The equation for the pH of a substance is pH = –log[H+], where H+ 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?
To find the approximate difference in the concentration of hydrogen ions between the two solutions, we need to first calculate the concentration of hydrogen ions for each solution using the given pH values.
For the basic solution with a pH of 11.2, we can use the equation pH = -log[H+] and rearrange it to find the concentration [H+].
pH = -log[H+]
11.2 = -log[H+]
Next, we can rearrange the equation again to isolate [H+] by taking the antilog (10^) of both sides:
[H+] = 10^(-pH)
Now we can substitute the pH value of 11.2 into the equation:
[H+] = 10^(-11.2)
Using a scientific calculator, we find that [H+] is approximately 6.31 x 10^(-12) M.
Similarly, for the acidic solution with a pH of 2.4, we can follow the same steps:
[H+] = 10^(-2.4)
Using a scientific calculator, we find that [H+] is approximately 3.98 x 10^(-3) M.
Finally, to find the approximate difference in the concentration of hydrogen ions between the two solutions, we can calculate the ratio of the concentrations:
Ratio = [H+] of basic solution / [H+] of acidic solution
Ratio = (6.31 x 10^(-12)) / (3.98 x 10^(-3))
Dividing these values, we find that the ratio is approximately 1.58 x 10^(-9).
Therefore, the approximate difference in the concentration of hydrogen ions between the basic and acidic solutions is 1.58 x 10^(-9) times.