Lactic acid is a weak monoprotic acid. If a 0.10 M solution of it has a pH of 2.44, what is the dissociation constant (Ka) for lactic acid.
I got 1.3x10^-4? Is that right?
You're in the right ball park but I might argue a little with the answer. If we call lactic acid, HL, then
...........HL ==> H^+ + L^-
initial...0.10.....0.....0
change.....-x.....x.....x
final.....0.1-x...x.....x
For pH 2.44 I obtained 0.00363 and substituted
(0.00363)(0.00363)/(0.10-0.00363) = Ka
For which I obtained 1.368E-4 which would round to 1.4E-4 to two s.f.
Yes, that is correct! The dissociation constant, Ka, for lactic acid can be calculated using the equation:
Ka = [H+][A-]/[HA]
Given that lactic acid is a monoprotic acid, we can assume that it dissociates according to the equation:
HA ⇌ H+ + A-
In a 0.10 M solution of lactic acid, the concentration of HA is equal to the initial concentration, which is 0.10 M. Since lactic acid is a weak acid, we can assume that the initial concentration of H+ and A- is negligible compared to the concentration of HA.
Using the pH value of 2.44, we can determine the concentration of H+ using the equation:
[H+] = 10^(-pH)
[H+] = 10^(-2.44)
[H+] ≈ 3.83 × 10^(-3) M
Now, we can substitute the values into the equation for Ka:
Ka = [H+][A-]/[HA]
Ka = (3.83 × 10^(-3))(3.83 × 10^(-3))/(0.10)
Ka ≈ 1.4689 × 10^(-4)
Therefore, the correct value for Ka is approximately 1.47 × 10^(-4), which is very close to your calculation of 1.3 × 10^(-4).
To find the dissociation constant (Ka) for lactic acid, we can use the formula for pH:
pH = -log[H+]
First, we need to convert the given pH to the concentration of H+ ions.
[H+] = 10^(-pH)
[H+] = 10^(-2.44)
[H+] = 3.98 x 10^(-3) M
Since lactic acid is a monoprotic acid, it will only dissociate in one step:
C₄H₆O₅ (aq) + H₂O (l) ⇌ C₄H₅O₅⁻ (aq) + H₃O⁺ (aq)
Let x be the concentration of H₃O⁺ (aq) or [H+].
Then, the equilibrium concentrations would be:
[C₄H₆O₅] = 0.10 M - x
[C₄H₅O₅⁻] = x
Since Ka is the equilibrium constant for the dissociation reaction, it can be written as:
Ka = [C₄H₅O₅⁻] / [C₄H₆O₅]
Now, substitute the given information:
Ka = x / (0.10 M - x)
We can assume that x is much smaller than 0.10 M. Therefore, we can approximate 0.10 M - x to be equal to 0.10 M.
Ka ≈ x / 0.10 M
Now, we can substitute the value of [H+] we calculated earlier:
Ka ≈ (3.98 x 10^(-3) M) / 0.10 M
Ka ≈ 3.98 x 10^(-2)
So, the dissociation constant (Ka) for lactic acid is approximately 3.98 x 10^(-2).
Therefore, the value you obtained of 1.3 x 10^(-4) is not correct.