Determine the pH

Question

Determine the pH of the solution that is produced by mixing 8.22 mL of 7.72x10^-5 M HNO₃ with 822 mL of 2.35x10^-4 M KOH.

Answer 1

Hey Mika,

This problem involves a mixture of a strong acid and a strong base. For strong acids, the concentration of the acid equals the concentration of H3O+ ions in solution because it fully dissociates. Similarly, the concentration of a strong base equals the concentration of OH- ions in solution. We can use this to our advantage here. The first thing we want to do is figure out how many moles of H3O+ ions and OH- ions we have in solution. To do this, we use our volumes and molarities. For our strong acid, we put in 8.22 mL of a 7.72x10-5 M solution. What we do to figure out our moles of acid (which is equal to our moles of H3O+) is convert our volume unit to liters and multiply by the molarity:

8.22 mL / 1000 mL/L = .00822 L --> .00822 L x (7.72x10^-5 mol/L) = 6.35x10^-7 mol H3O+

Now we do something very similar for our base. We convert our volume to liters and multiply by that concentration. This gives us the moles of base, which since it's a strong base will be equal to the moles of OH- ion present.

822 mL / 1000 mL/L = .822 L --> .822 L x (2.3x10^-4 mol/L) = 1.93x10^-4 mol OH-

Now that we have our moles of each ion, we can figure out if we made an acidic solution or a basic solution. A solution that has more H3O+ ions present will be acidic and a solution with more OH- ions will be basic. In this case, we have more OH-, so we made a basic solution. Because H3O+ and OH- will react in a 1:1 ratio, we can find out how many moles of OH- we have left over by subtracting the moles of H3O+. We have 6.35x10^-7 mol H3O+. This will all completely react and it will use up the same amount of OH-. Here's how much OH- we'll have left after that reaction takes place:

1.93x10^-4 mol - 6.35x10^-7 mol = 2.34x10^-4 mol OH-

Now we now how many moles of OH- we have in our final solution. So how do we find pH? Well, the easiest thing to do is to find pOH first. pOH is -log[OH-]. We have moles of OH-, so all we need to do is divide by our total volume to find the concentration of OH-. represented by [OH-]. Our total volume is the sum of the two solutions we mixed, so the math goes as follows:

2.34x10^-4 mol / (.00822 L + .822 L) = 2.82x10^-4 M

Now that we have our [OH-], we take the negative log of this number to get pOH:

-log(2.82x10^-4) = 3.55

pOH and pH add to 14. So if we have found pOH, we simply subtract this number from 14 to get our pH:

14 - 3.55 = 10.45