There is no direct way to measure the consumption of reactants or products so we have to look at indirect ways. This involves looking at continuous and discontinuous reactions to measure rate of reaction. There are three ways of obtaining a rate value from a concentration against time graph plot, however these ways are indirect.
These indirect ways involve discontinuous and continuous experiments to find orders.
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Discontinuous experiments use many separate experiments with different starting concentrations. These obtain one reading per experiment, e.g. clock reactions: thiosulphate and acid.
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Continuous experiments use one experiment and many different readings can be taken as the experiment goes on, e.g. gas syringes; sampling experiments.
Methods of ‘following’ a reaction
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Titration – a reaction mixture is drawn up and samples are withdrawn from it, using a pipette. The reaction is then quenched and samples can then be nitrated in some way, which depends on what is in the reaction mixture.
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Colorimetry – if one of the reacting substances or products has a colour, the intensity of this colour will change during the reaction,
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Dilatometry – in the liquid stage of a reaction the volume of the whole mixture changes slightly during the reaction. If it does the change of volume can be followed by using an apparatus fitted with a capillary tube; dilatometry.
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Electrical conductance – the change in total number of ions can be measured through electrical conductivity of the solution. This uses alternating current so electrolysis of the solution is avoided.
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By measuring a gaseous product – a gas is given off in the reaction and can be collected in a gas syringe, and its volume measured.
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By measuring pH change – measuring the pH of the solution formed.
From the above methods of following a reaction the most suitable of the experiment is by measuring a gaseous product. This is because it is an easy experiment to set up and a wider range of results can be obtained. Other methods are either difficult to set up or the apparatus for them is not available.
Method 1
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Place in excess of 0.1g of magnesium in the side-arm test tube and have ready 10cm³ of Hydrochloric acid.
- Put the acid into the test tube and place bung over it to restrict any hydrogen gas escaping. Put the stopper on and start timing.
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Take readings of time taken to reach 20cc and 40cc of hydrogen gas. Repeat the following three times for each temperature (from 20-60°C), thereby increasing reliability of results.
- Repeat the above using ethanoic acid. Therefore the results can be compared; a weak acid versus a stronger acid.
Method 1 involves measuring the initial rate. The time taken has to be measured to collect 20cc and 40cc of hydrogen gas for a 1M solution of HCl and ethanoic acid. This method is an indirect method of measuring rate, where the rate can be worked out by 1/time.
Below the natural log of rate is plotted against temperature, 1/Kelvin, of the reaction where the activation energy can be measured from the gradient.
1/Kelvin
ln Rate or
ln k
A Gradient = A/B = - EA/R
(k = A e-EA/RT ) EA = -gradient X R
B
(R=gas constant = 8.31 JK‾¹ mol‾¹)
Method 2 – concentration
- Place in excess of 0.1g of magnesium in the side-arm test tube and have ready varying concentrations of Hydrochloric acid from 0.5–2.0M. Place test tube in water bath at room temperature.
- Put the acid into the test tube and place bung over it to restrict any hydrogen gas escaping. Put the stopper on and start timing.
- Take readings of volume of gas produced every 10 seconds.
- Repeat the following method three times, thereby increasing reliability of results.
- Repeat the above using ethanoic acid of 0.5-2.0M. Therefore the results can be compared; a weak acid versus a stronger acid.
For both acids, the original molarity of each 2M, therefore with varying concentrations from 0.5-2.0 of both acids it is important that the acids are diluted accurately. Remember 10cm³ of HCl and ethanoic acid will be used so dilutions have to be made up adding the correct amount of water to the acid.
This method involves measuring the concentration of the acid against the rate, 1/time. The formula, 1/time, for rate, is one that involves using the initial rate method. Below the concentration of Hydrochloric or ethanoic acid is plotted against the rate 1/time and there are three possible plots.
Rate (1/t)
[Acid]
- Plot [A] against time.
- Is it a straight line? If so then the order is 1.
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If the graph is not a straight line, rate is not first order. Plot rate against [A]2. A straight line shows the reaction is second order in A.
- When the line is horizontal the order of reaction is 0.
Method 2 also involves measuring Vf – Vt. For example
The third column in the table needs a little thought. When the reaction is over, the total volume of H2 collected (Vfinal) is proportional to the concentration of HCl/ethanoic acid at the moment when timing started, so (Vfinal – Vt) is proportional to the concentration of HCl/ethanoic cid at each time, t.
This method is used to calculate the half-life, to work out the order of reaction.
Half-life, t ½, is the time taken for the reactant concentration to half its value.
For a continuous experiment, to find the order of a reaction with respect to one of the reactants A is found by:
- Plot [A] against time.
- Work out the first half-life taken from the start of the experiment.
- The second half-life is taken from the end of the first half-life.
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When the first t ½ = 2nd t ½ the reaction is said to be first order with respect to [X]. First order reactions have a constant half-life, which is independent of the initial concentration.
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When the first t ½ ≠ 2nd t ½ the reaction is said to be second order with respect to [X].
[X]
Time
Determining orders of reactions by experiments
Three examples of this type of graph (showing zero order, first order, then second order) are shown below:
Rate
[X]
If the graph is not a straight line, the rate is not first order the rate has to be plotted against [X]²
Rate
[X]²
Rate
[X]
Consider this reaction
Magnesium(s) + Hydrochloric acid (l) → Magnesium Chloride (l) + Hydrogen (g)Mg(s) + 2HCl(l) → MgCl2 (l) + H2 (g)
2moles of HCl → 24 dm³
Concentration = moles/volume/1000 → 24 dm³
500 → 24 dm³
2.083 → 100 cm³
Molar mass of Mg = 24
24 → 24 dm³
y → 100
24/24000 X 100 = y
= 0.1g
Therefore, for the experiment it is advisable to use in excess of 0.1g of magnesium to enable completion of reaction. It was worked out to use in excess of 0.1g of magnesium ribbon (found to be 10.9 cm long). The Molecular Mass of magnesium is 24, therefore the moles of magnesium to be used are:
Moles=0.1/24
Moles=0.00416
In the reaction above, 1 mole of magnesium reacts with 2 moles of hydrochloric acid. The concentration of acid is 1mol/dm³. Therefore the volume of hydrochloric acid used will be:
Volume=0.00416X2
Volume=0.0083dm³
Volume=8.3cm³
It was decided to use an excess of hydrochloric acid to ensure all the magnesium reacts. Therefore 10cm³ of hydrochloric and ethanoic acid will be used in the experiment.
Apparatus
Water bath (20-60°C) – I will use an electronic water bath for maintaining the mixture at a temperature since the temperature is more accurate than a water bath above a Bunsen burner.
Magnesium – each strip in excess of 0.1g.
100cm³ gas syringe – should be appropriately accurate for measuring the gas produced since it is accurate to 1cm3 of gas.
10cm³-measuring cylinder – I have chosen to use 10cm³-measuring cylinder to measure the volumes of substances used since it is more accurate than a pipette.
Weighing balance – I will use a three-figure balance to measure the mass of magnesium.
Side-arm test-tube
Bung
Thermometer
Stop-watch
Diagram
Table of Results
Table for reaction with HCl and magnesium to produce 20 and 40cc -
Table for varying concentrations of HCl and ethanoic acid -
Table for gas produced for ten second intervals for HCl and ethanoic acid -
Volume of Hydrogen gas produced at
Table for Vf – Vt for HCl and ethanoic acid -
Preliminary data
The preliminary work that I will be conducting is to find out the correct amount of hydrochloric acid to use. To do this, I will measure out a volume of hydrochloric acid and react with in excess of 0.1g of magnesium ribbon and if there is still some magnesium left when the reaction has stopped effervescing then the volume of hydrochloric acid will have to be increased.
Apart from trying to find the optimum rate of reaction I also have to find out how to keep the temperature change down. As the reaction is taking place the temperature will rise because the reaction is exothermic, and this could cause my results to be inaccurate as the temperature change will heat up the acid and give the acid particles more energy so they will move faster and collide with the magnesium with greater force causing more successful collisions per second.
To show that the hydrogen gas is not being given of from the water in the hydrochloric acid I will have to conduct a control experiment. Magnesium ribbon will be reacted with distilled water to show that there is no reaction between magnesium and water and that the hydrogen gas is evolving from the hydrochloric acid when it is being broken down into magnesium chloride and hydrogen.
After my preliminary experiment, it was discovered that when using 5cm³ of hydrochloric acid the time to collect 40cc of hydrogen gas would be too long for the experiment considering repeats. Therefore, it was decided to increase the volume of the acid in order to increase the number of collisions between the acid particles and increase the rate of reaction. However, as temperature increased then so the rate of reaction increased, which is the trend that I will be looking for in the actual investigation.
Fair test - Variables
In order to keep my experiment a fair test I will have to make sure that I keep the following factors the same; for method 1 – investigating the time taken to collect 20cc and 40cc of H2 gas:
- The concentration of the acid.
- Volume of acid used (10cm³).
- Surface area of the magnesium.
- Clean the magnesium with emery paper before experiment.
- Amount of magnesium (in excess of 0.1g).
- I will also have to make sure that the gas syringe is correctly connected and that it is placed tightly enough so that no hydrogen gas escapes.
The factor that I will change is:
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The temperature of the reaction.
For method 2 - The volumes of hydrogen gas measured every 10 seconds for varying concentrations of a strong and weak acid. Therefore, the factors kept constant are:
- The temperature of the reaction.
- Volume of acid used (10cm³).
- Surface area of magnesium.
- Clean the magnesium with emery paper before each experiment.
- Amount of magnesium used (in excess of 0.1g).
- I will also have to make sure that the gas syringe is correctly connected and that it is placed tightly enough so that no hydrogen gas escapes.
The factor that I will change is:
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The concentration of the strong and weak acid.
For both experiments the Mg will be added to the test tube with acid at an angle. This will reduce the loss of H2 gas when the experiment is started.
Safety
See risk assessment:
- Wear safety goggles as I am using concentrated hydrochloric acid.
- Care to eyes and the skin besides all the other people is always vital and necessary.
- Care in using glassware since it is sharp when broken and can cut skin.
- Safe disposal of reagents and laboratory chemicals.
- Care when returning all used glassware and equipment at the end of the experiment
- Care when handling corrosive acids
Prediction
a). Mg(s) + 2HCl(l) → MgCl2 (l) + H2 (g)
Mg²+ + 2H + → Mg²+ + H2
b). Mg(s) + 2CH3COOH (l) → Mg(CH3COO)2 (l) + H2 (g)
Mg²+ + 2CH3COO‾ → (CH3COO‾)2 Mg²+ + H2
Form the above ionic equations the rate expressions can be written in order to show the effect of acid on the rate of reaction.
Rate ∞ [HCl]x [Mg]y
Rate ∞ [CH3COOH]x [Mg]y
From the above rate expressions it is clear that if the concentration of the acid is increased then the rate of the reaction will also increase. This is due to the collision theory. The larger the concentration of acid, the larger the number of acid particles present per 100cm³ of acid. Therefore, there will be more collisions per second, so the rate of reaction will increase.
If the concentration of the acid is doubled from 1M hydrochloric acid to 2M hydrochloric acid then I will expect to see the rate of the reaction double. This is because there are twice as many acid particles in 2M hydrochloric acid than in 1M hydrochloric acid, so there will be twice the amount of collisions per second. Therefore, there are twice the amounts of collisions per second and there will be twice as many successful collisions per second, increasing the rate of reaction.
We can compare how acid type may affect the activation energy for a reaction. It stands to reason that the weaker acid will have higher activation energy, because it must have this activation energy to start the collisions. The stronger acid will have a lower activation energy, because it does not need this extra energy to start the reaction.
As well as this the value of Ka, the dissociation constant for the acid can be worked using the Ka expression. This will enable us to determine the strength of the acid. HCl is a strong acid and therefore we would expect its Ka value to be large. Whereas, ethanoic acid is a weak acid and we would expect its Ka value to be small.
Ka = [CH3COO‾]² [Mg²+] / [CH3COOH]²
Ka = [H+]² [Mg²+] / [H+]²
I predict that as we increase the temperature the rate of reaction will increase. This is also due to the collision theory. As the temperature increases then so does the movement of particles. This increases the amount of the collisions between the particles and the rate of reaction increases. As a general rule I predict that as the temperature increases by 10°C the rate will double.
The collision theory states that molecules must collide before they react.
Only those molecules having energy above a certain minimum value will react when they collide. This minimum energy value is called the activation energy. The activation energy can be thought as an energy barrier to the progress of the reaction.
The transition state theory considers the details of the actual collision between two molecules. Repulsion between electron clouds pushes molecules apart unless they have enough energy to overcome the repulsion. If they get close to each other a rearrangement of electron clouds occurs and so new bonds are partially formed and partially broken. During this process the kinetic energy of the collision is converted into potential energy, which can be shown on an enthalpy diagram. The energy gap between the reactants and the peak is called the activation energy.
Molecules must have this activation energy, or greater, when they collide, if they are to react successfully. Thus the activation energy can be considered as a barrier to reaction and the greater its value the slower the reaction.
Energy
Reactant
∆H
Product
Path of reaction
Energy Product
Reactant ∆H
Path of reaction
The existence of an energy barrier explains why many energetically favourable reactions are not spontaneous at room temperature; there are may be no molecules with energy greater than the activation energy. The rate of reaction is directly related to the size of the activation energy.
The spread of energies in a sample of gas molecules is given by the Maxwell-Boltzmann distribution curve. Frequent collisions between molecules result in a spread of high and low energy. It can be seen that at any temperature only a few molecules have very low or very high energies, most being around the peak of the curves. As the temperature increases, the curve broadens out, the peak value decreases and moves towards a high-energy value. The area under the curve represents the number of molecules in the sample and is therefore constant. The area under the curve beyond the E (act) represents the number of molecules having energies greater than or equal to the activation energy. This increases as temperature increases and so therefore, does the rate of reaction.
Number of T¹
Molecules T² T² > T¹
Energy
Effect of Concentration on Rate (linking prediction to theory)
Consider the reaction: A + B = C + D. The rate equation can be expressed in several ways:
Volume of A
Gas
B
Time
The graph profile enables us to discuss how the rate changes, using the initial rates method. The following graph above is the basis for the concentration experiment and below gives an example of what a graph at different concentrations would look like. It is important to remember when varying concentration the factors that must be kept constant are;
- Temperature
- Pressure
- Partical size
Volume of 1.0M
Gas 0.75M
0.5M
0.25M
Time
To find how the rate varies with [A] or [B] it is necessary to perform a series of experiments in which one of the concentrations is kept constant and the other varied.
Usually it is found that:
- d [A] / dt is proportional to [A]x and [B]y
Or
- d [A] / dt = k [A]x [B]y
This is called the rate equation for the reaction. k is the rate constant at a given temperature.
The order of a reaction with respect to a given reactant is defined as:
‘power of its concentration in the rate equation’.
Mg²+ + 2H+ → Mg²+ + H2
Rate = [HCl]x [Mg]y
Example – order of reaction
For example, for the reaction between propanone and in the presence of hydrogen ions, the equation is;
r = k [CH3COCH3]1 [I2]0 [H+] 1
If the concentration of a reactant is raised to the power 0 (making it equal to 1), it has no effect on the rate - it is zero order. It does not really have to be included in the equation at all. If it is raised to the power of 1 (i.e. not changed at all), it affects the rate and is first order. If it is raised to the power of 2 (i.e. squared), it has an even stronger effect on the rate and is second order.
Zero order reactants decrease in at a constant rate throughout a reaction. First order reactants decrease at a rate that continually slows, with a constant . Second order reactants decrease at a rate that continually slows and has an increasing half-life.
The order of a reactant is related to its role in the actual chemical process. Reactions take place in steps, forming compounds. The slowest step determines the overall rate of the reaction and is indeed known as the . Only the reactants that are involved in or before this step will appear in the rate equation.
Determining rate constants
The rate constant, k, is a factor in the rate equation;
Rate∞ k [X] [Y]² Rate = k [X] [Y]²
The rate constant, k, is a constant only for a particular/ fixed temperature and so varies with temperature. Rate roughly doubles every 10°C temperature rise. Since concentration is not changed, it follows if rate doubles, then k must have doubled when temperature is increased by a 10°C rise. The rate is found for different concentrations of A. Then rate is plotted against [A], [A]2… until a straight line is obtained.
Since rate = k[A] the value of k is found by taking the gradient of the graph.
The rate constant, k, depends on temperature and on the of the molecules involved and, for many reactions, is approximately given by the :
k = A e-EA/RT
Where A is a pre-exponential factor relating to molecular orientation, EA is the of the reaction, R is the and T is the . e, of course, is just . As the temperature increases, EA/RT decreases, so e is being raised to a less negative number. Thus k increases, so the reaction goes faster.
The arrhenius equation can be used to show the effect of a change in temperature on the rate constant – and therefore on the rate of reaction. If the rate constant doubles, the rate of reaction will double and as a rule of thumb a 10°C rise causes the rate of reaction to double.
The frequency factor, A, in the equation is approximately constant for such a small temperature change. We need to look at e-EA/RT changes – the fraction of molecules with energies equal to or in excess of the activation energy.
Let’s assume activation energy of 50 Kj mol‾¹, 50,000 J mol‾¹. The value of the gas constant, for example, is 8 JK‾¹ mol‾¹. At 20°C (293K) the value of the fraction is:
e-EA/RT = e (-50000/(8 x 293))
= 5.45 x 10^‾8
By raising the temperature by 10°C (303K), the effect on the rate of reaction is:
e-EA/RT = e (-50000/(8 x 303))
= 1.1 x 10^‾9
You can see that the fraction of molecules able to react has almost doubled by increasing the temperature by 10°C. that causes the rate of reaction to almost double. This is the value used in rate of reaction work.
Determining reaction Mechanism
In organic chemistry, an organic reaction can happen in a number of successive steps. These steps are known as the mechanism of the reaction and there is no reason that all the steps take place at the same rate. However, it is clear that the whole reaction goes at the rate of the slowest of the steps in the mechanism. This slowest step is called the rate-determining step.
A major factor in interpreting results is the absence of an accepted mechanism for the reaction. Our effort at mechanistic theory argues by analogy with heterogeneous catalysis, and goes as follows;
- Hydrogen ions migrate to the metal surface
- Hydrogen ions accept electrons from the metal surface
- Hydrogen atoms combine to give hydrogen molecules
- Metal ions hydrate and diffuse away from the metal surface
We propose that steps 2 and 3 are surely fast steps and that, given efficient agitation step 4 should also be fast. This leaves step 1 as the most likely rate-determining step.
If the mechanism is correct it is important to remember that the reaction is between H+ (aq) and Mg(s). A strong acid is completely ionised but a weak acid is not. Energy will be needed to break bonds and produce the H+ ions in a weak acid, so I would expect the activation energy to be higher. This necessitates a change to step 1 of the mechanism.
