Question:
A solution of H2X of unknown concentration is given.
pH of the solution is 4.
ka1=2*(10)^-6 M
ka2=1*(10)^-11 M
Find the concentrations of [H2X] ,[HX-] and X^2- in the solution.
My thoughts on the question:
The temperature which the solution is kept is not given.So we don't know the kW value.So from what I know we can't consider hydrolysis as kh=kW/(ka1/ka2) ,we can't calculate the constant of hydrolysis.
So can we neglect ka2 and continue calculations?
(Considering pH=4 so [H+]=(10)^-4 M , and all those H+ ions come from H2X being dissociting to H+ and HX-?)
ka1=[H+]^2/[H2X]
So [H2X]=((10)^-4)^2)/(2*(10)^-6)=5*(10)^-3 M
I always assume that if T is not given that we assume Kw = 1E-14. Yes, you know (H^+) = 1E-4 and since ka2 is so much smaller than ka1 you ignore the H^+ from ka2. And you're right that H2X dissociats to H^+ and HX^- but you're incorrect after that.
Let Y = (H2X)
.......H2X ==> H^+ + HX^-
I.......Y......0.....0
C......-x......x.....x
E......Y-x.....x.....x
So you know x - 1E-4 and you plug in the numbers to Ka1.
Ka1 = (1E-4)(1E-4)/(Y-1E-4) = ? and solve for Y. That gives you (H^+) and (HX^-) and H2X. That leaves only X^2-. You get that from Ka2.
Ka2 = (H^+)(X^2-)/(HX^-)
But from Ka1 calculation, you know (H^+) = (HX^-). (H^+) in the numerator cancels with (HX^-) in the denominator of Ka2 and leave (X^2-) = Ka2.
To find the concentrations of [H2X], [HX-], and [X^2-] in the solution, we can use the information given about the pH and the acid dissociation constants (ka1 and ka2).
First, let's calculate the concentration of [H2X] using the equation [H2X] = ([H+]^2) / ka1. Given that the pH of the solution is 4, we can determine that [H+] is equal to (10^-4) M. Substituting this value into the equation, we have [H2X] = ((10^-4)^2) / (2 * (10^-6)) = 5 * (10^-3) M.
Next, let's consider the ionization reaction of H2X: H2X ⇌ H+ + HX-. The concentration of [HX-] in the solution can be assumed to be equal to [H+], as all the H+ ions come from the dissociation of H2X. Therefore, [HX-] = [H+] = (10^-4) M.
Finally, since ka1 represents the equilibrium constant for the reaction HX- ⇌ H+ + X2-, we can use this to find the concentration of [X^2-]. The equation is ka1 = ([H+][X^2-]) / [HX-]. Substituting the known values, we have (2 * (10^-6)) = ((10^-4)[X^2-]) / (10^-4). Simplifying the equation, we find [X^2-] = 2 * (10^-6) M.
Therefore, the concentrations of [H2X], [HX-], and [X^2-] in the solution are approximately 5 * (10^-3) M, 10^-4 M, and 2 * (10^-6) M, respectively.