The pH of a 0.175 M aqueous solution of a weak acid is 3.52. What is Ka for this acid ?
Weak acid is HA.
HA ==> H^+ + A^-
Ka = (H^+)(A^-)/(HA)
Convert pH to H^+, substitute into Ka expression for Ka and solve for Ka.
To find the value of Ka for the weak acid, we can use the equation Ka = [H3O+][A-] / [HA], where [H3O+] represents the concentration of the hydronium ion, [A-] represents the concentration of the conjugate base, and [HA] represents the concentration of the weak acid.
We already know the pH of the solution, which is 3.52. The pH is a measure of the acidity of a solution and is defined as the negative logarithm (base 10) of the hydronium ion concentration ([H3O+]).
To find the hydronium ion concentration, we can use the equation pH = -log[H3O+]. Rearranging this equation, we get [H3O+] = 10^(-pH).
Substituting the given pH value of 3.52 into this equation, we find [H3O+] = 10^(-3.52) = 2.5119 x 10^(-4) M.
Now, let's assume that the initial concentration of the weak acid is [HA], and at equilibrium, it dissociates to produce [H3O+] and [A-] in equal amounts ([HA] - [H3O+] = [A-]). Therefore, the concentration of [H3O+] and [A-] is half of [HA], which is [HA]/2.
Substituting the given concentration of the weak acid (0.175 M) into this equation, we find [HA]/2 = 0.175/2 = 0.0875 M.
Now, we have all the required concentrations to calculate the Ka value.
Ka = [H3O+][A-] / [HA]
= (2.5119 x 10^(-4) M) * (0.0875 M) / (0.175 M)
= 1.25595 x 10^(-4) / 0.175
= 7.1743 x 10^(-4)
Therefore, the value of Ka for this weak acid is approximately 7.1743 x 10^(-4).