   Chapter 16, Problem 129SCQ

Chapter
Section
Textbook Problem

Consider a salt of a weak base and a weak acid such as ammonium cyanide. Both the NH4+ and CN− ions interact with water in aqueous solution, but the net reaction can be considered as a proton transfer from NH4+ to CN−.NH4+(aq) + CN−(aq) ⇌ NH3(aq) + HCN(aq) (a) Show that the equilibrium constant for this reaction, Kact, is 1. K net = K a K b K w where Ka is the ionization constant for the weak acid NH4+ and Kb, is the constant for the weak base CN−. (b) Calculate Knet values fur each of the following, NH4CN, NH4CH3CO2, and NH4K Which salt has the largest value of Kact, and why? (c) Predict whether a solution of each of the compounds in (b) is acidic or basic. Explain how you made this prediction (Yon do not need a calculation to make this prediction.)

(a)

Interpretation Introduction

Interpretation:

The equilibrium constant for the reaction has to be determined.

Concept Introduction:

Equilibrium constants:

The equilibrium constant is used to quantitative measurement of the strength of the acid and bases in the water.

Ka is an acid constant for equilibrium reactions.

HA + H2OH3O++ A-Ka[H3O+][A-][HA]

Kb is base constant for equilibrium reaction.

BOH + H2OB++ OH-Ka[B+][OH-][BOH]

The value of Knet is derived from three equations. The three equations represent acid ionization constant for a weak acid, base ionization constant for a weak base and autoionization of water.

Explanation

For ammonium ion;

NH4+(aq)+H2O(l)NH3(aq)+H3O+(aq)                                                         (1)

From equation 1,

K1=Ka

For cyanide ion;

CN(aq)+H2O(l)HCN(aq)+OH(aq)                                                           (2)

From equation 2,

K2=Kb

For autoionization of water;

H3O+(

(b)

Interpretation Introduction

Interpretation:

The Knet values has to be calculated for three salts and salt with the largest value of the equilibrium constant is to be identified.

Concept Introduction:

The value of Knet is derived from three equations. The three equations represent acid ionization constant for a weak acid, base ionization constant for a weak base and autoionization of water.

Value of Knet is calculated for the three salts (of a weak acid and weak base) by using the equation given below:

Knet=KaKbKw

From a comparison of values of the acid dissociation constant and base dissociation constant, nature of the solution is predicted.

If the value of acid dissociation constant is more than the value of base dissociation constant, then the products will have more acidic species and therefore the nature of solution will be acidic.

On the same concept, if the value of base dissociation constant is more than acid dissociation constant then the solution will be basic.

If the value of acid and base dissociation constant is equal then the solution becomes neutral.

(c)

Interpretation Introduction

Interpretation:

Nature of solution of different salts is predicted according to their acid or base ionization constant.

Concept Introduction:

Equilibrium constants:

The equilibrium constant is used to quantitative measurement of the strength of the acid and bases in the water.

Ka is an acid constant for equilibrium reactions.

HA + H2OH3O++ A-Ka[H3O+][A-][HA]

Kb is a base constant for equilibrium reaction.

BOH + H2OB++ OH-Ka[B+][OH-][BOH]

Ion product constant for water

Kw= [H3O+][OH-]       =1.00×10-14 pH = -log[H3O+]pOH= -log[OH-]

Relation between pH and pOH

pH + pOH =14

The value of Knet is derived from three equations. The three equations represent acid ionization constant for a weak acid, base ionization constant for a weak base and autoionization of water.

Value of Knet is calculated for the three salts (of a weak acid and weak base) by using the equation given below:

Knet=KaKbKw

From a comparison of values of the acid dissociation constant and base dissociation constant, nature of the solution is predicted.

If the value of acid dissociation constant is more than the value of base dissociation constant, then the products will have more acidic species and therefore the nature of solution will be acidic.

On the same concept, if the value of base dissociation constant is more than acid dissociation constant then the solution will be basic.

If the value of acid and base dissociation constant is equal then the solution becomes neutral.

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