The first and second ionization constants of H ₂ X are 2.5 10⁻⁸ and 1.0 10⁻¹³ respectively. The concentration of X ²⁻ in 0.1 M H ₂ X solution is _ _ _ _ 10⁻¹⁵ M . (Nearest Integer)

Step-by-step solution

For a weak diprotic acid H₂X , the ionization steps are: H₂X H^+ + HX^- with K_ a1 = 2.5 10⁻⁸ HX^- H^+ + X²⁻ with K_ a2 = 1.0 10⁻¹³ Since K_ a1 K_ a2 , the concentration of H^+ is primarily determined by the first ionization. [H^+] K_ a1 C = 2.5 10⁻⁸ 0.1 = 2.5 10⁻⁹ = 5 10⁻⁵ M Also, from the first ionization, [HX^-] [H^+] = 5 10⁻⁵ M For the second ionization: K_ a2 = [H^+][X²⁻] [HX^-] Substituting the values: 1.0 10⁻¹³ = (5 10⁻⁵)[X²⁻] 5 10⁻⁵ Thus, [X²⁻] = K_ a2 = 1.0 10⁻¹³ M To express this in the form x 10⁻¹⁵ M : 1