General Chemistry
General Chemistry
4th Edition
ISBN: 9781891389603
Author: Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly
Publisher: University Science Books
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Chapter 22, Problem 22.95P
Interpretation Introduction

Interpretation:

The solubility of AgCH3COO(s) in solution buffered at pH=2,4,6,8 and10 should be calculated.

Concept Introduction:

Solubility is defined as the maximum quantity of solute dissolved in a given amount of solvent to make a saturated solution at a particular temperature.

Molar solubility is the number of moles of a solute that can be dissolved in one liter of a solution. It is expressed as mol/L or M (molarity).

Consider a general reaction:

  MnXm(s)nMm+(aq)+mXn+(aq)

The relation between solubility product and molar solubility is as follows:

  Ksp=[Mm+]n[Xn-]m

Here

The solubility product of salt is Ksp.

The molar solubility of Mm+ ion is [Mm+]

The molar solubility of Xn- ion is [Xn-]

pH definition:

The concentration of hydrogen ion is measured using pH scale. The acidity of aqueous solution is expressed by pH scale.

  pH=-log[H3O+]

Expert Solution & Answer
Check Mark

Answer to Problem 22.95P

The solubility of AgCH3COO(s) in solution buffered at pH=2,4,6,8 and10 are given as 1.02M, 1.02×03M, 1.02×105M, 1.02×107M and 1.02×109M respectively.

Explanation of Solution

Given data is as follows:

  pH =2.00

The concentration of hydronium ion can be calculated as follows:

  pH =2.00pH=log[H+][H+]=10(2)[H+]=0.01M

The solubility can be calculated as follows:

  AgCH3COO(s)Ag+(aq)+CH3COO(aq)                     (1)Ksp=[Ag+][CH3COO]=1.9×103M2AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)        (2)Kc=Ksp1Ka=(1.9×103M2)(5.5×104M1)= 104.5M

One Ag+ ion will be there for every formula unit of silver acetate that dissolves. Hence, the solubility will be equal to the concentration of Ag+ ion. Comparing the Ksp and Kc values, the value of Kc is much greater than Ksp and thus the additional contribution to solubility from (1) can be ignored.

  s=[Ag+]=[CH3COOH]

The solubility at pH =2.00 can be calculated as follows:

  AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)Initial1.0×102M0M0.200MChange+s+sEquilibrium1.0×102Mss

Substituting the values,

  Kc=[Ag+][CH3COOH][H3O+]= 104.5M104.5M=s×s[1.0×102M]210.2=s0.1s=1.02M

The solubility is calculated to be 1.02M.

The solubility at pH =4.00 can be calculated as follows:

  AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)Initial1.0×104M0M0.200MChange+s+sEquilibrium1.0×104Mss

Substituting the values,

  Kc=[Ag+][CH3COOH][H3O+]= 104.5M104.5M=s×s[1.0×104M]210.2=s1.0×104Ms=1.02×03M

The solubility is calculated to be 1.02×03M.

The solubility at pH =6.00 can be calculated as follows:

  AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)Initial1.0×106M0M0.200MChange+s+sEquilibrium1.0×106Mss

Substituting the values,

  Kc=[Ag+][CH3COOH][H3O+]= 104.5M104.5M=s×s[1.0×106M]210.2=s1.0×106Ms=1.02×105M

The solubility is calculated to be 1.02×105M.

The solubility at pH =8.00 can be calculated as follows:

  AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)Initial1.0×108M0M0.200MChange+s+sEquilibrium1.0×108Mss

Substituting the values,

  Kc=[Ag+][CH3COOH][H3O+]= 104.5M104.5M=s×s[1.0×108M]210.2=s1.0×108Ms=1.02×107M

The solubility is calculated to be 1.02×107M.

The solubility at pH =10.00 can be calculated as follows:

  AgCH3COO(s)+H3O+(aq)Ag+(aq)+CH3COOH(aq)+H2O(l)Initial1.0×1010M0M0.200MChange+s+sEquilibrium1.0×1010Mss

Substituting the values,

  Kc=[Ag+][CH3COOH][H3O+]= 104.5M104.5M=s×s[1.0×1010M]210.2=s1.0×1010Ms=1.02×109M

The solubility is calculated to be 1.02×109M.

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Chapter 22 Solutions

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