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The equation for the pH of a substance is [tex]pH = -\log \left[ H^+ \right][/tex], where [tex]H^+[/tex] is the concentration of hydrogen ions.

A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?

A. [tex]1.6 \times 10^{-9}[/tex]
B. [tex]4.0 \times 10^{-3}[/tex]
C. [tex]6.7 \times 10^{-1}[/tex]
D. [tex]1.6 \times 10^{11}[/tex]


Sagot :

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].
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