Question

Taking the activity coefficient effect into consideration, calculate the concentration of Fe³⁺ in a solution that is saturated with Fe₄[Fe(CN₆]₃ (Iron(III) ferrocyanide). The overall ionic strength of the solution is .01 M.

Iron(III) ferrocyanide Ksp = 3.3*10^-41.

The answer starts with 5.90... please show ALL steps

Answer 1

Fe₄[Fe(CN₆]₃ <---> 4Fe³⁺ + 3[Fe(CN₆]⁴⁺

K_sp =( a_Fe3+)⁴(a_[Fe(CN6]4+)³ = a₊⁴a_-³ = (c₊γ₊ )⁴ (c_- γ_- )³

= (c₊)⁴ (c_-)³ (γ₊)⁴(γ_-)³

= (c₊)⁴ (c_-)³ (γ_{+ -})⁷                     ; γ_{+ -} = mean ionic activity coefficient

If solubility of Fe₄[Fe(CN₆]₃ is S, then we can write, c₊ = 4S; c_- = 3S

K_sp = (4S)⁴ (3S)³ (γ_{+ -})⁷

= 6912* S⁷* (γ_{+ -} )⁷

According to Debye-Huckel limiting law;   log (γ_{+ -}) = - 0.509 Z⁺Z^- √I

or, log (γ_{+ -}) = - 0.509 * 3 * 4 √0.01 = 0.244

Activity solubility product, K_sp = 9.18 * 10^-41

= 6912* S⁷* (0.244 )⁷

or, S = 1.907*10^-6

[Fe³⁺] = 4S = 7.6 * 10^-6 M