Transcript 18.2 The Progress of Chemical Reactions

18.2 The Progress of Chemical Reactions >
Chapter 18
Reaction Rates and Equilibrium
18.1 Rates of Reaction
18.2 The Progress of Chemical
Reactions
18.3 Reversible Reactions
and Equilibrium
18.4 Solubility Equilibrium
18.5 Free Energy and Entropy
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18.2 The Progress of Chemical Reactions >
CHEMISTRY
& YOU
How is a bicycle race like a
chemical reaction?
Riders in the Tour
de France bicycle
race must cross
steep mountains
with heights of
1900 meters or
more.
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18.2 The Progress of Chemical Reactions > Rate Laws
Rate Laws
What is the relationship between
the value of the specific rate
constant, k, and the speed of a
chemical reaction?
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18.2 The Progress of Chemical Reactions > Rate Laws
The rate of a reaction depends in part on
the concentrations of the reactants.
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18.2 The Progress of Chemical Reactions > Rate Laws
The rate of a reaction depends in part on
the concentrations of the reactants.
• Suppose there were a reaction with only
one reactant and one product.
AB
• The rate at which A forms B can be
expressed as the change in A (ΔA) with time.
ΔA
rate = Δt
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18.2 The Progress of Chemical Reactions > Rate Laws
• The rate of disappearance of A is proportional
to the concentration of A.
ΔA
[A]

Δt
• The proportionality can be expressed as the
concentration of A, [A], multiplied by a
constant, k.
ΔA
rate = Δt = k × [A]
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18.2 The Progress of Chemical Reactions > Rate Laws
ΔA
rate = Δt = k × [A]
• This equation is a rate law, an expression for
the rate of a reaction in terms of the
concentration of the reactants.
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18.2 The Progress of Chemical Reactions > Rate Laws
ΔA
rate = Δt = k × [A]
• This equation is a rate law, an expression for
the rate of a reaction in terms of the
concentration of the reactants.
• The specific rate constant (k) for a reaction
is a proportionality constant relating the
concentrations of reactants to the rate of the
reaction.
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18.2 The Progress of Chemical Reactions > Rate Laws
The value of the specific rate
constant, k, in a rate law is large if
the products form quickly; the
value is small if the products form
slowly.
ΔA
rate = Δt = k × [A]
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18.2 The Progress of Chemical Reactions > Rate Laws
First-Order Reactions
The order of a reaction is the power to
which the concentration of a reactant
must be raised to match the experimental
data on concentration and rate.
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18.2 The Progress of Chemical Reactions > Rate Laws
First-Order Reactions
The order of a reaction is the power to
which the concentration of a reactant
must be raised to match the experimental
data on concentration and rate.
• In a first-order reaction, the rate is directly
proportional to the concentration of only one
reactant.
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18.2 The Progress of Chemical Reactions > Interpret Graphs
Over time, the rate of reaction decreases
because the concentration of the reactant
is decreasing.
• The reaction A  B is a
first-order reaction.
• If [A] is reduced by one
half, the reaction rate is
reduced by one half.
• The rate (ΔA/Δt) at any
point on the graph
equals the slope of the
tangent to the curve at
that point.
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18.2 The Progress of Chemical Reactions > Rate Laws
Higher-Order Reactions
In some reactions, two substances react to
produce products.
• In the general equation for a double-replacement
reaction below, the coefficients are represented
by lowercase letters.
aA + bB  cC + dD
For the reaction of A with B, the rate of reaction is
dependent on the concentrations of both A and B.
rate = k[A]x[B]y
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18.2 The Progress of Chemical Reactions > Rate Laws
Higher-Order Reactions
rate = k[A]x[B]y
When each exponent in the rate law equals
1 (that is, x = y = 1) the reaction is said to
be first order in A and first order in B.
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18.2 The Progress of Chemical Reactions > Rate Laws
Higher-Order Reactions
The overall order of a reaction is the sum of
the exponents for the individual reactants.
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18.2 The Progress of Chemical Reactions > Rate Laws
Higher-Order Reactions
The overall order of a reaction is the sum of
the exponents for the individual reactants.
• A reaction that is first order in A and first order
in B is thus second order overall.
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18.2 The Progress of Chemical Reactions > Rate Laws
Higher-Order Reactions
The overall order of a reaction is the sum of
the exponents for the individual reactants.
• A reaction that is first order in A and first order
in B is thus second order overall.
• The actual order of a reaction must be
determined by experiment.
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18.2 The Progress of Chemical Reactions >
Sample Problem 18.1
Finding the Order of a Reaction from
Experimental Data
Consider the reaction aA  B. The rate law for this
reaction is Rate = k[A]x. From the data in the table,
find the order of the reaction with respect to A and
the overall order of the reaction.
Trial Initial concentration of
A (mol/L)
1
0.050
2
3
18
0.10
0.20
Initial rate
(mol/(L·s))
3.0  10–4
12  10–4
48  10–4
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18.2 The Progress of Chemical Reactions >
Sample Problem 18.1
1 Analyze List the knowns and the unknowns.
Use the first two trials to calculate the order and
the third to evaluate your answer.
KNOWNS
[A]1 = 0.050 mol/L
[A]2 = 0.10 mol/L
Rate1 = 3.0  10–4 mol/(L·s)
Rate2 = 12  10–4 mol/(L·s)
UNKNOWN
Order of reaction with respect to A = ?
Overall order of the reaction = ?
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18.2 The Progress of Chemical Reactions >
Sample Problem 18.1
2 Calculate Solve for the unknowns.
• Start with the rate law for each initial
concentration of A.
Rate1 = k [A1]x
Rate2 = k [A2]x
• Divide the second expression
by the first expression.
]x
Rate2
k [A2
Rate1 = k [A1]x =
20
x
( )
[A2]
[A1]
The rate law
of the reaction
and the
specific rate
constant, k, is
the same for
any initial
concentration
of A.
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18.2 The Progress of Chemical Reactions >
Sample Problem 18.1
2 Calculate Solve for the unknowns.
• Substitute the known quantities into
the equation.
12  10–4 mol/(L·s)
3.0  10–4 mol/(L·s) =
(
0.10 mol/L
0.050 mol/L
x
)
4.0 = 2.0x
• Determine the value of x.
x=2
The reaction is second order in A.
Since A is the only reactant, the reaction must
be second order overall.
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18.2 The Progress of Chemical Reactions >
Sample Problem 18.1
3 Evaluate Does this result make sense?
• If the reaction was first order in A, doubling
the concentration would double the rate.
• However, Rate2 is four times Rate1.
• So, the reaction is second order for A and
second order overall because A is the only
reactant.
• As a further test, look at what happens to the
rate when the concentration doubles again
from 0.10 mol/L to 0.20 mol/L.
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18.2 The Progress of Chemical Reactions >
The following reaction is a second-order
reaction.
aA  bB + cC
If the initial concentration of A is 2.0 mol/L
and the initial rate is 9.6  10–7 mol/(L·s),
what is the concentration when the rate is
1.2  10–7 mol/(L·s)?
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18.2 The Progress of Chemical Reactions >
The following reaction is a second-order
reaction.
aA  bB + cC
If the initial concentration of A is 2.0 mol/L
and the initial rate is 9.6  10–7 mol/(L·s),
what is the concentration when the rate is
1.2  10–7 mol/(L·s)?
(
[A2]
1.2 
mol/(L·s)
=
9.6  10–7 mol/(L·s)
2.0 mol/L
[A2] = 0.71 mol/L
10–7
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2
)
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
Reaction Mechanisms
How do most reactions progress
from start to finish?
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
A balanced equation does not tell you
how a reaction occurred.
• Plants use photosynthesis to capture and
store light energy.
• The process can be summarized by stating
that carbon dioxide and water yield simple
sugars and oxygen.
• However, the process of photosynthesis is
not as simple as this summary implies.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
One-Step and Multistep Reactions
An elementary reaction is a reaction in
which reactants are converted to products
in a single step.
• This type of reaction has only one activationenergy peak and one activated complex.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
One-Step and Multistep Reactions
Most chemical reactions consist of
two or more elementary reactions.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
One-Step and Multistep Reactions
Most chemical reactions consist of
two or more elementary reactions.
• The series of elementary reactions or steps
that take place during the course of a
complex reaction is called a reaction
mechanism.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
One-Step and Multistep Reactions
An intermediate is a product of one step
in a reaction mechanism and a reactant in
the next step.
• An intermediate has a more stable structure
and longer lifetime than an activated
complex.
• Intermediates do not appear in the overall
chemical equation for a reaction.
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18.2 The Progress of Chemical Reactions > Interpret Graphs
The figure below shows a reaction
progress curve for a complex chemical
reaction.
• A reaction progress
curve shows all the
energy changes that
occur as reactants
are converted to
products.
• The graph has a peak
for each activated
complex and a valley
for each intermediate.
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18.2 The Progress of Chemical Reactions >
CHEMISTRY
& YOU
In the mountain stage of the Tour de France,
a rider encounters a series of peaks and
valleys. In terms of energy, how does the
trip through the mountains compare to what
happens during a multistep reaction?
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18.2 The Progress of Chemical Reactions >
CHEMISTRY
& YOU
In the mountain stage of the Tour de France,
a rider encounters a series of peaks and
valleys. In terms of energy, how does the
trip through the mountains compare to what
happens during a multistep reaction?
Riders need extra energy each time they must
climb a peak. This extra energy compares to
the activation energy needed in a chemical
reaction. Each time they ride down into a
valley, they are in an intermediate state.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
Rate-Determining Steps
In a multistep chemical reaction, the steps
do not all progress at the same rate.
• One step will be slower than the others.
• The slowest step will determine, or limit, the
rate of the overall reaction.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
Rate-Determining Steps
Consider the reaction mechanism for the
decomposition of nitrous oxide (N2O).
Experiments have shown that the mechanism
consists of the two steps shown below.
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N2O(g)
N2(g) +O(g)
N2O(g) + O(g)
N2(g) + O2(g)
2N2O (g)
2N2(g) + O2(g)
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
Rate-Determining Steps
N2O(g)
N2(g) +O(g)
N2O(g) + O(g)
N2(g) + O2(g)
2N2O (g)
2N2(g) + O2(g)
In the first step, nitrous oxide decomposes into
nitrogen gas and oxygen atoms.
• The oxygen atoms are an intermediate.
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18.2 The Progress of Chemical Reactions > Reaction Mechanisms
Rate-Determining Steps
N2O(g)
N2(g) +O(g)
N2O(g) + O(g)
N2(g) + O2(g)
2N2O (g)
2N2(g) + O2(g)
For the decomposition of nitrous oxide, the first
step is the rate-determining step.
• To increase the rate of the overall reaction, you
would need to increase the rate of the first step.
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18.2 The Progress of Chemical Reactions >
In the following reaction mechanism,
which is an intermediate?
A2
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2A
2A + B2
2AB
A2 + B2
2AB
A. A2
C. A
B. B2
D. AB
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18.2 The Progress of Chemical Reactions >
In the following reaction mechanism,
which is an intermediate?
A2
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2A
2A + B2
2AB
A2 + B2
2AB
A. A2
C. A
B. B2
D. AB
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18.2 The Progress of Chemical Reactions > Key Concepts and
Key Equations
The value of the specific rate constant, k, in a
rate law is large if the products form quickly;
the value is small if the products form slowly.
Most chemical reactions consist of two or
more elementary reactions.
Rate = DA
Dt = k  [A]
Rate = k[A]x[B]y
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18.2 The Progress of Chemical Reactions > Glossary Terms
• rate law: an expression relating the rate of a
reaction to the concentration of the reactants
• specific rate constant: a proportionality
constant relating the concentrations of
reactants to the rate of the reaction
• first-order reaction: a reaction in which the
reaction rate is proportional to the
concentration of only one reactant
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18.2 The Progress of Chemical Reactions > Glossary Terms
• elementary reaction: a reaction in which
reactants are converted to products in a
single step
• reaction mechanism: a series of elementary
reactions that take place during the course of
a complex reaction
• intermediate: a product of one of the steps
in a reaction mechanism; it becomes a
reactant in the next step
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18.2 The Progress of Chemical Reactions >
END OF 18.2
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