4. More examples of
graphs from 'rate of reaction' experiments
GCSE level
Chemistry: More examples of graphical analysis from rate of reaction
experiments
Doc Brown's
Chemistry KS4 science GCSE/IGCSE Revision Notes  Factors
affecting the SpeedRates of
Chemical Reactions Doc Brown's
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Rates of
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4.
More examples of interpreting
graphical results ('graphing'!)
PLOTTING GRAPHS  PLOTS OF GRAPHS OF DATA
AND HOW TO INTERPRET THEM
BUT first, a more detailed look at the single graph
shown below
The graph below illustrates how to measure the rate of reaction at a
specific time by constructing a tangent through that specific time/
Imagine a reaction evolving a gas,
and you measure the volume of the product gas at regular time intervals.
The rate at which the gas is evolved is the measure of the speed of the
reaction.
The vertical y scale is the gas
volume (2 mm = 1 cm^{3}, 2 mm squares).
The horizontal x scale is time (1 mm
= 1 s, 2 mm squares).
You plot the points (deliberately
omitted here) and join them up with the 'best curve' as shown!
The diagram shows how to measure and
calculate the initial rate at the start of the reaction in
cm^{3}/s
from the gradient of the first purple triangle on the left at the start of the
reaction. Calculation on diagram.
In this case
the initial rate of gas evolution is 20 cm^{3} / 10 s =
2.0 cm^{3}/s
Then, if you wish, to know the speed
at any other point, you must draw a tangent at that specific time (e.g.
46 s), construct the second purple triangle to obtain the gradient, carefully read the graph scales and
calculate the reaction rate e.g. in cm^{3}/s.
The calculation on diagram
for the rate of gas production is:
(39  23) cm^{3} /
(74  16) s = 16 / 58 =
0.28 cm^{3}/s
Note how the gradient gets smaller
and smaller as the reaction proceeds and eventually falls to zero, when the
reaction stops, due to one of the reactants being all used up.
It is easy to calculate an
average speed over a specific period of time e.g.
Over the first 20 seconds 21
cm^{3} of gas is evolved, average speed = 21/20 =
1.05 cm^{3}/s
BUT, this is not as accurate
as the other initial rate calculation above, which gives nearly twice the
speed calculated here (2.0 cm^{3}/s).
The reason average rates are
not as accurate is due the speed of reaction constantly changing, as it
decreases as the reactant are used up e.g. decrease in concentration or
surface area of a solid reactant.
PLEASE Note
(i) rate of
reaction = speed, (ii)
see
other introductory graphs and notes at the start of this topic
(ii) Graphs 4.1, 4.2 and
4.5 just show the theoretical shape of a graph for a single
particular experiment. Graphs 4.3 and 4.4 (temperature), 4.6 and 4.7
(concentration) and 4.8 (several factors illustrated) shows
the effect of changing a variable on the rate of the reaction and hence
the relative change in the curveshape of the graph line.
(iii) The rate of
reaction may be expressed as the reciprocal of the reaction time
(1/time) e.g. for the
time for
sulfur formation (to obscure the X) in the sodium thiosulfate
 hydrochloric acid reaction
or where a
fixed volume of gas is formed, though in this can also be expressed
as gas volume/time too as cm^{3}/s or cm^{3}/min
even though the gas volume is the same for a given set of results of
changing one variable whether it be concentration or temperature.
If you have
detailed data e.g. multiple gas volume readings versus time, the
best method for rate analysis is the
initial rate method described on and below the diagram of the gas
syringe gas collection system on the introduction page.
(iv) for detailed
observations of gas versus time see individual factor pages, and I've
added new data tables and graphs to them, but I've retained the
'simplified graphs' below.
Graph
4.1 shows the decrease in the amount of a solid reactant with time.
The graph is curved, becoming less steep as the gradient
decreases because the reactants are being used up, so the speed
decreases. Here the gradient is a measure of the rate of the
reaction. In the first few minutes the graph will (i) decline
less steeply for larger 'lumps' and (ii) decline more steeply
with a fine powder i.e. (i) less surface area gives slower
reaction and (ii) more surface area a faster reaction. 
Graph 4.2 shows
the increase in the amount of a solid product with time. The
graph tends towards a maximum amount possible when all the solid
reactant is used up and the graph becomes horizontal. This means
the speed has become zero as the reaction has stopped. Here the
gradient is a measure of the rate of the reaction. However, I
don't know of any practical method of following a reaction by
measuring the amount of solid formed. 
Graph
4.3 shows the decrease in reaction time with increase in temperature
as the reaction speeds up. The reaction time can represent how long
it takes to form a fixed amount of gas in e.g. in the first few minutes of a
metal/carbonate  acid reaction, or the time it
takes for so much sulfur to form in the sodium thiosulfate  hydrochloric
acid reaction. The time can be in minutes or seconds, as long as you stick
to the same unit for a set of results e.g. a set of experiments varying the
concentration of one of the reactants.
Theory of
temperature effect 
Graph 4.4
shows the increase in speed of a reaction with increase in temperature
as the particles have more and more kinetic energy. The rate of
reaction is proportional to 1/t where t = the reaction time. See
the notes on rate in the Graph 4.7
paragraph below and the
theory of temperature effect. 
Graph
4.5 shows the increase in the amount of a gas formed in a reaction with time.
Here the gradient is a measure of the rate of the reaction.
Again, the graph becomes horizontal as the reaction stops when
one of the reactants is all used up!
More on this type of graph
in introduction. 
Graph
4.6 shows the effect of increasing concentration, which
decreases the reaction time, as the speed increases because the
greater the concentration the greater the chance of fruitful
collision. See the notes on rate in the
Graph 4.3
paragraph above and the
theory of concentration effect. 
Graph
4.7 shows the rate/speed of reaction is
often
proportional to the concentration of one particular reactant.
This is due to the chance of a fruitful collision forming
products being proportional to the concentration. The initial gradient of the
producttime graph e.g. for gas in cm^{3}/min
(or /s if faster, for timing the speed/rate of the reaction) gives an accurate measure of how fast the gaseous product is being formed
for the initial concentration. The reciprocal of the reaction time,
1/time, can also be used
as a measure of the speed of a reaction. The time can e.g. represent how long
it takes to make a fixed amount of gas, or the time it
takes for so much sulfur to form in the sodium thiosulfate  hydrochloric
acid reaction. The time can be in minutes or seconds, as long as you stick
to the same unit for a set of results for a set of experiments varying the
concentration or mass of one of the reactants.
Theory of
concentration effect 
Graph 4.8
Some general interpretations of a set of results for the same reaction
that produces a gaseous products from e.g. adding a reactant
solid to a reactant solution.
(i) The
graph lines W, X, original experiment E, Y and Z on the left diagram are typical of when
a gaseous product is being collected.
The middle graph might represent the original experiment 'recipe' i.e. in
terms of initial concentration, initial amount of solid and its
particle size and
of course at a specific initial and constant temperature. Then the experiment repeated with variations
of the controlling factors producing different graphs e.g.
typically graphs W, X, Y and Z.
The average rate of reaction at 2
mins for each of the five experimental runs would be 31.0/2 =
15.5 cm^{3}/min for W, 20.0/2 = 10 cm^{3}/min
for X, 16.0/2 = 8.0 cm^{3}/min for E, 10.0/2 = 5.0
cm3/min for Y and 6.0/2 = 3.0 cm3/min for Z. BUT some of these
values would be significantly different from the initial rate
e.g. for run X the graph is very curved and you can see the
initial rate is more like 6.0/0.2 = 30 cm^{3}/min, very
different from that calculated at 2 mins. Ideally you should try
and measure the tangent gradient close to the start of the
reaction where you should observe a short 'linear' portion on
the graph line.
(ii) X could be the same
'recipe'
as the original experiment
but a catalyst added, forming the same amount of product, but faster
 steeper initial gradient.
You would get a similar result by increasing the temperature of
the reactants, as long as you measure the gas volume itself at
the same temperature and pressure.
(iii) Initially,
the increasing order of rate of reaction represented on the
graph by curves Z to X i.e. in terms of speed of reaction X > original
E > Y > Z might
represent one of the following situations ..
progressively increasing concentrations of reactant
progressively
higher
temperature of reaction
progressively smaller
lumpsparticle/increasing surface area of a solid reactant.
All three
trends in changing a reactant/reaction condition variable produce a progressively
faster reaction
shown by the increasing INITIAL gradient in cm^{3}/min which
represents the rate/speed of the reaction.
(iv) Z could represent taking
half the amount of solid reactants or half the original concentration.
The
initial reaction rate is slower (halved) and only
half as much product gas is formed.
(v) W might represent taking
double the quantity of reactants, forming twice as much gas e.g. same volume
of reactant solution but doubling the concentration, so producing twice as
much gas, initially at double the speed (gradient twice as steep).
More details of laboratory
investigations ('labs') involving 'rates of reaction' i.e.
experimental methods for observing the speed of a reaction are given in
the INTRODUCTION 
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reaction notes INDEX
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