   Chapter 17, Problem 59PS

Chapter
Section
Textbook Problem

Compare the solubility, in milligrams per milliliter, of silver iodide, AgI, (a) in pure water and (b) in water that is 0.020 M in AgNO3.

a)

Interpretation Introduction

Interpretation:

The solubility of silver iodide AgI salt in milligrams per milliliter unit has to be calculated in pure water.

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.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)xAy+(aq)+yBx(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[Bx]y (1)

The ICE table (1) for salt AxBy, which relates the equilibrium concentration of ions in the solution is given as follows,

EquationAxByxAy++yBxInitial(M)00Change(M)+xs+ysEquilibrium(M)xsys

From the table,

[Ay+]=xs[Bx]=ys

Substitute xs for [Ay+] and ys for [Bx] in equation (1).

Ksp=(xs)x(ys)y=xxyy(s)x+y

Rearrange for s.

s=(Kspxxyy)1/(x+y)

Here,

• x is the coefficient of the cation A+y.
• y is the coefficient of the anion Bx.
• s is the molar solubility.

The value of Ksp is calculated by using molar solubility of the salt.

Explanation
• The solubility of the salt AgI in pure water is calculated below.

Given:

Refer to the Appendix J in the textbook for the value of Ksp.

The value of solubility product constant,Ksp of AgI is 8.5×1017.

The balanced chemical reaction for the dissolution of AgI in water is,

AgI(s) Ag+(aq)+ I(aq)

The ICE table(2) is as follows,

EquationAgI(s)Ag+(aq)+I(aq)Initial (M)00Change (M)+s+sEquilibrium (M) ss

The Ksp expression for AgI is,

Ksp=[Ag+][I1] (2)

From the table,

[Ag+]=s[I1]=s

Substitute s for [Ag+] and [I1] in equation (2).

Ksp=(s)(s)

Here,

• Ksp is solubility product constant
• s is the molar solubility of the salt AgI.

Ksp=s2

Rearrange for s.

s=Ksp2

Substitute 8.5×1017 for Ksp.

s=8.5×10172= 9.22×109molL1

• Calculation of the solubility of AgI in pure water in milligrams per milliliter unit

(b)

Interpretation Introduction

Interpretation:

The solubility of salt AgI has to be calculated in the presence of 0.02 MAgNO3 in water and also it has to be compared with the solubility value in pure water.

Concept introduction:

The solubility of a salt decreases if in the solution one of the ions common to the dissolved ion of salt is already present before the dissolution of salt due to common ion effect. This can be explained on the basis of Le-Chatelier’s principle. According to which reaction will be more on the left side rather than right if one the ion from product side is already present before equilibrium.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)xAy+(aq)+yBx(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[Bx]y (3)

For example, if anion Bx is already present in the solution before equilibrium, therefore a modified ICE table (3) is used to give the concentration relationships between ions.

EquationAxBy(s)=xAy+(aq)+yBx(aq)Initial(M)0s'Change(M)+xs+ysEquilibrium(M)xss'+ys

Here,

• s' is the initial concentration of the anion Bx (common ion coming from strong electrolyte) present in the solution before the dissociation of a weak salt.

From the ICE table (3),

[Ay+]=xs[Bx]=s'+ys

Substitute xs for [Ay+] and s'+ys for [Bx] in equation (3).

Ksp=(xs)x(s'+ys)y

The value of s is very small in comparison to the value of s'. Therefore it can be neglected and the expression of Ksp changes to,

Ksp=(xs)x(s')y

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 