The correct answer is option D, that is, 3 × 10⁻³ M.
The following is the equation that represent the equilibrium for the formation of tetramminecopper (II) ion:
Kf = [Cu(NH₃)₄)] / [Cu] [NH₃]₄ ----------- Equation (i)
It is known that 99.9 % of copper is in the form of ammonia complex and 0.01 % of it is found in its free state, the reaction will be:
[Cu(NH₃)₄] / [Cu] = 0.999 / 0.001
Substituting the equation (i) we get:
1.1 × 10¹³ = 0.999 / (0.001) (NH₃)₄
After solving for ammonia we get:
[NH₃] = (999 / 1.1 × 10¹³)1/4
[NH₃] = 3.08 × 10⁻³ M