5
How Unit do we predict chemical change?
The central goal of this unit is to help you identify and
apply the different factors that help predict the
likelihood of chemical reactions.
Chemistry XXI
M1. Analyzing Structure
M2. Comparing Free Energies
Comparing the relative stability
of different substances
Determining the directionality and
extent of a chemical reaction.
M3. Measuring Rates
Analyzing the factors that
affect reaction rate.
M4. Understanding Mechanism
Identifying the steps that
determine reaction rates.
Unit 5
How do we predict
chemical change?
Chemistry XXI
Module 2: Comparing Free Energies
Central goal:
To quantitatively
determine the
directionality and extent
of chemical reactions.
The Challenge
Transformation
How do I change it?
Chemistry XXI
Imagine that you were interested
in QUANTITATIVELY determining
which of two or more chemical
processes could have occurred
on the primitive Earth.
What measurable properties of the system can be
used to make the prediction?
How could we actually quantify the directionality
and extent of a chemical reaction?
Relevant Factors
Chemistry XXI
The directionality and extent of a chemical
reaction depend on three main factors:
ENERGETIC FACTORS
Hrxn
ENTROPIC FACTORS
Srxn
TEMPERATURE T
But
how?
What Changes?
Chemistry XXI
Consider this chemical process:
CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
Is this a favored process? Why?
The Facts
It may be favored if the process:
a) leads to more energetically stable compounds.
energy is released (Exothermic: Hrxn < 0).
q
Chemistry XXI
Hrxn < 0 (-)
CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
The Facts
It may be favored if the process:
b) Leads to the formation of substances with
more distinguishable configurations:
Srxn> 0 (+)
Chemistry XXI
CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)
Srxn > 0 (+)
Certainly favored:
Hrxn < 0 (-) (exothermic)
Srxn > 0 (+)
Lets Think
Consider the possible decomposition of CO2 in
the atmosphere:
Chemistry XXI
CO2(g) C(s) + O2(g)
Analyze the sign of Hrxn and Srxn
and decide whether the process is favored or not.
The Facts
If, as in the previous case,
Chemistry XXI
But what happens if:
or
Hrxn > 0 (+) (exothermic)
Srxn < 0 (-)
?
Hrxn < 0 (-) (endothermic)
Srxn > 0 (+)
?
The outcome depends on the TEMPERATURE.
The Law
In general, energetic effects become less relevant at
high temperature, where entropic effects dominate.
The sign of this quantity (Gibbs Free Energy, G):
Grxn = Hrxn T Srxn
Chemistry XXI
can be used to determine process directionality.
2nd Law of Thermodynamics
At constant T and P:
Grxn < 0
for thermodynamically favored processes.
Reaction Extent
Experimental results indicate that processes at
constant T and P occur in the direction in which
the Gibbs free energy G of the system decreases.
A B
Grxn = GB - GA < 0
Exergonic Favored
Grxn = GD GC > 0
C D
Endergonic
Chemistry XXI
Unfavored
The more negative Grxn,
the larger the extent of the reaction.
The more negative Grxn,
the more thermodynamically stable the
products than the reactants.
Evaluating Likelihood
The quantitative analysis of the extent of reactions is
crucial to determine, for example, what were the
likely components of our primitive atmosphere.
Chemistry XXI
H2 is suspected to be an
important component of the
very early atmosphere.
Was CO2 or CH4 more stable
in this environment?
How does temperature affect
the answer?
Lets explore it!
Hydrogen constitutes ~75% of
the Universes elemental mass
Lets Think
Consider this data:
Reaction
CO2(g) + 4 H2(g) CH4(g) + 2 H2O(l)
Horxn (kJ) Sorxn (J/K)
-252.7
-410.3
Chemistry XXI
Which compound of C (CO2 vs CH4) is most stable in
the presence of H2 at 25 oC?
Hint: Are reactants or products favored in the
reaction?
Lets Think
Horxn (kJ)
Sorxn
(J/K)
CO2(g) + 4 H2(g) CH4(g) + 2 H2O(l)
Chemistry XXI
Reaction
-252.7
-410.3
Are there any temperatures at which CO2 is
favored?
Lets Think
Reaction
Horxn (kJ)
Sorxn
(J/K)
CO2(g) + 4 H2(g) CH4(g) + 2 H2O(l)
-252.7
-410.3
As T increases, the energetic contribution becomes
less important. There is a temperature at which:
Chemistry XXI
Grxn = HrxnT Srxn = 0.
Above this temperature, the reverse reaction is
favored.
Quantitative Data
Chemistry XXI
Our discussion highlights the importance of
measuring or calculating Hrxn, Srxn, and Grxn if
we want to make predictions about the
thermodynamic likelihood of a reaction.
We have already
discussed how to
calculate Srxn given
available data for the
standard molar entropies
of formation Sof.
A+B C+D
Sorxn = Soproducts Soreactants
Basic Assumption:
So (perfect crystal) = 0
at 0 K.
How do we get Hrxn and Grxn for any process?
Heat of Reaction
We have seen that the heat of a reaction Hrxn can
be measured by calorimetry.
Chemistry XXI
However, we can also calculate this quantity using
measured standard enthalpies of reaction Hof for
the substances involved in the process.
Lets consider a reaction involved in the production of
CO2 in the primitive atmosphere:
C(graphite) + 2 H2O(l) CO2(g) + 2 H2(g)
How could we evaluate Horxn given this information:
C(graphite) + O2(g) CO2(g)
H2(g) + O2(g) H2O(l)
Hof = -393.5 kJ/mol
Hof = -285.8 kJ/mol
Alternative Routes
C(graphite) + 2 H2O(l) CO2(g) + 2 H2(g)
We could think of the reaction as combination of a
decomposition and a combination steps:
1st: 2 H2O(l) 2 H2(g) + O2(g)
2 : C(graphite) + O2(g) CO2(g)
Chemistry XXI
nd
Horxn = 2 (+285.8) kJ
H
o
rxn
= -393.5 kJ
+
C(graphite) + 2 H2O(l) CO2(g) + 2 H2(g)
Horxn = 2 (285.8) - 393.5 = +178.1 kJ
This approach is based on the central idea
that, no matter what path we follow,
the total energy transfer should be the same.
Hesss
Law
Generalizing
All reactions can be conceived as a sequence of
decompositions and combinations steps:
Take the general reaction: a A + b B c C + d
D
Imagine it happens in the following steps:
Energy Transfer
a x (- Hof,A)
Decomposition of b moles of B
Chemistry XXI
Reaction
Decomposition of a moles of A
b x (- Hof,B)
Formation of c moles of C
c x Hof,C
Formation of d moles of D
d x Hof,D
Horxn = c Hof,D + d Hof,D a Hof,A b Hof,B
Horxn = Hof,products - Hof,reactants
Reference State
Horxn = Hof,products - Hof,reactants
It is important to notice that in this relationship,
we only need the Hof of the
chemical COMPOUNDS involved, not of any
elements.
Chemistry XXI
HOW SO?
H0
Elements
Reactants
Products
We are taking
Hof = 0 for
the elements
in their
standard
state.
Gibbs Free Energy
An identical procedure can be used to calculate the
Gorxn given the Gof for the different
chemical COMPOUNDS involved in the reaction:
Gorxn = Gof,products - Gof,reactants
Gof = 0 for elements in their standard state.
Chemistry XXI
Alternatively, we can also calculate Gorxn as:
Gorxn = HorxnT Sorxn
This route is useful
in estimating the
effect of T on the
value of G.
Lets Think
One central question in the theories about the
origin of life is how complex organic compounds
were synthesized from simpler molecules such as
H2, N2, CH4, NH3, and H2O.
Consider these possibilities in the synthesis of the
simplest amino acid, glycine (C2H5NO2):
Chemistry XXI
2 CO(g) + NH3(g) + H2(g) C2H5NO2(s)
2 CH4(g) + NH3(g) + 2 H2O(l) C2H5NO2(s) + 5 H2(g)
1. Calculate Horxn, Sorxn, and Gorxn for these two
processes.
Lets CO(g) Think
2 + NH3(g) + H2(g) C2H5NO2(s)
2 CH4(g) + NH3(g) + 2 H2O(l) C2H5NO2(s) + 5 H2(g)
Hof (kJ/mol)
Gof (kJ/mol)
Sof (J/(mol K)
H2(g)
0
0
130.7
CH4(g)
Chemistry XXI
Substance
-74.6
-50.5
186.3
CO(g)
-110.5
-137.2
197.7
NH3(g)
-45.9
-16.4
192.8
H2O(l)
-285.8
-237.1
70.0
C2H5NO2(s)
-528.4
-368.8
103.5
Lets Think
Horxn
Sorxn
Gorxn
(kJ)
Reaction
(J/K)
(kJ)
Chemistry XXI
2 CO(g) + NH3(g) + H2(g)
C2H5NO2(s)
2 CH4(g) + NH3(g) + 2 H2O(l)
C2H5NO2(s) + 5 H2(g)
2. Identify which reactions are product-favored
and discuss the effect of temperature on the
extent of each process.
Lets Think
Chemistry XXI
2 CO(g) + NH3(g) + H2(g)
C2H5NO2(s)
2 CH4(g) + NH3(g) + 2 H2O(l)
C2H5NO2(s) + 5 H2(g)
Horxn
Sorxn
Gorxn
(kJ)
Reaction
(J/K)
(kJ)
Reaction Extent
Although the change in Gibbs free energy Gorxn
allows us to make predictions about reaction
directionality, the actual number tells us little about
the final relative amounts of product to reactants.
Chemistry XXI
How can we better quantify reaction extent?
Experimental results
indicate that chemical
reactions tend to reach an
equilibrium state in which
the concentration of
products and reactants
does not vary over time.
C
o
n
c
e
n
t
r
a
t
i
o
n
Time
Equilibrium Constant
At chemical equilibrium, the following ratio of the
concentrations, or gas pressures,
of reactants to products remains constant:
Equilibrium Constant
Chemistry XXI
aA+bB cC+dD
For reaction involving
gases, the equilibrium
constant may be
expressed in terms of
the partial pressures
exerted by each gas:
c
d
[C ] [ D]
Kc =
a
b
[ A] [ B]
cd
CD
ab
AB
PP
Kp =
PP
Gorxn vs. K
The value of the equilibrium constant K is directly
related to the Gorxn for the process:
G
o
rxn
= RT ln K
Chemistry XXI
Then:
K =e
K =e
o
Grxn
(
)
RT
o
o
H rxn S rxn
(
+
)
RT
R
In general:
R = 8.314 J/(K mol)
Product-Favored Process:
Gorxn < 0
K>1
Reactant-Favored Process:
Gorxn > 0
K<1
Chemistry XXI
Lets Think
Predict the
effect of
changing
Horxn, Sorxn,
and T on the
value of K and
the reaction
extent.
K =e
o
o
H rxn S rxn
(
+
)
RT
R
Reaction Extent
As we have seen, different reaction reach
equilibrium states with different proportion of
products and reactants in the system.
For example, combustion reactions tend to have
very large K values:
CH4(g) + O2(g) CO2(g) + 2 H2O(g)
Gorxn = -800.9 kJ
Chemistry XXI
K = 2.07 x 10140 at 25 oC
For all practical purposes, this reaction fully goes to
completion at all temperatures ( Horxn < 0, Sorxn> 0):
CH4(g) + O2(g)
CO2(g) + 2 H2O(l)
Reaction Extent
But what about a reaction such as this:
Gorxn =
CO(g) + H2O(l) CH2O2(l)
-12.9 kJ
Chemistry XXI
K = 182.0 at 25 oC ( Horxn < 0, Sorxn < 0)
which may have played a central role in the
formation of complex molecules in our planet?
Whether this reaction is product- or reactant-favored
depends on the actual conditions of the process.
Thus, it is better to represent it as:
CO(g) + H2O(l)
CH2O2(l)
to highlight the importance of chemical equilibrium.
Chemical Evolution
In 1956, Urey and Miller conducted a classic
experiment on the origin of life.
Chemistry XXI
The experiment
showed that biological
molecules, such as
amino acids, can form
from simple reactants.
Since then, many
experiments have been
performed with different
reactant mixtures and
sources of energy
(heat, UV, X-rays, etc.)
Primitive Mixtures
These are two of the reactant
mixtures that have been tested:
H2O, CH4, NH3, H2
CO, N2, H2
Results indicate that the elemental composition
(presence of C, H, N, O) of the mixture is more
relevant than the kinds of molecules used. Why?
Chemistry XXI
No matter the mixture, the concentration of species
seems to be controlled by these equilibriums:
CH4(g) + 2 H2O(g)
CO2(g) + 4 H2(g)
CO2(g) + H2(g
CO(g) + 3 H2O(g)
N2(g) + 3 H2(g)
2 NH3(g)
Likely
occurring
between
500-1000 oC.
Lets Think
CH4(g) + 2 H2O(g)
CO2(g) + H2(g)
N2(g) + 3 H2(g)
CO2(g) + 4 H2(g)
CO(g) + H2O(g)
2 NH3(g)
Substance Hof (kJ/mol) Sof (J/(mol K)
Chemistry XXI
H2(g)
Estimate K for
these processes
at 500 oC
and 800 oC.
0
130.7
CH4(g)
-74.6
186.3
CO2(g)
-393.5
213.8
CO(g)
-110.5
197.7
NH3(g)
-45.9
192.8
H2O(g)
-241.8
188.8
N2(g)
-108.6
191.6
Lets Think
o
o
H rxn S rxn
K = exp(
+
)
RT
R
R = 8.314 J/(K mol)
CH4(g) + 2 H2O(g)
Chemistry XXI
CO2(g) + H2(g)
N2(g) + 3 H2(g)
CO2(g) + 4 H2(g)
CO(g) + H2O(g)
2 NH3(g)
Discuss which compounds
of C, H, N, and O are more
likely to exist at each T.
Hor
Sor
(kJ)
Reactions
(J/K)
K500
K800
Chemistry XXI
Lets apply!
Assess what you know
Lets apply!
Going Up-Hill
The synthesis reactions for the formation of many
amino acids, proteins, carbohydrates and fats
starting from simple molecules have Gorxn > 0.
Chemistry XXI
One central question in the origin of life is how it
was possible to induce and sustain the
synthesis of these types of substances.
6 CO2(g) + 6 H2O(l) C6H12O6(s) + 6 O2(g)
Gorxn = 2880 kJ
Glucose
Lets apply!
Forced Reactions
A chemical reaction with Gorxn > 0 is not favored
thermodynamically, but can be forced to happen
by coupling it with other favored reactions.
This commonly happens in biological systems.
For example, consider an hypothetical reaction:
Chemistry XXI
A + B AB
Go1 > 0.
Reactions like this in living organisms are often
coupled with the favored hydrolysis of ATP:
ATP(aq) + H2O(l) ADP(aq) + Pi(aq)
Go2 = -30.5 kJ
Lets apply!
Forced Reactions
Chemistry XXI
The coupling is often accomplished by the
following mechanism:
The formation of
A-Pi facilitates
the addition of B.
A + ATP + H2O A-Pi + ADP
A-Pi + B AB + Pi
A + B + ATP + H2O AB + ADP + Pi
Gorxn = Go1 + Go2 < 0
Predict
Lets apply!
For example, glutamine is an amino acid
synthesized many organisms from another amino
acid, called glutamic acid.
B
C
Chemistry XXI
AB
Gorxn = 14.2 kJ
Glutamic Acid
AB + C AC + B
AC
Glutamine
Express and calculate K for this reaction at 25 oC.
Lets apply!
Predict
Write the overall reaction when the synthesis of
glutamine is coupled to the hydrolysis of ATP and
calculate its K at 25 oC.
Chemistry XXI
AB + C AC + B
kTP
AJ (aq) + H2O(l) ADP(aq) + Pi(aq)
Go1 = 14.2
Go2 = -30.5 kJ
Propose a mechanism for the coupled process.
Lets apply!
Glutamic Acid (AB)
Chemistry XXI
AB + C AC + B
kJ
ATP(aq) + H2O(l) ADP(aq) + Pi(aq)
Predict
Glutamine (AC)
Go1 = 14.2
Go2 = -30.5 kJ
Chemistry XXI
Discuss with a partner how the
values of Horxn, Sorxn, and Gorxn
affect the directionality and extent
of a chemical process.
Comparing Free Energies
Summary
At constant T and P:
Grxn = Hrxn T Srxn < 0
for thermodynamically favored processes.
Chemistry XXI
a A + b B c C + d D
Horxn Sorxn
DIRECTIONALITY?
Gorxn
-
+
-
Product-favored
+
-
+
Reactant favored
-
-
Depends on T P fav at low T
+
+
Depends on T P fav at high T
Equilibrium Constant
a A + b B c C + d D
c
EXTENT?
d
[C ] [ D]
Kc =
a
b
[ A] [ B]
o
Grxn = RT ln K
Chemistry XXI
K =e
o
o
H rxn S rxn
(
+
)
RT
R
In general:
Product-Favored Process:
Gorxn < 0
K>1
Reactant-Favored Process:
Gorxn > 0
K<1
Chemistry XXI
For next class,
Investigate how the rate of a chemical reaction
can be measured or calculated.
How can we use experimental data to track the
rate of a chemical reaction
as a function of time?