To find the pH of a solution given its hydrogen ion concentration [tex]\([H^{+}] = 1.25 \times 10^{-10} \, \text{M}\)[/tex], we use the formula:
[tex]\[ \text{pH} = -\log \left[ H ^{+} \right] \][/tex]
Here's the step-by-step process:
1. Plug in the value of the hydrogen ion concentration into the formula:
[tex]\[ \text{pH} = -\log (1.25 \times 10^{-10}) \][/tex]
2. Calculate the logarithm part:
[tex]\[ \log (1.25 \times 10^{-10}) = \log (1.25) + \log (10^{-10}) \][/tex]
3. The logarithm of [tex]\(10^{-10}\)[/tex] is [tex]\(-10\)[/tex], because:
[tex]\[ \log (10^{-10}) = -10 \][/tex]
4. Now, let’s calculate [tex]\(\log (1.25)\)[/tex]:
Using a calculator, [tex]\(\log (1.25) \approx 0.09691\)[/tex]
5. Add these values together:
[tex]\[ \log (1.25 \times 10^{-10}) = 0.09691 - 10 \][/tex]
6. Combine the results:
[tex]\[ 0.09691 - 10 = -9.90309 \][/tex]
7. Finally, take the negative of this result to find the pH:
[tex]\[ \text{pH} = -(-9.90309) = 9.90309 \][/tex]
Rounding it to two decimal places, the pH is approximately:
[tex]\[ \text{pH} \approx 9.90 \][/tex]
Therefore, the pH of the solution is [tex]\(9.90\)[/tex]. The correct answer is:
[tex]\[ \boxed{9.90} \][/tex]
