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Okay, so now we've developed lots of
equations for
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different orders reactions from zero
through two second order reactions.
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How would we actually go about in
determining these orders?
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Experimentally.
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Well, there are a number of different ways
to do this.
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The first one is called the integration
method.
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And this essentially involves just
determining a concentration
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of the reactants at a series of times t.
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Now, when you determine the concentration,
you can either just determine the amount
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of the component, let's call that x, or
you can determine the amount remaining.
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Which should be the initial amount of say
a, a zero minus x.
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Either way, ultimately you need to be able
to
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determine the concentration of a, at a
given time.
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After that you then make a series of plots
of relevant functions.
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The relevant functions, which we have
determined in the previous exercise.
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So, for example, if it was a zero
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order reaction, we're going to plot the
function A.
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Versus time, and that would be for an
order of reaction zero.
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If it's a first order then we're going to
plot the natural log
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of a, versus time and that would be for a
first order process.
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And then finally for a second order
process, we're going to plot one over a.
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Versus time and that'd be for a second
order process.
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Then we'll just check to see which gives
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the best straight lines, we'll make
several plots.
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And the best straight line will give you
the order of the reaction.
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So that is what we've done here, we've
plotted on the y-axis.
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The function, depending on the order of
reaction, against time on the x-axis.
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So, here we have three plots, taken for,
from a set of data.
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So, the line here, the straight line here
is.
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Plotting the function just a concentration
against time.
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This plot up here, the curve, is plotting
natural log of A against time.
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And this other curve is plotting one over
A versus time, so we have the zero
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order plot, the first order and the second
order plot and for this set of data.
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Only the zero order plot is giving us a
straight line, and so we can, can conclude
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from this set of data that the process
we're looking at is a zero order reaction.
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Now, it's quite important that when you
measure these functions, you
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notice that all functions are, in fact,
linear over a small time interval.
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So if I was to take, say this green plot
down here, right, just
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to choose a very small time interval, then
this would be a linear plot.
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As would the first order if I took it over
a small time interval.
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So it's very important that you consider
over a large time
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interval to assess the difference between
the different orders of reaction.
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The next method is something called the
isolation method, and this is
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particularly useful if the reaction
contains more than one reactant.
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So, for example if we had A plus B going
to products, so we've
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got two things that are changing, and
let's suppose that
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the rate of this reaction which is given
by minus dA by dt if we
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consider it in terms of the change in
concentration of A.
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Let's suppose it's equal to a second order
rate
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constant times concentration of A times
the concentration of B.
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So, a second, second order process.
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Here we have the concentration of both A
and B changing as a function of time.
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So it's a little bit complicated.
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In order to make things easier for
ourselves, what I'm going
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to do is I'm going to have a large excess
of B.
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By that mean we mean that, the
concentration of
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B is going to be much larger than A.
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So we start the reaction, the initial
concentration of B is B zero, and
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that's going to be very much greater than
the concentration of A zero.
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So what is that going to do for us?
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Well, you imagine we have an awful lot of
B,
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and much less A, and we look at the
process here.
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Well, for every molecule of B we use up,
we use up one molecule of A.
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Well, if B, there is an awful lot of B at
the beginning.
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Then the concentration of B is not going
to
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change very much as a percentage of, of
it's concentration.
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Where as concentration of A will change by
a very large amount.
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So by doing the process in this manner,
the
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concentration of B will hardly vary during
the reaction.
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And therefore, the concentration of B to
all
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intents and purposes is going to be
approximately equal
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to the concentration of B zero, and that's
going
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to be true at all times during the
reaction.
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So then, with this approximation, the rate
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of reaction is going to be simplified
because now we have.
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The rate constant times the concentration
of B, which we've said
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is approximately equal to B zero times the
concentration of A.
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Now we know that this thing here is a
constant.
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And therefore everything here at the
beginning of the
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expression is indeed a constant, so now we
just have a,
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another constant which we'll call K 1
prime times A.
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We're going to call it K 1.
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Because this is now really behaving as a
first order
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process, we've only got one thing varying,
which is A.
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So K 1 prime is what we call a pseudo
first order rate constant.
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Once we've done that, we can then just go
back and determine
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the reaction order, this by the
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integration method, which we've described
before.
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The next method is something called the
Half-Life
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method, and this is useful for reactions
of the
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type A going to products, so we can note
that the
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Half-Life for a process is actually
related to the
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order of the reaction and it's
proportional to the
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concentration of A initially raised to the
power 1
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minus the order of reaction n, so n here
is the order.
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Of the reaction.
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[SOUND] So we can say that this is equal
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to a constant of proportionality
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times the concentration a zero
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raised to the power 1-n.
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Then, all we need to do is, take log
rhythms of both sides of this equation.
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So, we take a log rhythm of the left hand
side.
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We're going to have log of [INAUDIBLE],
one half.
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Then on the right hand side were going to
have, log of C.
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Plus (1 - n) times the log of the
concentration of A zero.
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Notice that the (1 - n) comes out to the
front of the log, because log of sum
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raised to the power is the same as that
thing, that power, multiplied by the log.
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So now we have a, an equation for a
straight line.
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Where we plot log of [INAUDIBLE] one half
against log of A zero.
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This will behave in a straight line
manner.
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So, here is the straight line plot.
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On the x-axis, we're plotting log of the
initial concentration of A zero.
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And on the y-axis we're plotting log of
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the half life that gives you a straight
line.
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The slope will give you directly the order
because the slope is (1 - n) and
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then all you need to do is vary the
initial concentration A zero and then
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measure the time for half reaction, and
make a plot of this manner.
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The final method is something called the
initial rate method.
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Sometimes referred also as the
differential method.
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So, in this case, if we consider a process
such as A plus B going to products.
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And let's suppose that the rate is some
arbitrary rate k2, times the concentration
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of A raised to some power A, and the
concentration of B raised to some power B.
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Well, we can see that if we are at
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the beginning of the reaction, when time
equals 0.
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Then, the rate will be the initial rate of
reaction, and the concentrations of A will
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be the initial concentration of A, and B
will be the initial concentration of B.
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Now, we take logarithms of both sides of
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this equation, so we have log initial
rate.
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Equals log of k 2, plus, because we're
taking
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logs of something we multiply and we, we
add on.
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The a comes down to the front of the log,
that's the power drops
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to the front, log of concentration A zero,
plus B which drops to the front.
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Times the logarithm of B zero.
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So here are orders of reaction A and B,
which we wish to determine.
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The trick now to make this a straight line
plot
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is to keep B zero constant whilst varying
A zero.
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So, if B zero is a constant, then this
whole term here will become a constant.
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This is also a constant.
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And now we have the equation of a straight
line.
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We can plot log of the initial rate
against log of A zero.
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And if we do that, we will get a straight
line plot.
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The slope of that plot is going to be
equal to A.
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And we have determined the order with
respect to A.
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If we want to do the same thing for B, all
we need to do is now keep a zero
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constant, and then we will make a straight
line plot
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and we will determine the order with
respect to B.
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