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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 Speed-Rates of Chemical Reactions Doc Brown's chemistry revision notes: basic school chemistry science GCSE chemistry, IGCSE  chemistry, O level & ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old science students for national examinations in chemistry

Rates of reaction notes INDEX

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4. More examples of interpreting graphical results ('graphing'!)


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/

measuring gradient tangent from product-time graph to get rate of a reaction speed gcse chemistry igcse international chemistry

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 cm3, 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 cm3/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 cm3 / 10 s = 2.0 cm3/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 cm3/s.

The calculation on diagram for the rate of gas production is:

(39 - 23) cm3 / (74 - 16) s = 16 / 58 = 0.28 cm3/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 cm3 of gas is evolved, average speed = 21/20 = 1.05 cm3/s

BUT, this is not as accurate as the other initial rate calculation above, which gives nearly twice the speed calculated here (2.0 cm3/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.


(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 curve-shape 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 cm3/s or cm3/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.

(c) doc bGraph 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.

(c) doc b 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.

(c) doc bGraph 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

(c) doc b 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.

(c) doc bGraph 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.
(c) doc bGraph 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.
(c) doc bGraph 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 product-time graph e.g. for gas in cm3/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
(c) doc b

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 cm3/min for W, 20.0/2 = 10 cm3/min for X, 16.0/2 = 8.0 cm3/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 cm3/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 lumps-particle/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 cm3/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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Rates of reaction notes INDEX