Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 16, Problem 16.89QA
Interpretation Introduction

To find:

The pH of 0.100 M FeNO33.

Expert Solution & Answer
Check Mark

Answer to Problem 16.89QA

Solution:

pH of 0.100 M FeNO33 is 1.80

Explanation of Solution

1) Concept:

To determine the pH of the solutions of a variety of metal ions, we will find that these ions act as weak acids in a solution. When FeNO33 dissolves in water, the Fe3+ ions react with water to give a hydrated ferric ion,FeH2O63+. A shift in electron density occurs in hydrated metal ions having a generic formula MH2O6n+ when n2. The electrons in the O-H bonds of the water molecules surrounding the metal ions are attracted to the positively charged ions. The resulting distortion in electron density increases the likelihood of one of these O-H bonds ionizing and donating a H+ ion to a neighboring molecule of water.

2) Formula:

i) Ka=A-H3O+HA

Where, Ka= acid ionization constant of weak acid.

A-= concentration of conjugate base

HA= concentration of acid

ii) pH= -logH3O+

iii) Quadratic equation, ax2+bx+c=0

iv) x= -b±b2-4ac2a

3) Given:

i) FeNO33=0.100 M

ii) For Fe3+ (aq), Ka=3×10-3

The Ka value is taken from table A5.2 of Ka values of hydrated metal ions mentioned in the book.

4) Calculation:

FeNO33 is a salt which shows complete dissociation in an aqueous medium.

FeNO33aqFe3+ aq+3NO3- (aq)

The formula for hydrated metal ion can be written as,FeH2O63+. The hydrated Fe3+ cation draws electron density away from the water molecules of its inner coordination sphere, which makes it possible for one or more of these molecules to donate a H+ ion to a water molecule outside the sphere. The hydrated Fe3+ ion is left with one fewer H2O ligand and a bond between the complex and OH- ion.

FeH2O63+ aq+H2O l FeH2O5(OH)2+ aq+H3O+ (aq)

Now draw the RICE table incorporating the concentrations.

FeH2O63+ M FeH2O5(OH)2+ M H3O+ M
Initial (I) 0.100 0 0
Change (C) -x +x +x
Equilibrium (E) 0.100-x x x

Ka=FeH2O5(OH)2+H3O+FeH2O63+

3×10-3= xx0.100-x

3×10-4-3×10-3x=x2

x2+ 3×10-3x-3×10-4=0

Therefore,  a=1, b= 3×10-3 and c= -3×10-4.

x= -b±b2-4ac2a

x= -0.003± 0.0032-(41-3×10-4)2×1 

x= -0.003 ± 0.0012092

x= 0.01588 and x= -0.01888

The negative value of x has no physical meaning because it gives us a negative H3O+ value. Therefore,

x=H3O+=0.01588 M

Calculating the pH:

pH= -logH3O+= -log(0.01588)

pH=1.80

pH of 0.100 M FeNO33 is 1.80

Conclusion:

With the help of the RICE table, the pH of a hydrated metal ion is calculated.

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Chapter 16 Solutions

Chemistry: An Atoms-Focused Approach

Ch. 16 - Prob. 16.12QACh. 16 - Prob. 16.13QACh. 16 - Prob. 16.14QACh. 16 - Prob. 16.16QACh. 16 - Prob. 16.17QACh. 16 - Prob. 16.18QACh. 16 - Prob. 16.19QACh. 16 - Prob. 16.20QACh. 16 - Prob. 16.21QACh. 16 - Prob. 16.22QACh. 16 - Prob. 16.23QACh. 16 - Prob. 16.24QACh. 16 - Prob. 16.25QACh. 16 - Prob. 16.26QACh. 16 - Prob. 16.27QACh. 16 - Prob. 16.28QACh. 16 - Prob. 16.29QACh. 16 - Prob. 16.30QACh. 16 - Prob. 16.31QACh. 16 - Prob. 16.32QACh. 16 - Prob. 16.33QACh. 16 - Prob. 16.34QACh. 16 - Prob. 16.35QACh. 16 - Prob. 16.36QACh. 16 - Prob. 16.37QACh. 16 - Prob. 16.38QACh. 16 - Prob. 16.39QACh. 16 - Prob. 16.40QACh. 16 - Prob. 16.41QACh. 16 - Prob. 16.42QACh. 16 - Prob. 16.43QACh. 16 - Prob. 16.44QACh. 16 - Prob. 16.45QACh. 16 - Prob. 16.46QACh. 16 - Prob. 16.47QACh. 16 - Prob. 16.48QACh. 16 - Prob. 16.49QACh. 16 - Prob. 16.50QACh. 16 - Prob. 16.51QACh. 16 - Prob. 16.52QACh. 16 - Prob. 16.53QACh. 16 - Prob. 16.54QACh. 16 - Prob. 16.55QACh. 16 - Prob. 16.56QACh. 16 - Prob. 16.57QACh. 16 - Prob. 16.58QACh. 16 - Prob. 16.59QACh. 16 - Prob. 16.60QACh. 16 - Prob. 16.61QACh. 16 - Prob. 16.62QACh. 16 - Prob. 16.63QACh. 16 - Prob. 16.64QACh. 16 - Prob. 16.65QACh. 16 - Prob. 16.66QACh. 16 - Prob. 16.67QACh. 16 - Prob. 16.68QACh. 16 - Prob. 16.69QACh. 16 - Prob. 16.70QACh. 16 - Prob. 16.71QACh. 16 - Prob. 16.72QACh. 16 - Prob. 16.73QACh. 16 - Prob. 16.74QACh. 16 - Prob. 16.75QACh. 16 - Prob. 16.76QACh. 16 - Prob. 16.77QACh. 16 - Prob. 16.78QACh. 16 - Prob. 16.79QACh. 16 - Prob. 16.80QACh. 16 - Prob. 16.81QACh. 16 - Prob. 16.82QACh. 16 - Prob. 16.83QACh. 16 - Prob. 16.84QACh. 16 - Prob. 16.85QACh. 16 - Prob. 16.86QACh. 16 - Prob. 16.87QACh. 16 - Prob. 16.88QACh. 16 - Prob. 16.89QACh. 16 - Prob. 16.90QACh. 16 - Prob. 16.91QACh. 16 - Prob. 16.92QACh. 16 - Prob. 16.93QACh. 16 - Prob. 16.94QACh. 16 - Prob. 16.95QACh. 16 - Prob. 16.96QACh. 16 - Prob. 16.97QACh. 16 - Prob. 16.98QACh. 16 - Prob. 16.99QA
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