A very old and tired , grey haired AP Chem instructor wanted to determine the Ka of an unlabelled monoprotic acid in his stockroom. He dissolved an unknown amount of acid in an unknown amount of water and proceeded to titrate the sample with a solution of NaOH of unknown molarity. After adding 10.0 ml of NaOH, he uttered that famous first order expletive “Oh, Michigan State”. He stopped and measured the pH of the solution at that point and found pH= 5.0. He continued to add NaOH until he realized he didn’t add phenolphthalein to the solution. He added 3 drops and the solution remained colorless. He continued the titration and found the equivalence point to be 32.22 ml of the NaOH solution. Can our intrepid hero calculate the Ka? Hint: he can. So calculate the Ka. Show all of your work.
At the first point where he stopped and measured the pH, the H+ ion concentration is 1*10^-5 and the OH- ion concentration is 1*10^-9. This is as far as I've gotten, I can't figure out what to do with this information.
0mL|......10mL|.................32.22 mL|
I figure at 10 mL, where the pH = 5, at that point some of the "base"(the anion) has been formed so you should be able to use the Henderson-Hasselbalch equation and calculate pKa.
pH = pKa + log(base)/(acid)
5.0 = pKa + log (base)/(acid)
At 10 mL it seems to me that the base formed is 10/32.22 How much of the acid is left at this point? It has neutralized 10 mL so it has another 22.22 mL to go so that fraction is 22.22/32.22. Substitute into the HH equation and solve for pKa.
Check my thinking.
I plugged those numbers into the HH equation and came up with 2.22*10^-5 for the Ka.
Does that sound right?
It's actually 4.5*10^-6.
5=pKa+log(10/22.22)
To calculate the Ka (acid dissociation constant), we need to use the information provided in the question. Here's how we can do it step by step:
Step 1: Identify known parameters:
- Volume of NaOH solution added before pH measurement = 10.0 ml
- pH measurement at this point = 5.0
- Volume of NaOH solution added at the equivalence point = 32.22 ml
Step 2: Determine moles of NaOH added:
We need to convert the volume of NaOH solution added at the equivalence point into moles. To do this, we'll use the balanced equation between the acid and the base:
H3A + NaOH -> NaH2A + H2O
Since it's a monoprotic acid, we only have one H+ ion being neutralized by one OH- ion. Therefore, the mole ratio between the NaOH and the acid is 1:1. So, the moles of NaOH added can be calculated as:
moles NaOH = volume (in L) * concentration (in M)
moles NaOH = 32.22 ml * (1 L / 1000 ml) * [concentration of NaOH (unknown)]
Step 3: Determine moles of H+ ions neutralized:
Since the moles of NaOH and the acid are equal, the moles of H+ ions neutralized are also equal to the moles of NaOH added.
moles H+ = moles NaOH
Step 4: Calculate the initial concentration of H+ ions:
The pH at the first point (before adding phenolphthalein) is given as 5.0. We can use the formula pH = -log[H+], rearranged to solve for [H+]:
[H+] = 10^(-pH)
[H+] = 10^(-5.0)
Convert this value to concentration by multiplying it by 1 mole/L (since 1 mole of H+ ions is equivalent to 1 L):
initial concentration of H+ ions = [H+] * 1 mole/L
Step 5: Calculate the initial concentration of the acid:
Since the acid is monoprotic, the initial concentration of the acid is equal to the initial concentration of H+ ions.
initial concentration of acid = initial concentration of H+ ions
Step 6: Calculate the initial moles of the acid:
To find the initial moles of the acid, we'll use the formula:
moles acid = concentration of acid * volume of water
However, the volume of water used to dissolve the acid is unknown. So, we can't fully determine the moles of the acid.
Step 7: Determine the moles of the acid at the equivalence point:
Since moles of H+ ions = moles of acid (from Step 3), we can calculate the moles of acid at the equivalence point as:
moles acid at equivalence point = moles H+ ions
Step 8: Determine the volume of acid at the equivalence point:
The volume of acid at the equivalence point can be calculated using the formula:
volume of acid = (moles acid at equivalence point) / (concentration of acid)
However, we can't calculate the volume of acid without knowing the concentration. Hence, we can't fully determine the volume of acid at the equivalence point.
Step 9: Calculate the Ka:
The Ka can be calculated using the following formula:
Ka = (concentration of H+ ions at equivalence point)^2 / (concentration of undissociated acid at equivalence point)
However, since we don't have the necessary information, i.e., the concentration of the acid and the volume of acid at the equivalence point, we can't calculate the Ka.
In conclusion, based on the provided information and calculations, we cannot determine the Ka of the unlabelled monoprotic acid.