To address the problem, we need to follow these steps:
1. Calculate the concentration of hydrogen ions for the basic solution with a pH of 11.2:
[tex]\[
\left[ H^+ \right]_{\text{basic}} = 10^{-\text{pH}_{\text{basic}}} = 10^{-11.2}
\][/tex]
This gives us the hydrogen ion concentration for the basic solution as [tex]\(6.31 \times 10^{-12}\)[/tex] M.
2. Calculate the concentration of hydrogen ions for the acidic solution with a pH of 2.4:
[tex]\[
\left[ H^+ \right]_{\text{acidic}} = 10^{-\text{pH}_{\text{acidic}}} = 10^{-2.4}
\][/tex]
This results in the hydrogen ion concentration for the acidic solution as [tex]\(3.98 \times 10^{-3}\)[/tex] M.
3. Calculate the difference in the concentration of hydrogen ions between the two solutions:
[tex]\[
\Delta [H^+] = \left[ H^+ \right]_{\text{basic}} - \left[ H^+ \right]_{\text{acidic}}
\][/tex]
Substituting the values, we get:
[tex]\[
\Delta [H^+] = 6.31 \times 10^{-12} - 3.98 \times 10^{-3} = -3.98 \times 10^{-3} \text{ M}
\][/tex]
4. Identify which given answer option is closest to the calculated difference:
- [tex]\(1.6 \times 10^{-9}\)[/tex]
- [tex]\(4.0 \times 10^{-3}\)[/tex]
- [tex]\(6.7 \times 10^{-1}\)[/tex]
- [tex]\(1.6 \times 10^{11}\)[/tex]
The calculated absolute difference is approximately [tex]\(-3.98 \times 10^{-3}\)[/tex], which is closest to the option [tex]\(4.0 \times 10^{-3}\)[/tex].
Thus, the approximate difference in the concentration of hydrogen ions between the two solutions is:
[tex]\[
4.0 \times 10^{-3}
\][/tex]
