To determine the pH of a solution with a given hydrogen ion concentration [tex]\([H^+]\)[/tex], we use the formula:
[tex]\[
pH = -\log [H^+]
\][/tex]
Here, we are given the hydrogen ion concentration:
[tex]\[
\left[ H^{+} \right] = 1.25 \times 10^{-10} \text{ M}
\][/tex]
1. Substitute the value of [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[
pH = -\log (1.25 \times 10^{-10})
\][/tex]
2. To calculate the logarithm:
[tex]\[
\log (1.25 \times 10^{-10}) = \log 1.25 + \log 10^{-10}
\][/tex]
From properties of logarithms, we know:
[tex]\[
\log 10^{-10} = -10
\][/tex]
So the expression becomes:
[tex]\[
\log (1.25) + (-10)
\][/tex]
3. The common logarithm of 1.25 (approximately) is:
[tex]\[
\log 1.25 \approx 0.09691
\][/tex]
Thus:
[tex]\[
pH = - (0.09691 - 10)
\][/tex]
4. Finally, simplify the expression:
[tex]\[
pH = - 0.09691 + 10
\][/tex]
[tex]\[
pH \approx 9.903089986991944
\][/tex]
5. Now, we compare the calculated pH value with the possible answers given:
[tex]\[
-10.1, -9.90, 7.90, 9.90
\][/tex]
The value that is closest to our calculated pH of 9.903 is:
[tex]\[
9.90
\][/tex]
Therefore, the pH of the solution is approximately 9.90.
