The stepwise formation of ${{\left[Cu{\left(N{H}_3\right)}_4\right]}^2}^{+}$  is given below:

$C{u}^{2+}+N{H}_3\stackrel{k_1}{?}{\left[Cu\left(N{H}_3\right)\right]}^{2+}$            

${\left[Cu\left(N{H}_3\right)\right]}^{2+}+N{H}_3\stackrel{k_2}{?}{\left[Cu{\left(N{H}_3\right)}_2\right]}^{2+}$        

  ${\left[Cu{\left(N{H}_3\right)}_2\right]}^{2+}+N{H}_3\stackrel{k_3}{?}{\left[Cu{\left(N{H}_3\right)}_3\right]}^{2+}$          

${\left[Cu{\left(N{H}_3\right)}_3\right]}^{2+}+N{H}_3\stackrel{k_4}{?}{\left[Cu{\left(N{H}_3\right)}_4\right]}^{2+}$            

The value of stability constants k₁, k₂, k₃ and k₄ are  $10^4,1.58\times 10^3,5\times 10^{2}and10^2$ respectively.

The overall equilibrium constants for dissociation of   ${\left[Cu{\left(N{H}_3\right)}_4\right]}^{2+}isx\times 10^{-12}.$ The value of x is________ (Rounded off to the nearest integer)

<p>Stability constant are :</p><p>K₁ = 10⁴</p><p>K₂ = 1.58 × 10³</p><p>K₃ = 5 × 10²</p><p>K₄ = 10²</p><p>Overall stability constant K will be</p><p>K = K₁ × K₂ × K₃ × K₄</p><p>&nbsp;= 7.9 × 10¹¹</p><p>Now, overall equilibrium constant for dissociation of [Cu (NH₃)₄]<strong>²⁺ </strong>is</p><p><span contenteditable="false"> <math> <mrow> <mi>K</mi> <mo>'</mo> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>K</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>7</mn> <mo>.</mo> <mn>9</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>1</mn> <mn>2</mn> <mn>6</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>1</mn> </mrow> </msup> </mrow> </math> </span> &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816690932"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p>= 1.26 × 10^-12</p><p>So; x = 1 (Rounded off to the nearest integer)</p>

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