Reaction Rates and Orders

1
Reaction Rates and Orders Kinetics or reaction
dynamics is the study of how fast chemical
reactions go, i.e., the rate of chemical
reactions. From both a thermodynamic and kinetic
perspective comment on the statement diamonds are
forever C (diamond) ------gt C (graphite)
DGo298 K - 2.900 kJ/mole Kinetic data usually
consists of reactant or product concentrations or
some property that can be related to them as a
function of time. Consider the following kinetic
data for the isomerization at 25.0 oC of ammonium
cyanate to urea NH4OCN (aq)
------gt NH2CNH2 (aq) A ------gt
U time (sec) NH4OCN (M) time (sec)
NH4OCN (M)
0.287 0.269 0.254 0.240 0.228 0.217 0.207 0.197 0.
189 0.181
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 18
0.0 200.0
220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0 38
0.0 400.0
1.000 0.816 0.689 0.596 0.525 0.469 0.424 0.387 0.
356 0.330 0.307
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The rate can be expressed in terms of the
disappearence of reactants, the formation of
products, or the extent of the reaction or the
progress of the reaction as measured by the
variable x A ------gt U
Ao - x x rate - dA / dt
dU / dt dx / dt Why is there a minus
sign in front of the time rate of change of the
concentration of A? Is the rate of a reaction
always positive? The rate law or rate equation
expresses the observation that rates of reactions
are some function of (and are often proportional
to) the concentrations of the reactants (but
sometimes products are involved) raised to some
power - dA / dt k An The
proportionality constant, k, is called the rate
constant and is a function of temperature, but
not of reactant or product concentrations. In the
above rate law n is the order of the reaction
with respect to A. The order with respect to a
given reactant or product is often, but does not
have to be, an integer. The overall order of a
reaction is the sum of the orders of the species
involved in the rate law. For some more
complicated rate laws it is not possible to
define an overall order for the reaction.
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Reactions are often classified according to their
overall order with 0th, 1st (particularly), and
2nd order reactions being fairly common. In
zeroeth order reactions the rate is independent
of the concentrations of the reactants Why do
you think that reactions of gases on surfaces at
high pressure provide an example of zeroeth order
reactions? A -----gt products - dA / dt
k0 A n0 k0 The above equation involving a
derivative is a differential equation and is the
differential form of the rate law for a 0th order
reaction. This differential equation can be
solved by separating variables and integrating
(as can many of the differential rate laws that
are common in kinetics) Ao?AdA - 0 ?
t k0 dt yielding the integrated rate law, i.e.,
an analytical function describing how the
concentrations depend on time A Ao -
k0 t
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If the reaction is 0th order, then a plot of A
versus time should be linear
This plot for the ammonium cyanate isomerization
data shown below
Is the isomerization 0th order?
5
Derive the expression showing how the
concentration of ammonium cyanate should depend
on time, if the isomerization were 1st
order Derive the expression showing how
the concentration of ammonium cyanate should
depend on time, if the isomerization were 2nd
order
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An expected to be linear plot of the data based
on the 1st order assumption is shown below
Is the isomerization 1st order?
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An expected to be linear plot of the data based
on the 2nd order assumption is shown below
k2 slope 0.0113 M - 1 sec - 1
Is the isomerization 2nd order?
8
In an autocatalysis reaction the products
contribute to the rate of the forward reaction.
Consider the reaction A -----gt B which
follows the differential rate law - dA / dt
k A B a. What is the overall order of
this reaction? b. Find the integrated rate
law which gives B as a function of time. Take
the initial concentrations of A and B to be Ao
and Bo, respectively. c. Plot how you would
expect B to vary with time.
This problem has a lot in common with the views
Thomas Malthus expressed in his essay An Essay on
the Principle of Population as posted by Ed
Stephan of Western Washington University. Could
you write down and solve a plausible differential
rate law for an autoinhibited reaction in which
the products inhibit the rate of the forward
reaction? A -----gt B
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Consider the data for the reaction 2 NOCl (g)
-----gt 2 NO (g) Cl2 (g) at 200 oC time
(sec) 0 200 300 500 NOCl
(M) 0.0200 0.0159 0.0144 0.0121 Assuming that
there is no reverse or back reaction, what is the
order and rate constant for this reaction?
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Take Aways Chemical kinetics (sometimes called
reaction dynamics) is the study of how fast
reactions occur (their rates) and the elementary
steps or mechanisms by which they occur. A rate
measures something that occurs in a given period
of time and has units of time in the
denominator. The rate of the general chemical
reaction a A b B ----gt x X y Y
. is defined unambiguously as rate
- (1/a) dA/dt - (1/b) dB/dt
(1/x) dX/dt (1/y) dY/dt Rates of
chemical reactions are some function of the
concentrations or some property that is
proportional to the concentrations of the
reactants and/or products in the chemical
reaction and the rate constants that govern how
fast the elementary processes that comprise the
overall reaction occur. rate function ( ki,
i ) Rate constants are not functions of the
concentrations, but usually are functions of
temperature.
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• The explicit functional dependence of the rate on
  the rate constants and concentrations is a
  differential equation and is known as the rate
  law.
• Often the rate law will take the form of a simple
  product of concentrations of reactants and/or
  products raised to some power
• rate k ? ij
• i, j
• For example
• A B -------gt products
• dA/dt k A2 B
• The order of the reaction with respect to A is 2.
  The order of the reactions with respect to B is
  1. The overall order is the sum of the
  individual orders and in this case is 2 1 3,
  i.e., 3rd order.
• In composite reactions (reactions composed of
  simpler reactions) the powers on the
  concentrations are not necessarily equal to the
  coefficients in the reaction.
• Some rate laws are so complex that an order can
  not be defined.
• Reactions are often classified by their orders
  with 0th, 1st, and 2nd orders being common.
• Reaction orders do not have to be integers, but
  in general will be rational numbers.
• Postulated rate laws are tested by comparing the
  experimental time dependence of the
  concentrations against that dependence predicted
  by the integrated rate law, which is obtained by
  solving the differential rate equation.

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In an autocatalyzed reaction the formation of
products increases the rate of the reaction. In
an autoinhibited reaction the formation of
products decreases or inhibits the rate of the
reaction.