Ascorbic acid is a weak organic acid also known as vitamin C. A student prepares a 0.20 mol/L aqueous solution of ascorbic acid and measures its pH as 2.40. Based on this evidence, what is the Ka of ascorbic acid?
Based on what I can find on the internet, ascorbic acid is a monoprotic acid. If that is so, then let's call ascorbic acid HC.
Then HC ==> H^+ + C^-
Ka = ((H^+)(C^-)/(HC)
If pH = 2.40, then (H^+) = 0.00398/
(C^-) is the same.
(HC) = 0.2 = 0.00398
Plug in the Ka expression and solve for Ka. I get a little over 8 x 10^-5 which gives a pKa of 4.09 which isn't far from the pKa listed in my quant book of 4.17.
Thank you! Umm...Whats a quant book? A book read by extraterrestrials??:P
Quantitative analysis chemistry book
To determine the Ka of ascorbic acid, we need to use the pH and concentration of the solution. Ka is the acid dissociation constant, which tells us how readily an acid dissociates into its constituent ions in a solution.
First, we need to understand the relationship between pH and the concentration of hydronium ions (H3O+) in a solution:
pH = -log[H3O+]
Given that the pH of the ascorbic acid solution is 2.40, we can determine the concentration of H3O+ ions using the inverse of the equation:
[H3O+] = 10^(-pH)
[H3O+] = 10^(-2.40)
[H3O+] = 0.00398 mol/L
Since ascorbic acid is a weak acid, it will only partially dissociate in aqueous solution. Let's assume x moles of ascorbic acid (HA) dissociate into H+ and A-.
HA ⇌ H+ + A-
At equilibrium, the concentration of H+ ions will be equal to x, and the concentrations of HA and A- ions will be (0.20 - x) each.
We can now set up the expressions for the equilibrium concentrations:
[H+] = x
[HA] = 0.20 - x
[A-] = 0.20 - x
From the balanced equation, we know that the concentration of H+ ions is equal to [H3O+], which we calculated as 0.00398 mol/L.
[H+] = [H3O+] = 0.00398 mol/L
Substituting these values into the equation for Ka:
Ka = ([H+][A-]) / [HA]
Ka = (0.00398 * (0.20 - x)) / (x)
Since the concentration of HA is much greater than the concentration of H+, we can approximate (0.20 - x) as 0.20:
Ka = (0.00398 * 0.20) / (x)
Now, substituting the known value of Ka (from the problem) and solving for x:
Ka = (0.00398 * 0.20) / (x) = ?
Only the value of x remains unknown in this equation. To solve for x, we need additional information. Unfortunately, the problem does not provide any data that will allow us to determine the value of x.
Therefore, without additional information, we cannot determine the exact value of the Ka of ascorbic acid.