   Chapter 17, Problem 76PS

Chapter
Section
Textbook Problem

The chemistry of silver(I) cyanide: (a) Calculate the solubility of AgCN(s) in water from the Ksp value. (b) Calculate the value of the equilibrium constant for the reaction A g C N ( s ) + C N − ( a q ) ⇄ [ A g ( C N ) 2 ] − ( a q ) from Ksp and Kf values and predict from this value whether AgCN(s) would dissolve in KCN(aq). (c) Determine the equilibrium constant for the reaction A g C N ( s ) + 2   S 2 O 3 2 − ( a q ) ⇄ [ A g ( S 2 O 3 ) 2 ] 3 − ( a q ) + C N − ( a q ) Calculate the solubility of AgCN in a solution containing 0.10 M S2O32− and compare the value to the solubility in water [part (a)].

(a)

Interpretation Introduction

Interpretation:

The solubility of AgCN in water has to be calculated using Ksp value for AgCN.

Concept introduction:

The solubility of a salt is defined as the maximum amount of salt that can be dissolved in definite amount of solvent. It is expressed in moles per liter or grams per liter. Solubility in terms of moles per liter is called molar solubility and is defined as the number of moles of solute (salt) dissolved in per liter of solution.

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Ksp of a salt is given as,

AxBy(s)xAy+(aq)+yBx(aq)Ksp=[Ay+]x[Bx]y

The solubility of AgCN in water is 7.75×109.

Explanation

Solubility product constant Ksp for AgCN is 6.0×1017.

AgCN dissociates as follows in water,

AgCN(s)Ag+(aq)+CN1(aq)

The expression for Ksp,

Ksp=[Ag+][CN1] (1)

The ICE table (1) is as follows,

EquationAgCN(s)Ag+(aq)+CN1(aq)Initial (M)00Change (M)+s+sEquilibrium (M) ss

Here, s is the molar solubility of AgCN

(b)

Interpretation Introduction

Interpretation:

The value of the net equilibrium constant Knet has to be calculated for the given reaction.

AgCN(s)+CN1(aq)Knet[Ag(CN)2](aq)

Concept introduction:

Some metal ions when present in an aqueous solution containing anions or neutral species called Lewis base or ligands having a tendency to donate electron pairs to metal ions then complex ion formation will take place.

Example of metal ions that form complex ions includes,Cd2+,Fe2+,Zn2+,Ni2+ etc.

Example of Lewis bases includes,NH3,OH etc.

The complex ion remains in equilibrium with the metal ion and the ligand called complex ion formation equilibrium and the equilibrium constant is called as formation constant Kf.

A larger value of Kf implies that the complex ion formed is more stable. Kf is the measure of the strength of the interaction between the metal ions and the Lewis base to form the complex ion.

For example for general complex ion formation reaction,

xM+yL[MxLy]

Kf can be given as

Kf=[MxLy][M]x[L]y

Here,

• [MxLy] is the equilibrium concentration of complex ion.
• [M] is the equilibrium concentration of metal ion.
• [L] is the equilibrium concentration of the ligand.
• x and y are the coefficients of metal ion and ligand respectively.

Complex ions are stable and thus formation of these increase the solubility of the salt containing the metal ions same as in complex ions. Effect of complex ion formation on the solubility of salt can be explained as below,

AgBr when dissolved in water does not dissolve completely and dissociates as follows,

AgBr(s)KspAg+(aq)+Br(aq) (1)

For this reaction Ksp expression is,

Ksp=[Ag+][Br]

Ag+ ions are capable of forming complex with ligand so when aqueous ammonia solution (strong ligand) is added to the saturated solution of AgBr, Ag+ ions present in the solution form complex with NH3.

Ag+(aq)+2NH3(aq)Kf[Ag(NH3)2]+(aq) (2)

The expression for formation constant Kf is given as,

Kf=[[Ag(NH3)2]+][Ag+][NH3]2

Complex formation leads to the decrease in the concentration of the Ag+ ions in the solution, as a result, according to Le Chatelier’s principle the equilibrium in equation (1) move in the forward direction producing more of the Ag+ ions and the solubility of the slightly soluble salt AgBr increases.

Adding two equilibrium equation (1) and (2) new overall equilibrium constant can be defined.

Net chemical equation:

Ag+(aq)+2NH3(aq)Knet[Ag(NH3)2]+(aq)+Br(aq) (3)

Net equilibrium constant can be given as,

Knet=(Ksp)(Kf) (4)

(c)

Interpretation Introduction

Interpretation:

The value of the net equilibrium constant Knet has to be calculated for the given reaction.

AgCN(s)+2S2O32(aq)Knet[Ag(S2O3)2]3(aq)+CN(aq)

Concept introduction:

The net equilibrium constant, Knet for the equation is given as,

Knet=Ksp×Kf

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