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Chapter 16: Problem 90

Silver cyanide \((\mathrm{AgCN})\) is an insoluble salt with \(K_{\mathrm{sp}}=2.2 \times 10^{-12}\) . Compare the effects on the solubility of silver cyanide by addition of \(\mathrm{HNO}_{3}(a q)\) or by addition of \(\mathrm{NH}_{3}(a q).\)

Short Answer

Expert verified
The addition of both \(\mathrm{HNO}_3\) and \(\mathrm{NH_3}\) increases the solubility of silver cyanide (AgCN) in the solution. The addition of \(\mathrm{HNO}_3\) reacts with \(\mathrm{CN^-}\) to form \(\mathrm{HCN}\), shifting the equilibrium to the right according to Le Chatelier's principle. On the other hand, the addition of \(\mathrm{NH}_3\) reacts with \(\mathrm{Ag^+}\) to form the soluble complex \([\mathrm{Ag(NH_3)_2}]^+\), also shifting the equilibrium to the right and increasing solubility. The overall effect on solubility depends on factors such as concentrations and the individual reactions with the ions.

Step by step solution

01

Write the balanced solubility equilibrium reaction of AgCN

Silver cyanide \((\mathrm{AgCN})\) is an insoluble salt, which breaks into its constituent ions in a saturated solution given by the following equilibrium equation: \[\mathrm{AgCN}(s) \rightleftharpoons \mathrm{Ag^+}(aq) + \mathrm{CN^-}(aq)\]
02

Write the solubility product expression for AgCN

The solubility product expression for AgCN can be written as: \[K_{sp} = [\mathrm{Ag^+}][\mathrm{CN^-}]\] Given that \(K_{sp} = 2.2 \times 10^{-12}\), we can use this value to analyze how the addition of the species affects the solubility.
03

Analyze the effect of adding HNO3 (aq) on the solubility of AgCN

When \(\mathrm{HNO}_3\) is added to the system, it reacts with \(\mathrm{CN^-}\) to form \(\mathrm{HCN}(aq)\), as shown in the reaction below: \[\mathrm{HNO_3}(aq) + \mathrm{CN^-}(aq) \rightarrow \mathrm{HCN}(aq) + \mathrm{NO_3^-}(aq)\] The reaction shifts the solubility equilibrium to the right, which increases the solubility of AgCN and decreases the concentration of \(\mathrm{CN^-}\). This follows Le Chatelier's principle: if a stress is applied to an equilibrium system, such as reacting with one of its ions, the system will shift to minimize this stress.
04

Analyze the effect of adding NH3 (aq) on the solubility of AgCN

When \(\mathrm{NH}_3\) is added, it will react with \(\mathrm{Ag^+}\) to form a soluble complex ion \([\mathrm{Ag(NH_3)_2}]^+\), as shown by the reaction below: \[\mathrm{NH_3}(aq) + \mathrm{Ag^+}(aq) \rightarrow \mathrm{[Ag(NH_3)_2]^{+}}(aq)\] The formation of the soluble complex shifts the equilibrium to the right. As \(\mathrm{Ag^+}\) concentration decreases, the solubility of AgCN increases.
05

Compare the effects of adding HNO3 and NH3 on the solubility of AgCN

Both additions increase solubility of AgCN by reacting with the ions, causing the equilibrium to shift to the right. Adding \(\mathrm{HNO}_3\) reacts with \(\mathrm{CN^-}\) forming \(\mathrm{HCN}\), while adding \(\mathrm{NH_3}\) reacts with \(\mathrm{Ag^+}\) forming the soluble complex \([\mathrm{Ag(NH_3)_2}]^+\). The overall effect on solubility will depend on factors such as the concentrations of \(\mathrm{HNO}_3\) and \(\mathrm{NH_3}\) and their reactions with the respective ions; however, both will increase the solubility of silver cyanide (AgCN) in the solution.

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Most popular questions from this chapter

Calculate the molar solubility of $\mathrm{Cd}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=5.9 \times 10^{-15}.$

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