The dissociation constant Ka for weak acid HA is 0.25× 10⁻⁷.
Equilibrium constant of a chemical reaction is known as dissociation associated with acid-base reactions. Species HA is an acid that dissociates into the conjugate base of the acid, A , and the hydrogen ion, H⁺ .
First, write the balanced formula for the partial ionization of the acid,
HA(aq) + H₂O(l) ⇌ A⁻ (aq)+H₃O⁺(aq)
Note that there is a 1:1 molar ratio everywhere For every mole of acid that ionizes in aqueous solution, you get 1 mole of its conjugate base and 1 mole of the hydronium ion H₃O⁺.
The equilibrium concentration of hydronium ions can now be calculated from the pH value of the solution.
pH = - log ( [ H₃O⁺]) = [ H₃O⁺ ]= 10⁻ᵖᴴ
For the given question we have a pH of 3.87 which means [H₃O⁺] = 10⁻³·⁸⁷
and concentration of H₂O is 0.400M.
By definition the acid dissociation constant Ka equals to
Ka = [ A⁻ ] [H₃O⁺ ] / [HA]
The acid dissociation constant equation is written using equilibrium concentrations. Therefore, if the reaction produced a hydronium ion concentration equal to 10⁻⁴ M, it also produced a conjugate base concentration equal to 10⁻⁴M. The initial concentration of the acid is much higher than the concentrations of the conjugate base and hydronium ion, so they can be approximated as constants.
Ka = 10⁻⁴ × 10⁻⁴/ 0.400 = 0.25× 10⁻⁷
Hence, the dissociation constant of acid Ka is 0.25× 10⁻⁷.
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