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.
M1. Analyzing Structure M2. Comparing Free Energies M3. Measuring Rates
M4. Understanding Mechanism
Comparing the relative stability of different substances
Determining the directionality and extent of a chemical reaction.
Chemistry XXI
Analyzing the factors that affect reaction rate. Identifying the steps that determine reaction rates.
Unit 5
How do we predict chemical change? Module 3: Measuring Rates
Chemistry XXI Central goal: To analyze the effect of concentration and temperature on the rate of chemical reactions.
The Challenge
Imagine that you were interested in comparing the rates at which different substances appeared or were decomposed on the primitive Earth.
Transformation How do I change it?
Chemistry XXI
How could we evaluate the kinetic stability of a substance? How could we determine the effect of concentration and temperature on reaction rates?
Time Issues
Consider these two possible routes for the synthesis of glycine, the simplest amino acid, on the primitive Earth: Chemistry XXI
Activation Energy
G
Thermo vs. Kinetics
Occurs readily a t 2 5 oC
Chemistry XXI
Themodynamically favored, but does not occur for all practical purposes
Reaction Coordinate
Analyzing Stability
Analyzing chemical systems from both the thermodynamic and kinetic point of view is crucial in making decisions about the actual stability of substances. For example, the decomposition or transformation of a substance may be favored thermodynamically, but can take millions of years to occur. How stable is it then?
Chemistry XXI
C(diamond) C(graphite)
Kinetic Stability
The analysis of the kinetic stability of biomolecules has been crucial in the analysis of different theories about the origin of life.
For example, it has been proposed that amino acid synthesis could have occurred deep in the Earth's crust and that these amino acids were subsequently shot up along with hydrothermal fluids into cooler waters.
Chemistry XXI
How stable are amino acids under such conditions?
Unstable?
Many aqueous solutions of amino acids are thermodinamically unstable. Lets consider the case of alanine:
2 3 3
2
+
2
Decarboxylation
Alanine (Ala)
Ethyl Amine
Chemistry XXI
The kinetics of this reaction has been thoroughly explored by measuring the concentration of alanine [Ala] as a function of time (t) in aqueous solutions at various temperatures.
Lets Think
How would you quantify the rate of decomposition of alanine at any given time?
o
Chemistry XXI
Reaction Rate
o
Chemistry XXI
Lets Think
What does this data tell you about the kinetic stability of alanine as a function of concentration and temperature? Hint: How does the rate change with C and T? (The higher the rate, the lower the kinetic stability)
o
o
Chemistry XXI
Reaction Rate
o
The slope decreases
o
Chemistry XXI
Kinetic stability is a function of [R] and T.
Rate Laws
The effect of temperature and concentration on reaction rates can be modeled mathematically: xA+yB+zC wD+yE+zF RATE LAW Rate = k [A] [B] [C]
a b c
Reaction order
Rate Constant Chemistry XXI
a
k depends on the value of T, E , and other relevant factors for each reaction.
a
Concentration Effects
How can determine reaction orders and rate constants? Rate Law
Rate = k[ Ala ]
a
Reaction order?
Rate constant?
What are their values?
We may assume values for the reaction order a and analyze the implications: Chemistry XXI If a = 1 (first-order): By integration of this differential equation we get:
d [ Ala ] Rate = = k[ Ala ] dt
[ Ala ] = [ Ala ]o e kt ln[ Ala ] = ln[ Ala]o kt
Graphical Analysis
If the reaction is first-order:
For example, is the decomposition of alanine at 150 C (423 K)
ln[ Ala ] = ln[ Ala]o kt
y
ln[Ala] ln[Ala]o
=
b
+ mx
1 t (years)order?: [Ala] (mM)
0 2 4 6 8 10 12 14 t 16 1.000 0.8705 0.7578 0.6597 0.5743 0.5000 0.4352 0.3789 0.3298
Chemistry XXI
m = -k
Reaction Order
t (years) [Ala] 0 (mM) 2 4 6 8 10 12 14 16 1.000 0.8705 0.7578 0.6597 0.5743 0.5000 0.4352 0.3789 0.3298 ln[Ala] 0 -0.1387 -0.2773 -0.4160 -0.5546 -0.6931 -0.7914 -0.9704 -1.1092
We have a first-order
Chemistry XXI
Lets Think
Given the Rate Law: Rate = 0.0693[Ala]
If [Ala] = 1.00 mM, predict the time it will take for
Chemistry XXI
Half Life
A half-life is the time it takes for the concentration of a reactant to be reduced in half.
Chemistry XXI
t=0
t = 1 half-life
t = 2 half-lives t = 3 half-lives
Half Life
For first order reactions:
[C ] ln = kt [C ]o
If [C] = [C]o/2
1 ln = o kt1/ 2 2
Chemistry XXI
t1/ 2
ln(1 / 2) = k
Independent of Concentration
Concentration Effects
If the reaction is first-order Rate = k[C]:
ln[C ] = ln[C ]o kt
What if Rate = k[C]a with a = 2 (second-order)?
1/[C]
d [C ] Rate = = k[C ]2 dt
Chemistry XXI By integration we get:
1 1 = + kt [C ] [C ] o
1/[C]o
m=k
t
Lets Think
Is half-life for second order reactions independent of the initial concentration of reactant?
Chemistry XXI
Temperature Effects
How can we predict how rate varies with temperature? The decomposition of alanine at different temperatures illustrates the effect of T on the reaction rate. T (K) 323 373 423 473 523 573 k (y-1) Larger T Larger rate constant Shorter half lives. Ho do we explain it and make quantitative predictions?
Chemistry XXI
Collision Rate Model
According to this model: 1. For a reaction to occur, the reactant particles must collide. 2. Colliding particles must be positioned so that the reacting groups interact effectively. Chemistry XXI 3. Colliding particles must have enough energy to reach a transition state that leads to the formation of the new products.
Ep Transition State Ea R H P
Reaction Coordinate
Arhenius Equation
The fraction of molecules with enough energy to react at a given T is proportional to:
e
Chemistry XXI
Ea RT
The rate constant k is then given by:
Ea ln(k ) = + ln( A) RT
y = mx + b y ln(k) x 1/T
k = Ae
Ea RT
Likelihood of collisions
Lets Think
ln(k ) =
Ea + ln( A) RT
Chemistry XXI
T (K) 323 373 423 473 523 573 623
k (y-1)
3
2 3
2
+
2
Lets apply!
Chemistry XXI
Assess what you know
Lets apply!
Analyze
Go back and analyze the notes for the decomposition of Alanine. Based on our overall results, analyze the likelihood of amino acids forming in hydrothermal vents on the primitive Earth.
Chemistry XXI
Lets apply!
New Data
Recent experimental results indicate that there may be other reactions that compete with the decomposition of amino acids at T > 100 oC:
2
Dimerization
2
3
2 3 3
+ H2O
Peptide Bond
Chemistry XXI
The formation of dimers and polymers may have helped amino acids to accumulate on the planet.
Lets apply!
Analyze
Go to: http://www.chem.arizona.edu/chemt/C21/sim (Dimerization) or use the simulation on the next page.
Use the simulation of the dimerization of alanine to: Determine the order of the reaction; Chemistry XXI Compare the half-lives of the process for a 1 M solution of alanine at 100 oC and 200 oC.
Lets apply!
Analyze
Chemistry XXI
Chemistry XXI
Identify with a partner two important ideas discussed in this module.
Measuring Rates
Summary
Reaction rates allow us to follow the kinetic evolution of a chemical process. xA yB
RateInst
d [ A] = dt
The effect of temperature and concentration on a process reaction rate is summarized in the RATE LAW: Chemistry XXI RATE LAW Rate = k [A]
a
Reaction order
Rate Constant
C and T Effects
Given a rate law, we can derive information about how the concentration of reactants or products changes with time. xA yB If a = 1 (first-order): If a = 2 (second-order): Chemistry XXI Rate = k [A]a
ln[ A] = ln[ A]o kt 1 1 = + kt [ A] [ A] o
Temperature effects on reaction rate are determined by Arhenius Equation for the rate constant k:
k = Ae
Ea RT
For next class,
Chemistry XXI Investigate how the overall rate of a reaction is related to the reaction mechanism. How can we use the reaction mechanism to derive the rate law or use the rate law to evaluate the reaction mechanism?