To determine the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex] in a solution with a pH of 5.9, we use the formula:
[tex]\[ [\text{H}^+] = 10^{-\text{pH}} \][/tex]
Here are the steps to find the correct answer:
1. Identify the given pH value:
The pH value given in the problem is 5.9.
2. Apply the formula:
The formula to calculate the hydrogen ion concentration from the pH is [tex]\[ [\text{H}^+] = 10^{-\text{pH}} \][/tex].
3. Substitute the given pH into the formula:
[tex]\[ [\text{H}^+] = 10^{-5.9} \][/tex]
4. Calculate the value:
To find [tex]\(10^{-5.9}\)[/tex], you can use a scientific calculator or logarithmic tables. The result is approximately:
[tex]\[ 10^{-5.9} \approx 1.2589 \times 10^{-6} \, M \][/tex]
5. Compare the result with the given choices:
Let's review the choices:
- A. [tex]\(5.0 \times 10^{-9} \, M\)[/tex]
- B. 5.9 M
- C. [tex]\(7.9 \times 10^5 \, M\)[/tex]
- D. [tex]\(1.3 \times 10^{-6} \, M\)[/tex]
Since our calculated hydrogen ion concentration is [tex]\(1.2589 \times 10^{-6} \, M\)[/tex], we compare this with the choices given.
None of the provided choices exactly match the calculated value [tex]\(1.2589 \times 10^{-6} \, M\)[/tex]. However, the closest choice is:
- D. [tex]\(1.3 \times 10^{-6} \, M\)[/tex]
Therefore, the nearest correct answer is [tex]\(1.3 \times 10^{-6} \, M\)[/tex]. So:
The hydrogen ion concentration of the solution is [tex]\(1.3 \times 10^{-6} \, M\)[/tex], which corresponds to choice D.
