A student prepares a 0.20 mol/L aqueous solution of ascorbic acid and meausres its pH as 2.40. Based on theis evidence, what is the Ka of ascorbic acid?
H+ = 0.00398
C- is the same
(HC) = 0.2 = 0.00398
(0.00398)(0.00398) / 0.0199
=0.000796
Hi DrBob222 you told me you got 8.0 x 10^-5 how did you get this as an answer?
0.00398*0.00398/(0.2-0.00398) =
(0.00398)(0.00398)/0.196 = 8.08 x 10^-5
Note the 0.0199 in the denominator should have been 0.196. I try to proof these things but sometimes I miss them like the denominator above. Check my 8.08 x 10^-5
I am still getting the wrong answer. YOu are positive this is the answer? Perhaps my computer system is wrong?
I'm usually never sure of anything. I found information on the internet and in The Merck Index on ascorbic acid. It has two pka values. pK1 is 4.17 (k1=6.7 x 10^-5) and pK2 is 11.6 (k2=2.5 x 10^-12). You aren't titrating this acid, you are making a 0.2 M solution, placing that in water, and measuring the pH. That means ONLY the stronger acid will be measured because the weaker acid is about 30,000,000 times weaker than the stronger one and it will have neglibible effect on the total hydrogen ion. So I forget the weaker acid, and we treat it as a monorotic acid.
HC ==> H^+ + C^-
pH = 2.40 makes (H^+) = 0.00398
If (H^+) = 0.00398, then anion is 0.00398, and the unionized ascrobic acid is 0.2 - 0.00398 = 0.196
Ka = (H^+)(C^-)/(HC) =
(0.00398)(0.00398)/(0.196) = 8.08 x 10^-5 for pK1 value of 4.09 (which compares favorably with the 4.17 listed in the books.)I don't see any error I've made which is why I went back over it in detail. Of course you know than some errors just keep popping up when we check these things. I'd be interested in knowing how to solve the problem if this is wrong. One extra note. In The Merck Index, they list 5 mg/mL and 50 mg/mL as being pH = 3 and 2 respectively. That is about 0.28 M which is about what your problem has.
To calculate the Ka (acid dissociation constant) of ascorbic acid, we can use the formula:
Ka = [H+]^2 / [HC-]
In this case, we are given the concentration of H+ ions, which is 0.00398 M. We also know that the concentration of HC- (the conjugate base of ascorbic acid) is the same as the concentration of ascorbic acid itself, which is 0.2 M.
Substituting these values into the formula, we get:
Ka = (0.00398)^2 / 0.2
= 0.0000159204 / 0.2
= 0.000079602
So, the calculated Ka value is 0.000079602.
Now, you mentioned that DrBob222 got an answer of 8.0 x 10^-5. It's possible that there was an error in the calculations or in the original data provided. I would recommend double-checking the pH measurement and concentration values used, as well as re-calculating the Ka to ensure accuracy.