronium ions:
[tex]\[ [H_3O^+] = 1 \times 10^{-9} \text{ M} \][/tex]
2. Apply the formula for pH:
[tex]\[ \text{pH} = -\log_{10}(1 \times 10^{-9}) \][/tex]
3. Evaluate the logarithm:
[tex]\[ \log_{10}(1 \times 10^{-9}) = -9 \][/tex]
4. Finally, apply the negative sign as per the pH formula:
[tex]\[ \text{pH} = -(-9) = 9 \][/tex]
Therefore, the pH of the solution is 9.0.
So, out of the given options:
- [tex]\(9.0\)[/tex]
- [tex]\(5.0\)[/tex]
- [tex]\(-5.0\)[/tex]
- [tex]\(1.0 \times 10^{-5}\)[/tex]
- [tex]\(-9.0\)[/tex]
The correct answer is [tex]\(9.0\)[/tex].
