11.2 Reaction Rate and Concentration
YOU ARE EXPECTED TO BE ABLE TO:
• Define the initial rate of a reaction as the
instantaneous rate at the start of the reaction.
• Write a rate law expression for a given reaction
given experimental results that show the variation
of initial rate with concentration.
• Define the concept of order of reaction and
determine the order of a given reaction from initial
rate vs concentration data
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Initial Rate of Reaction
• The initial rate of reaction is the
instantaneous rate measured at the start of
the reaction
• The initial rate can be used as a benchmark
• Measurements of the initial rate for a
reaction at different starting concentrations
can be used to determine the effect of
concentration on rate
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The Rate Expression or Rate Law
• In general:
– Reactions occur as a result of collisions
– The higher the concentration of molecules, the greater
the rate
• In some reactions, the rate is directly proportional
to the concentration
• In other cases, the rate may increase much more
quickly than the concentration
• The relationship between rate and concentration is
known at the rate law or rate expression
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Determining the Rate Law
Expression
• The rate law MUST be determined from
experiment – it is not related to the stoichiometry
of the equation for the reaction
• Examine the concentration vs time graph for N2O5
– Determine instantaneous rates at different times and
concentrations of N2O5
– Plot instantaneous rate vs [N2O5 ]
– This is a straight line, (equation y = mx + b)
• Rate = k[N2O5] ; this is the rate law expression; k
is the rate constant
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Using Initial Rates to determine
the rate Law
• Measurements of the initial rate of reaction
at different initial concentrations can be
used to determine the rate law expression
• If a graph of initial concentration vs initial
rate is a straight line, then rate is directly
proportional to concentration:
rate = k [reactant]
• If a graph is a curve, then rate = k[reactant]m
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Order of Reaction
• The rate law expression is of the form:
Rate = k[A]m
• The power to which the concentration is
raised is called the order of reaction
• If m = 0, then “zero order”
• If m = 1, then “first order”
• If m = 2, then “second order”
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Calculating the Order of Reaction
when there is One Reactant
• If m is not equal to 1, the order of the
reaction can be determined by comparing
two rates at two different concentrations:
• Rate1 = k[A]1m
• Rate2 = k[A]2m
Rate1 = k[A]1m = [A]1 m
Rate2 k[A]2m [A]2
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Example 11.1
• CH3CHO(g)  CH4(g) + CO(g)
[ ]
0.10M 0.20M
0.30M 0.40M
Rate (mol/L.s) 0.085
0.34
0.76
• Choose the first two concentrations
Rate2
Rate1
=
1.4
0.34 = 4.0
0.085
[CH3CHO]2
[CH3CHO]1
=
0.20 = 2.0
0.10
4.0 = (2.0)m ; m = 2
Rate = k[CH3CHO]2 The reaction is second order
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Calculate the Rate Constant
• Rate = k[CH3CHO]2
• Choose one set of data
0.085mol/L.s = k x (0.10 mol/L)2
k = 0.085mol/L.s = 8.5 L/mol.s
(0.10 mol/L)2
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Order of Reaction with More
Than One Reactant
• Most reactions involve >1 reactant
aA + bB  products
• General rate law expression is:
rate = k[A]m x [B]n
– m is “order with respect to A
– n is order with respect to B
– Overall order is m + n
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Determining the Order
• Hold concentration of one reactant constant
and vary other - measure initial rate
• Repeat, holding concentration of other
reactant constant
• See Example 11.2, page 308
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Determining the Order of
Reaction Graphically
• As an alternative to calculating the order of
reaction by comparing two pieces of data, a
graphical process can be used
• Plot rate vs concentration
• If the result is a straight line, there is a first order
reaction, slope = k
• If the result is a curve, it is necessary to construct
a graph of (natural) log rate vs (natural) log
concentration to determine m
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Why Use a Logarithm?
• If rate = k[A]m
• Then ln rate = ln k + m ln [a]
• This will be a straight line with slope m
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Zero Order Reactions
• In rare cases, the rate of reaction is
independent of the concentration of
reactant(s)
• In these cases
– Rate = k[A]0
• A plot of rate vs [A] would be a horizontal
straight line
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