Step-by-step explanation:
To calculate the amount of water needed to dilute the solution of potassium hydroxide and change its pH from 12.0 to 11.0, we need to use the formula for calculating the pH of a diluted solution.
The formula is:
pH = -log[H+]
where [H+] is the concentration of hydrogen ions in moles per liter.
Since we are diluting the solution by adding water, the concentration of [OH-] (hydroxide ions) will decrease proportionally to the volume of water added. This means that we can use the following equation to calculate the new concentration of [OH-]:
[OH-]1V1 = [OH-]2V2
where V1 is the initial volume of the solution, [OH-]1 is the initial concentration of hydroxide ions, V2 is the final volume of the solution after dilution, and [OH-]2 is the final concentration of hydroxide ions.
We know that the initial pH is 12.0, which means that [OH-]1 = 10^-2.0 M = 0.01 M.
We want to change the pH to 11.0, which means that [OH-]2 = 10^-11.0 M = 1 x 10^-11 M.
We also know that we are adding water to dilute the solution, but we don't know how much water we need to add yet. Let's call this volume of water "Vw".
Using the equation above, we can solve for V2:
[OH-]1V1 = [OH-]2V2
(0.01 M)(100 ml) = (1 x 10^-11 M)(100 ml + Vw)
V2 = (0.01 M)(100 ml)/(1 x 10^-11 M) - Vw
V2 = 10^12 ml - Vw
Now we can use this value for V2 in the pH formula to calculate the new pH:
pH = -log([H+])
[H+] = Kw/[OH-]
Kw is the ion product constant for water, which is equal to 1 x 10^-14 at room temperature.
[H+] = (1 x 10^-14)/(1 x 10^-11)
[H+] = 1 x 10^-3 M
pH = -log(1 x 10^-3)
pH = 3
We want to achieve a pH of 11.0, so we need to add enough water to bring down the pH from 12.0 to 11.0. This means that we need to add enough water so that V2 becomes:
V2 = (0.01 M)(100 ml)/(1 x 10^-11 M) - Vw = 10^11 ml
Therefore, we need to add:
Vw = V2 - initial volume of solution
Vw = (10^11 ml) - (100 ml)
Vw = 99999900 ml or approximately 100 million ml or 100 cubic meters of water.
So, in order to change the pH of a solution of potassium hydroxide with a pH of 12.0 to a pH of 11.0 by adding water only, you would need to add approximately 100 million milliliters or about 100 cubic meters of water.