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.

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Answer #1

Mathematical expression for [Ca2+]

From Eqn 1: Ksp = [Ca2+][CO32-] ........................ (1)

From Eqn 2 : k2 = [HCO3-] /[CO32-] [H+] .................(2)

or   [HCO3-] = k2 [CO32-] [H+] ...............................(3)

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

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

K1 = 1 /  k2 [CO32-] [H+] [H+] ....................(5)

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

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

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

K1 = [OH-] /  Kw . k2 [CO32-] [H+] or

[CO32-] = [OH-] /  K1. Kw . k2  [H+] ...................(8)

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

Ksp = [Ca2+] [OH-] /  K1. Kw . k2  [H+] or

   [Ca2+] = Ksp. K1. Kw . k2  [H+] / [OH-]  or

  [Ca2+] = Ksp. K1. Kw . k2  [H+]2 / Kw  

= Ksp. K1. k2  [H+]2

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