Carolyn B. answered • 06/19/21
Chemistry, Physics, and Biology Tutoring
The question gives us the concentration of OH-. Remember that brackets [ ] are used to express concentrations, and the concentration itself uses the unit of M. Also remember that H3O+ and H+ mean the exact same thing. So don't be confused if a question on your final exam asks you to find [H+], because [H+] is the same thing as [H3O+].
We can find the H3O+ concentration even if we know only the concentration of OH-. First, we need to find the pOH. In case you didn't know, the "p" means -log. (This is read as "negative log".) So, to find the pOH, all we need to do is put -log [OH-] into our calculator by typing the negative sign and then pushing the log button. Let's do the first OH- concentration together. The problem says that [OH-] = 2.0 x 10-2 M. So in our calculator, we type -log (2.0 x 10-2). The calculator says that -log (2.0 x 10-2) = 1.69897. So now we know that the pOH = 1.69897.
Now that we have the pOH, we can find the pH by using the following equation:
pOH + pH = 14
We already found that if the OH- concentration is 2.0 x 10-2, the pOH is 1.69897. So we just put 1.69897 in for the pOH. Our equation now looks like this:
1.69897 + pH = 14
Now we subtract 1.69897 from both sides of the equation to get pH by itself. Our equation looks like this:
pH = 14 -- 1.69897
And now we use our calculator to calculate 14 -- 1.69897 = 12.301. So we know that the pH = 12.3 . Remember the pH scale: a pH from 0 to 6.9 is acidic, a pH of 7.0 is neutral, and a pH from 7.01 to 14 is basic. We have a pH of 12.301 so this solution is definitely basic.
Now let's figure out what the [H3O+] is. In order to go from the pH to the [H3O+], we must do the following:
[H3O+] = 10-pH
We have already figured out that the pH is 12.301. So in our calculator, we type 10-12.301. Make sure that you remember the negative sign before the pH. The calculator says that 10-12.301 = 5.00 x 10-13. So we know that the [H3O+] is 5.00 x 10-13. This very tiny number makes sense for a basic solution. If a solution is basic, the [H3O+] will be tiny compared to the [OH-]. And our H3O+ concentration (5.00 x 10-13) is tiny compared to the OH- concentration (2.0 x 10-2).
Remember that the correct unit for concentration is M. Our answer should have 2 significant figures since the number we were given in the question, 2.0 x 10-2, has 2 significant figures. Thus, our final answer is
[H3O+] = 5.0 x 10-13 M.
Final answer if [OH-] = 2.0 x 10-2: The solution is basic and [H3O+] = 5.0 x 10-13 M.
Now let's calculate the [H3O+] and pH if the [OH-] = 6.0 x 10-10 M. We need to find the pOH first. Remember that pOH = -log [OH-]. So we type -log (6.0 x 10-10) into our calculator. The calculator says that
-log (6.0 x 10-10) = 9.2218. So the pOH = 9.2218.
Now remember that we use the equation pOH + pH = 14. If we use pOH = 9.2218, the equation looks like:
9.2218 + pH = 14
We subtract 9.2218 from both sides of the equation to get pH by itself. The equation now looks like:
pH = 14 -- 9.2218
We use our calculator to figure out that 14 --9.2218 = 4.778. So the pH is 4.778. Remember that a pH between 0 and 6.9 is acidic, so a pH of 4.778 indicates an acidic solution. So the solution is acidic.
Now we use the pH to find the [H3O+]. Remember that [H3O+] = 10-pH. Be sure not to forget the negative sign. The pH is 4.778, so our equation looks like this:
{H3O+] = 10-4.778
The calculator says that 10-4.778 = 1.667 x 10-5. So the [H3O+] = 1.667 x 10-5. This concentration makes sense because in an acidic solution, [H3O+] is much higher than [OH-].
And our answer of [H3O+] = 1.667 x 10-5 is much higher than [OH-] = 6.0 x 10-10.
Remember that the correct unit for concentration is M. Our answer should have 2 significant figures since the number we were given in the question, 6.0 x 10-10, has 2 significant figures. Thus, our final answer is
[H3O] = 1.7 x 10-5 M.
Final answer if [OH-] = 5.0 x 10-10: The solution is acidic and [H3O+] = 1.7 x 10-5 M.
