
Concept explainers
Answers to all problems are at the end of this book. Detailed solutions are available in the Student Solutions Manual, Study Guide, and Problems Book.
Polyprotic Adds: Phosphate Species Abundance at Different pHs What are the approximate fractional concentrations of the following phosphate species at pH values of 0,2, 4, 6, 8, 10, and 12?
- H3PO4
- Η2ΡΟ4-
- HPO42-
- PO43-

(a)
To calculate:
The approximate fractional concentrations of H3PO4 at pH values of 0,2,4,6,8,10, and 12.
Concept Introduction:
Phosphoric acid has three H+ dissociations.
The Henderson-Hasselbalch equation is as follows:
Explanation of Solution
Rearranging the Henderson-Hasselbalch equation as follows:
At particular pH,
Fraction of any species at a particular pH is concentration of the species divided by the sum of the concentration of all species.
We can rewrite the above equation as a function of x, y, and z.
We can manually calculate x, y, z and fractions of each species, but it is time consuming. Therefore, for efficiency we can calculate them using a spread sheet as follows:
pH | x | y | z |
0 | 0.00707946 | 6.3096E-08 | 3.9811E-13 |
2 | 0.70794578 | 6.3096E-06 | 3.9811E-11 |
4 | 70.7945784 | 0.00063096 | 3.9811E-09 |
6 | 7079.45784 | 0.06309573 | 3.9811E-07 |
8 | 707945.784 | 6.30957344 | 3.9811E-05 |
10 | 70794578.4 | 630.957344 | 0.00398107 |
12 | 7079457844 | 63095.7344 | 0.39810717 |
Thus,
pH | Fraction of H3PO4 |
0 | 0.993 |
2 | 0.585 |
4 | 0.014 |
6 | 0.000 |
8 | 0.000 |
10 | 0.000 |
12 | 0.000 |

(b)
To calculate:
The approximate fractional concentrations of H2PO4- at pH values of 0,2,4,6,8,10, and 12 should be calculated
Introduction:
Phosphoric acid has three H+ dissociations.
The Henderson-Hasselbalch equation is as follows:
Explanation of Solution
Rearranging the Henderson-Hasselbalch equation as follows:
At particular pH,
Fraction of any species at a particular pH is concentration of the species divided by the sum of the concentration of all species.
We can rewrite the above equation as a function of x, y, and z.
We can manually calculate x, y, z and fractions of each species, but it is time consuming. Therefore, for efficiency we can calculate them using a spread sheet as follows:
pH | x | y | z |
0 | 0.00707946 | 6.3096E-08 | 3.9811E-13 |
2 | 0.70794578 | 6.3096E-06 | 3.9811E-11 |
4 | 70.7945784 | 0.00063096 | 3.9811E-09 |
6 | 7079.45784 | 0.06309573 | 3.9811E-07 |
8 | 707945.784 | 6.30957344 | 3.9811E-05 |
10 | 70794578.4 | 630.957344 | 0.00398107 |
12 | 7079457844 | 63095.7344 | 0.39810717 |
Thus,
pH | Fraction of H2PO4- |
0 | 0.007 |
2 | 0.415 |
4 | 0.985 |
6 | 0.941 |
8 | 0.137 |
10 | 0.002 |
12 | 0.000 |

(c)
To calculate:
The approximate fractional concentrations of HPO42- at pH values of 0,2,4,6,8,10, and 12.
Introduction:
Phosphoric acid has three H+ dissociations.
The Henderson-Hasselbalch equation is as follows:
Explanation of Solution
Rearranging the Henderson-Hasselbalch equation as follows:
At particular pH,
Fraction of any species at a particular pH is concentration of the species divided by the sum of the concentration of all species.
We can rewrite the above equation as a function of x, y, and z.
We can manually calculate x, y, z and fractions of each species, but it is time consuming. Therefore, for efficiency we can calculate them using a spread sheet as follows:
pH | x | y | z |
0 | 0.00707946 | 6.3096E-08 | 3.9811E-13 |
2 | 0.70794578 | 6.3096E-06 | 3.9811E-11 |
4 | 70.7945784 | 0.00063096 | 3.9811E-09 |
6 | 7079.45784 | 0.06309573 | 3.9811E-07 |
8 | 707945.784 | 6.30957344 | 3.9811E-05 |
10 | 70794578.4 | 630.957344 | 0.00398107 |
12 | 7079457844 | 63095.7344 | 0.39810717 |
Thus,
pH | Fraction of HPO42- |
0 | 0.000 |
2 | 0.000 |
4 | 0.001 |
6 | 0.059 |
8 | 0.863 |
10 | 0.994 |
12 | 0.715 |

(d)
To calculate:
The approximate fractional concentrations of PO43- at pH values of 0,2,4,6,8,10, and 12.
Concept Introduction:
Phosphoric acid has three H+ dissociations.
The Henderson-Hasselbalch equation is as follows:
Explanation of Solution
Rearranging the Henderson-Hasselbalch equation as follows:
At particular pH,
Fraction of any species at a particular pH is concentration of the species divided by the sum of the concentration of all species.
We can rewrite the above equation as a function of x, y, and z.
We can manually calculate x, y, z and fractions of each species, but it is time consuming. Therefore, for efficiency we can calculate them using a spread sheet as follows:
pH | x | y | z |
0 | 0.00707946 | 6.3096E-08 | 3.9811E-13 |
2 | 0.70794578 | 6.3096E-06 | 3.9811E-11 |
4 | 70.7945784 | 0.00063096 | 3.9811E-09 |
6 | 7079.45784 | 0.06309573 | 3.9811E-07 |
8 | 707945.784 | 6.30957344 | 3.9811E-05 |
10 | 70794578.4 | 630.957344 | 0.00398107 |
12 | 7079457844 | 63095.7344 | 0.39810717 |
Thus,
pH | Fraction of PO43- |
0 | 0.000 |
2 | 0.000 |
4 | 0.000 |
6 | 0.000 |
8 | 0.000 |
10 | 0.004 |
12 | 0.285 |
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Chapter 2 Solutions
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- BiochemistryBiochemistryISBN:9781305577206Author:Reginald H. Garrett, Charles M. GrishamPublisher:Cengage Learning
