Commercial silver plating operations frequently use a solution containing the co

Question

Commercial silver plating operations frequently use a solution containing the complex [Ag?(CN)_2]^- ion. Because the formation constant K_1 is quite large, this procedure ensures that the free Ag^+ concentration in solution is low to promote uniform electrodeposition. In one process, a chemist added 9.0 L of 5.4M NaCN to 90.0 L of 0.17 M AgNO_3. Calculate the concentration of free Ag^+ ions at equilibrium. K_1 for this reaction is 1.0 times 10^21. times 10^_________M Enter your answer in scientific notation.

Explanation / Answer

moles of NaCN = 5.4 M x 9 L = 48.6 mols

moles of AgNO3 = 0.17 M x 90 L = 15.3 mols

Ag+ + 2CN- <==> [Ag(CN)2]-

formed [Ag(CN)2]- = 15.3 mols/99 L = 0.154 M

remaining [CN-] = (48.6 - 2 x 15.3)mol/99 L = 0.182 M

                       Ag+   +   2CN- <==> [Ag(CN)2]-

initial                -            0.182               0.154

change            +x           +2x                   -x

Eq                   +x        0.182+2x        0.154-x

----

Kf = 1 x 10^21 = (0.154 -x)/(x)(0.182 + 2x)^2

4 x 10^-21x^3 + 7.28 x 10^20x^2 + 3.3 x 10^19x - 0.154 = 0

Free [Ag+] = x = 4.66 x 10^-21 M

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