To determine the approximate difference in the concentration of hydrogen ions between the two solutions, we follow these steps:
1. Understanding the pH formula:
The pH of a solution is given by the equation:
[tex]\[
pH = -\log [H^+]
\][/tex]
where [tex]\([H^+]\)[/tex] is the concentration of hydrogen ions.
2. Calculate the concentration of hydrogen ions ([tex]\([H^+]\)[/tex]) for the basic solution:
Given that the pH of the basic solution is 11.2, we can calculate the concentration of hydrogen ions as follows:
[tex]\[
[H^+]_{\text{basic}} = 10^{-\text{pH}_{\text{basic}}} = 10^{-11.2} \approx 6.31 \times 10^{-12}
\][/tex]
This is the concentration of hydrogen ions in the basic solution.
3. Calculate the concentration of hydrogen ions ([tex]\([H^+]\)[/tex]) for the acidic solution:
Given that the pH of the acidic solution is 2.4, we can calculate the concentration of hydrogen ions as follows:
[tex]\[
[H^+]_{\text{acidic}} = 10^{-\text{pH}_{\text{acidic}}} = 10^{-2.4} \approx 3.98 \times 10^{-3}
\][/tex]
This is the concentration of hydrogen ions in the acidic solution.
4. Determine the difference in concentration:
The difference in the concentration of hydrogen ions between the acidic solution and the basic solution is given by comparing [tex]\([H^+]_{\text{acidic}}\)[/tex] and [tex]\([H^+]_{\text{basic}}\)[/tex]:
[tex]\[
\text{Difference} = \frac{[H^+]_{\text{acidic}}}{[H^+]_{\text{basic}}} = \frac{3.98 \times 10^{-3}}{6.31 \times 10^{-12}} \approx 6.31 \times 10^8
\][/tex]
5. Conclusion:
The approximate difference in the concentration of hydrogen ions between the two solutions is:
[tex]\[
6.31 \times 10^8 \approx 630957344.4801924
\][/tex]
This is closest to the option:
[tex]\[
1.6 \times 10^{11}
\][/tex]
Hence, the correct answer is [tex]\(1.6 \times 10^{11}\)[/tex].
