Lactic acid, C3H6O3. If the initial concentration of lactic acid is 0.12 mol/L and the pH is 2.39, what is the Ka for lactic acid?
To determine the Ka (acid dissociation constant) for lactic acid, we need to consider the relationship between the concentration of the dissociated ions and undissociated form of the acid. In this case, lactic acid is a weak acid, so it partially dissociates in water.
The dissociation reaction of lactic acid can be represented as follows:
C3H6O3 (aq) ⇌ H+ (aq) + C3H5O3- (aq)
The Ka expression is given by:
Ka = [H+][C3H5O3-] / [C3H6O3]
Given:
Initial concentration of lactic acid, [C3H6O3] = 0.12 mol/L
pH = 2.39
Now, let's calculate the concentration of H+ ions using the given pH.
pH = -log[H+]
2.39 = -log[H+]
To find [H+], we need to take the inverse of the logarithm:
[H+] = 10^(-pH)
[H+] = 10^(-2.39)
Next, we can assume that the concentration of [H+] and [C3H5O3-] are equal because they are in a 1:1 ratio according to the balanced chemical equation.
Therefore, [H+] = [C3H5O3-] = x (let's assume)
Also, [C3H6O3] - x ≈ [C3H6O3] (since x is much smaller than the initial lactic acid concentration)
Now, we can substitute these values into the Ka expression:
Ka = (x)(x) / ([C3H6O3] - x)
Substituting the given initial concentration of lactic acid:
Ka = (x)(x) / (0.12 - x)
Since the value of x is small compared to 0.12, we can approximate 0.12 - x as 0.12.
Ka = (x)(x) / 0.12
To solve for x, we need to convert the pH back to [H+]. We can use the equation [H+] = 10^(-pH) as mentioned earlier.
[H+] = 10^(-2.39)
Now, substitute this value of [H+] into the equation for x:
Ka = ([H+])([H+]) / 0.12
Ka = (10^(-2.39))(10^(-2.39)) / 0.12
Finally, calculate the Ka value using a calculator or math software to obtain the answer.