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Question
The stepwise formation of [Cu(NH3)4]2+ is given below:
\[\ce{Cu^{2+} + NH3 <=>[K1] [Cu(NH3)]^{2+}}\]
\[\ce{[Cu(NH3)]^{2+} + NH3 <=>[K2] [Cu(NH3)2]^{2+}}\]
\[\ce{[Cu(NH3)2]^{2+} + NH3 <=>[K3] [Cu(NH3)3]^{2+}}\]
\[\ce{[Cu(NH3)3]^{2+} + NH3 <=>[K4] [Cu(NH3)4]^{2+}}\]
The value of stability constants K1, K2, K3 and K4 are 104, 1.58 × 102, 5 × 103 and 102 respectively. The overall equilibrium constant for dissociation of [Cu(NH3)4]2+ is x × 10−12. The value of x is ______. (Rounded-off to the nearest integer)
Options
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Solution
The stepwise formation of [Cu(NH3)4]2+ is given below:
\[\ce{Cu^{2+} + NH3 <=>[K1] [Cu(NH3)]^{2+}}\]
\[\ce{[Cu(NH3)]^{2+} + NH3 <=>[K2] [Cu(NH3)2]^{2+}}\]
\[\ce{[Cu(NH3)2]^{2+} + NH3 <=>[K3] [Cu(NH3)3]^{2+}}\]
\[\ce{[Cu(NH3)3]^{2+} + NH3 <=>[K4] [Cu(NH3)4]^{2+}}\]
The value of stability constants K1, K2, K3 and K4 are 104, 1.58 × 102, 5 × 103 and 102 respectively. The overall equilibrium constant for dissociation of [Cu(NH3)4]2+ is x × 10−12. The value of x is 1.
Explanation:
Equilibrium constant for the overall reaction,
\[\ce{Cu^{2+} + 4NH3 <=> [Cu(NH3)4]^{2+}}\]
∴ K = K1 × K2 × K3 × K4
K = 104 × 1.58 × 103 × 5 × 102 × 102
= 7.9 × 1011
For dissociation of [Cu(NH3)4]2+
∴ Equilibrium constant
K' = `1/"K"`
= `1/(7.9 xx 10^11)`
= 1.26 × 10−12
Therefore x = 1 (rounded off to the nearest integer)
