Question

Given the following equilibrium for the dissoluton of calcite, CaCO3 (Quant Analysis)

Given the following equilibrium for the dissolution of calcite, CaCO3 H2O ←→ H++ OH' ; Kw 2+ 1. Use the systematic approach to equilibrium to derive a mathematical expression for [Ca?] concentration in terms of [H], Ksp, K1 and K2 2. Use your textbook to get values for Ksp, K and K and then calculate the solubility of Caco, at pH 8.

Answer 1

Mathematical expression for [Ca²⁺]

From Eqn 1: K_sp = [Ca²⁺][CO₃^2-] ........................ (1)

From Eqn 2 : k₂ = [HCO₃^-] /[CO₃^2-] [H⁺] .................(2)

or   [HCO₃^-] = k₂ [CO₃^2-] [H⁺] ...............................(3)

From Eqn 3: K₁ = 1 / [HCO₃^-] [H⁺] .........................(4)

Now put the value of (3) in (4)

K₁ = 1 /  k₂ [CO₃^2-] [H⁺] [H⁺] ....................(5)

From Eqn 4: K_w =  [H⁺] [OH^-] or ........................(6)

[H⁺] = K_w / [OH^-] ..................................(7)

Now put the value of (7) in (5)

K₁ = [OH^-] /  K_w . k₂ [CO₃^2-] [H⁺] or

[CO₃^2-] = [OH^-] /  K_1. K_w . k₂  [H⁺] ...................(8)

Now put the value of (8) in (1)

K_sp = [Ca²⁺] [OH^-] /  K_1. K_w . k₂  [H⁺] or

   [Ca²⁺] = K_sp. K_1. K_w . k₂  [H⁺] / [OH^-]  or

  [Ca²⁺] = K_sp. K_1. K_w . k₂  [H⁺]² / K_w  

= K_sp. K_1. k₂  [H⁺]²