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)

विकल्प

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Answer 1

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)