What is the molar solubility of AgCl (Ksp = 1.80 x 10-¹0) in 0.690 MNH? (Kf of Ag(NH₂), is 1.7 x 107)

The equilibirum reaction for the dissolution of AgCl is given below.The equilibrium for the…

Answered: What is the molar solubility of AgCl…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

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What is the molar solubility of AgCl (Ksp = 1.80 x 10-¹0) in 0.690 M
NH? (Kf of Ag(NH₂), is 1.7 x 107)

Expert Solution

Step 1: Determination of overall equilibrium reaction

The equilibirum reaction for the dissolution of AgCl is given below.

$A g C l left parenthesis s right parenthesis space left right double arrow A g to the power of plus left parenthesis a q right parenthesis space plus C l to the power of minus left parenthesis a q right parenthesis space space space space space space space space space space space space space space space space K subscript s p end subscript equals 1.80 cross times 10 to the power of negative 10 end exponent$

The equilibrium for the formation of complex is given below.

$A g to the power of plus left parenthesis a q right parenthesis space plus 2 N H subscript 3 left parenthesis a q right parenthesis left right double arrow A g left parenthesis N H subscript 3 right parenthesis subscript 2 to the power of plus left parenthesis a q right parenthesis space space space space space space space space space K subscript f space equals 1.7 cross times 10 to the power of 7$

Combine the above reactions to get the overall reaction.

$A g C l left parenthesis s right parenthesis space left right double arrow up diagonal strike A g to the power of plus left parenthesis a q right parenthesis end strike space plus C l to the power of minus left parenthesis a q right parenthesis space space space space space space space space space space space space space space space space K subscript s p end subscript equals 1.80 cross times 10 to the power of negative 10 end exponent up diagonal strike A g to the power of plus left parenthesis a q right parenthesis end strike space plus 2 N H subscript 3 left parenthesis a q right parenthesis left right double arrow A g left parenthesis N H subscript 3 right parenthesis subscript 2 to the power of plus left parenthesis a q right parenthesis space space space space space space space space space K subscript f space equals 1.7 cross times 10 to the power of 7 minus negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative A g C l left parenthesis s right parenthesis space plus space 2 N H subscript 3 left parenthesis a q right parenthesis space left right double arrow A g left parenthesis N H subscript 3 right parenthesis subscript 2 to the power of plus left parenthesis a q right parenthesis space plus C l to the power of minus left parenthesis a q right parenthesis space space space K space equals K subscript s p end subscript space cross times K subscript f space$

Explanation: when two equilibrium reactions are added, the corresponding equilibrium constants get multiplied to give the equilibrium constant for the overall reaction.

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