To determine the hydronium ion concentration [tex]\(\left(\text{H}_3\text{O}^+\right)\)[/tex] of a solution with a pH of 3.60, we can use the relationship between pH and hydronium ion concentration.
1. Understanding the pH Formula:
The pH of a solution is defined as the negative logarithm (base 10) of the hydronium ion concentration:
[tex]\[
\text{pH} = -\log \left[ \text{H}_3\text{O}^+ \right]
\][/tex]
2. Rearranging the Formula:
To find the hydronium concentration from the pH value, we rearrange the formula:
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] = 10^{-\text{pH}}
\][/tex]
3. Plugging in the pH Value:
The given pH value is 3.60. Substitute this into the formula:
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] = 10^{-3.60}
\][/tex]
4. Calculating the Hydronium Ion Concentration:
Evaluating [tex]\(10^{-3.60}\)[/tex],
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] = 0.00025118864315095795 \, \text{M}
\][/tex]
This can be expressed in scientific notation as:
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] \approx 2.5118864315095797 \times 10^{-4} \, \text{M}
\][/tex]
5. Comparing with the Given Options:
Among the given options:
- A. [tex]\(2.5 \times 10^{-4} \, \text{M}\)[/tex]
- B. [tex]\(3.0 \times 10^{-4} \, \text{M}\)[/tex]
- C. [tex]\(4.0 \times 10^{-11} \, \text{M}\)[/tex]
- D. [tex]\(4.5 \times 10^{-11} \, \text{M}\)[/tex]
The closest option to the calculated [tex]\(2.5118864315095797 \times 10^{-4} \, \text{M}\)[/tex] is:
A. [tex]\(2.5 \times 10^{-4} \, \text{M}\)[/tex].
Thus, the correct answer is [tex]\( \boxed{A} \)[/tex].
