Question

In the presence of aqueous ammonia, cobalt(III) forms the complex ion Co(NH3)63+. Determine the molar concentration of free cobalt(III) ion in solution when 0.170 mole of Co(NO3)3 is dissolved in a liter of 2.50 M aqueous ammonia.

Answer 1

The formation constants are very large. Since K_f is large, assume all the Co^{3+ i}s consumed and converted to complex ion, Co(NH₃)₆³⁺.

We can determine the concentration of Co³⁺ ions produced by the subsequent dissociation of the complex ion.

The formation constant 'K_f' for the complex ion, Co(NH₃)₆³⁺ is 5.0 10³¹

[NH₃] = 2.50 – 6 0.170 = 1.48

Co³⁺+ 6 NH₃   Co(NH₃)₆³⁺

0 1.180 170

x +6x -x

x 1.48 + 6x 0.170–x

Since x will be small, 1.48 + 6x ≈ 1.48 and 0.170–x ≈ 0.170

K_f = 5.00 x 10³¹= [Co(NH₃)₆³⁺]/([Co³⁺][NH₃]^₆)

Rearranging the above equation,

[Co³⁺] = [Co(NH₃)₆³⁺]/(NH₃]_⁶ Kf) = 0.170 /1.48⁶/5.00 x 10³¹ = 3.23 x 10^-34