Question

In the presence of aqueous ammonia, cobalt (III) forms the complex ion Co(NH3)6 3+. Determine the molar concentration of free cobalt (III) ion in solution when 0.250 mole of Co(NO3)3 is dissolved in a liter of 2.50 M aqueous ammonia.

Answer 1

Co(NO₃)₃ = Co(III)

Co(III) + 6NH₃ Co(NH₃)₆³⁺

Initial concentrations: 0.25 M 2.5 M 0 M

Equilib. conc. x 1+x 0.25-x

The formation constant (Kf) for Co(NH₃)₆³⁺ = 4.6*10³³

i.e. 4.6*10³³ = (0.25-x)/{x*(1+x)}

i.e. 4.6*10³³ = (0.25-x)/(x²+x)

i.e. 4.6*10³³x² + 4.6*10³³x = 0.25-x

i.e. 4.6*10³³x² + 4.6*10³³x - 0.25 = 0

By solving the above quadratic equation, you will get the value of x, which is the required concentration value of free cobalt(III) ion.

In fact, the molar concentration of free cobalt (III) ion in solution ~ 0 M