A 1.00 L solution contains 5.00 x 10-5 M Cu(NO3)2 and 1.00 x 10-3 M ethylenediamine. What is the concentration of Cu2 plus (aq) in the solution given for Cu(en)22 plus (aq) Kf 3.2 x 1019?

To find the concentration of ( \text{Cu}^{2+} ) in the solution, we can use the formation constant ( K_f ) for the complex ( \text{Cu(en)}_2^{2+} ). Given that ( K_f = 3.2 \times 10^{19} ), which is very large, we can assume that most of the ( \text{Cu}^{2+} ) will be complexed with ethylenediamine. The initial concentration of ( \text{Cu}^{2+} ) is ( 5.00 \times 10^{-5} , \text{M} ) and the concentration of ethylenediamine is ( 1.00 \times 10^{-3} , \text{M} ). Using the equilibrium concentrations and the large ( K_f ), we can assume that almost all ( \text{Cu}^{2+} ) forms the complex, leading to a negligible concentration of free ( \text{Cu}^{2+} ), approximately ( 1.56 \times 10^{-20} , \text{M} ).