II. Equilibrium Controlled Reactions
Chemistry 211
Learning Objectives:
1. Process: To recognize when assumptions might be necessary in an analytical process.
Fall 2013
2. Content: To apply The Relative Effect Assumption and Fundamental Energy Principles to understand how electron energies control the pK a s of acids.
Using pK a s, Assumptions and Fundamental Energy Principles to judge relative energies of different acids or bases:
1. Introduction:
As we discovered in the Acid-Base Reactions & Electron Energies-1, pK a s give information on the difference in energy between an acid and its conjugate base, but do not provide information concerning relative energies of two different conjugate acids or different conjugate bases. As indicated in the free energy diagram below, the pK a s give us the relative lengths of the solid arrows, but not where the arrows start or end relative to each other, the dotted arrows marked  G
H-D->H-E
and  G
D
-
->E
-.
O
CH
3
C CH
2
+
H
3
O
E
O
G
CH
3
C CH
3
H-E
+
H
2
O pK a
=20 D
G
D
-
->E
-
D
G
H-D->H-E
O
CH
3
C
H-D
O H
+ H
2
O pK a
=4.8
O
CH
3
C
O
D
+
H
3
O
HD & H-E D - & E -
Figure 1: Free Energy Diagram Comparing of Relative Energies to Two Acids and their Conjugate Bases
From Acid-Base Reactions & Electron Energies-1, Question 4 on p. 5.
2. ENERGIES OF CHEMICAL STRUCTURES:
Recall your experience with atomic structure. a. What sub atomic particle was related to energy in atoms? b. How were differences in energy of these particles expressed in atoms? c. What forces among subatomic particles were used to explain differences in energies of these particles in atoms?

Acid-Base Rxns and Electron Energy - 2 2 d. The considerations in a.-c. illustrate one Fundamental Energy Principle we will call the ELECTRON ENERGY PRINCIPLE
The energy of a chemical structure is the sum of the energies of its electrons.
3. CHEMICAL BONDS AND ENERGIES OF STRUCTURES: a. Draw illustrations of two hydrogen atoms (H
.
) and the structure of the hydrogen molecule (H
2
). Use
for protons for neutrons and for electrons. b. Considering your answers to question 2, predict whether the energy of 2 separate hydrogen atoms should be higher, lower or the same compared with a H
2 molecule.
Provide your warrant based on the forces identified in question 2. c. What is the difference in structure between HD and D- in Figure 1? What is the difference in structure between HE and E- in Figure 1? d. In Figure 1, we plotted the energies of the conjugate bases (D- & E-) at higher energies than their corresponding conjugated acids (H-D & H-E). We justified this order of energies on the positive values of pK a s indicating that  G˚ is positive. Is this order of energies consistent with your claim and warrant in 3b and your claim in 3c?
Provide your warrant. e. The considerations in a.-d. illustrate another Fundamental Energy Principle we will call the BOND FORMATION PRINCIPLE.
Forming a bond with a pair of electrons will lower the energy of the electrons due to increased electron-nuclear attractive force on the pair of electrons involved . So bonding electrons will have lower energy than non-bonding electrons in otherwise similar structures .
4. EFFECTS OF CHANGES IN STRUCTURE ON THE ENERGIES OF THE STRUCTURES: a. What is the difference in structure between HD and HE in Figure 1? What is the difference in structure between D- and E- in Figure 1?

Acid-Base Rxns and Electron Energy - 2 3 b. Considering your experience with questions 2 & 3, which unknown energy difference in Figure 1,  G
H-D->H-E
or  G
D
-
->E
- would you predict to be larger. Provide your warrant.
5. ASSUMPTION:
Since we have no additional information on the acids and bases in Figure 1, we need to make an assumption to relate the individual energies of the four structures in Figure
1. As has been discussed in class, it is often necessary to make assumptions in creating a usable hypothesis for making scientific predictions. When assumptions are needed, it is critical that we clearly define the assumptions and remain aware of them as we apply the resulting hypothesis. If we apply the hypothesis to a situation where one or more of our assumptions are invalid, it is likely to give poor predictions . Below is an assumption that comes out of our discussion related to question 4b. It will allow us to use pK a s to predict energy differences among different individual molecules or ions.
RELATIVE EFFECT ASSUMPTION : In general, the energies of higher energy structures are affected more by differences in structure than are the energies of lower energy structures . a. How did we decide which structure in an acid-base pair has the lower energy? (See question 3 c & d) b. Using the Relative Effect Assumption and the Fundamental Energy Principles , propose how Figure 1 might be modified to relate the energies of H-D & D- to those of H-E & E-. Modify the plot of H-E & E- in Figure 2 below to illustrate your proposal.
G
CH
3
O
C
O H
H-D
O
D CH
3
C
O pK a
=4.8
HD & H-E D
-
& E
-
Figure 2: Free Energy Diagram Comparing of Relative Energies to Two Acids and their Conjugate Bases using the RELATIVE EFFECT ASSUMPTION c. What does Figure 2, allow you to conclude about which energy difference,  G
H-D->H-E
or  G
D
-
->E
, is the primary cause of the higher pK a
value for H-E vs.
H-D? Provide a warrant citing the specific data and assumptions your group used to develop your claim.

Acid-Base Rxns and Electron Energy - 2 4

Acid-Base Rxns and Electron Energy - 2 5 d. Based on your experience with the Relative Effect Assumption and the Fundamental Energy Principles discovered in this activity, identify the specific electrons that should be primarily responsible for most of the energy difference between the acid and base forms of any acid. Provide a warrant citing the specific data and assumptions your group used to develop your claim. Recall the differences in structure between H-D & D- and between H-E & E- in question 3c.
6 Applications: a. Considering the Relative Effect Assumption and Fundamental Energy Principles list the conjugate bases in the order of decreasing energies. Provide your warrant.
Conjugate Acid
H-Cl
O
CH
3
C
O H
O O
CH
3
C CH
2
C CH
3
CH
3
H
2
O
O
C CH
3 pK a
(pK aH
)
-7
4.8
9
15.7
20
Conjugate Base
Cl
CH
3
O
C
O
O O
CH
3
C CH C CH
3
OH
CH
3
O
C CH
2
CH
3
CH
3 ~42
CH
3
CH
2
Table 2: pK a
Values of Selected Acids
From Acid-Base 1 Table 2 b. Which specific electrons are primarily responsible for the differences in the energies of the structures identified in 5 a? Provide your warrant.

Acid-Base Rxns and Electron Energy - 2
Reflector’s Report Discussion:
Identify the most important concepts you learned from this activity:
6
What questions remain?
Strategy Analyst’s Report Discussion:
Look back at the process used to develop the relationships between pK a s of acids and the energies of electrons in their conjugate acids and conjugate bases.
The development could be divided into the three phases outlined below. Briefly describe how the activity led your group through each phase, identify any problems your group had in the process and indicate any confusion that might still remain.
1. Recognition of the need for an assumption.
2. Recognition of which structures, conjugate acids or conjugate bases, that are primarily responsible for the determining the relative pK a of acids.
3. Correlating the relative energies of structures with the energies of specific electrons in the structure.