Question

If the dissociation constant of [Cu(NH₃)₄]²⁺ is X × 10¹². Determine X.

Cu²⁺ + NH₃ ⇌ [Cu(NH₃)]²⁺ K₁ = 10⁴

[Cu(NH₃)]²⁺ + NH₃ ⇌ [Cu(NH₃)]²⁺ K₂ = 1.58 × 10³

[Cu(NH₃)₂]²⁺ + NH₃ ⇌ [Cu(NH₃)₃]²⁺ K₃ = 5 × 10²

[Cu(NH₃)₃]²⁺ + NH₃ ⇌ [Cu(NH₃)₄]²⁺ K₄ = 10²

Answer 1

Explanation:

Degree of dissociation:

• The degree of association is classified as the fraction of the total number of molecules that are connected or combined, resulting in a larger molecule being created.
• The degree of dissociation is the phenomenon of producing free ions carrying current, which at a given concentration is dissociated from the fraction of solute.

The dissociation constant: The dissociation constant is the ratio of dissociated ions (products) to original acid (reactants). It is abbreviated as ${\mathrm{K}}_{\mathrm{a}}$.

$$\begin{gathered} {\mathrm{Cu}}^{2+}+{\mathrm{NH}}_3\stackrel{{\mathrm{K}}_1}{\rightleftharpoons }{\left[\mathrm{Cu}\left({\mathrm{NH}}_3\right)\right]}^{2+} \\ {\left[\mathrm{Cu}\left({\mathrm{NH}}_3\right)\right]}^{2+}+{\mathrm{NH}}_3\stackrel{{\mathrm{K}}_2}{\rightleftharpoons }{\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_2\right]}^{2+} \\ {\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_2\right]}^{2+}+{\mathrm{NH}}_3\stackrel{{\mathrm{K}}_3}{\rightleftharpoons }{\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_3\right]}^{2+} \\ {\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_3\right]}^{2+}+{\mathrm{NH}}_3\stackrel{{\mathrm{K}}_4}{\rightleftharpoons }{\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4\right]}^{2+} \\ {\mathrm{Cu}}^{2+}+4{\mathrm{NH}}_3\stackrel{\mathrm{K}}{\rightleftharpoons }{\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4\right]}^{2+} \end{gathered}$$

$$\begin{gathered} \mathrm{So} \\ \mathrm{K}={\mathrm{K}}_1\times {\mathrm{K}}_2\times {\mathrm{K}}_3\times {\mathrm{K}}_4 \\ ={10}^4\times 1.58\times {10}^3\times 5\times {10}^2\times {10}^2 \\ \mathrm{K}=7.9\times {10}^{11} \\ \mathrm{Where}\mathrm{K}\to \mathrm{Equilibrium}\mathrm{constant}\mathrm{for}\mathrm{formation}\mathrm{of}[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4{]}^{2+} \\ \mathrm{So}\mathrm{equilibrium}\mathrm{constant}(\mathrm{K}\text{'})\mathrm{for}\mathrm{dissociation}\mathrm{of}[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4{]}^{2+}\mathrm{is}\frac{1}{\mathrm{k}} \\ \mathrm{K}\text{'}=\frac{1}{\mathrm{k}} \\ \mathrm{K}\text{'}=\frac{1}{7.9\times {10}^{11}} \\ =1.26\times {10}^{-12}=(\mathrm{x}\times {10}^{-12}) \end{gathered}$$

So, the value of $\mathrm{X}=1.26$.