A graph such as this depicts second order, where the rate of reaction is directly proportional to the square of the concentration. This means a massive increase in rate for a relatively slight increase in concentration.
A graph with a straight horizontal line shows zero order, where changing the concentration of the reactant has no effect on the rate of reaction whatsoever.
If the order of reaction is zero for a reactant, changing the concentration will have no effect on the reaction’s rate. If it is first order, the rate of reaction is directly proportional to the concentration of the reactant. Second order means the rate of reaction is directly proportional to the square of the concentration, meaning just a slight increase can have a massive effect.
This supports the idea that simply increasing the concentration of the reactants increases the reaction rate, as it produces more collisions. However, this is not always the case, as a collision does not necessarily mean a successful collision.
Activation Enthalpy
*3
There is a minimum amount of energy required for the species involved in a collision to react, called the activation enthalpy, Ea, a term introduced by the Swedish scientist Svante Arrhenius in 1889. If the energy of the species exceeds or equals this value when they collide, the collision will be successful, thus a reaction will take place. If not, they may temporarily remain in contact then drift apart or they may simply bounce off of one-another.
Successful
Unsuccessful
The Ea of different reactions vary, and can be increased or reduced by altering the environment in which the reaction is taking place. It can be found by using the Arrhenius formula:
where R is the universal gas constant, A is the frequency factor, which depends on how often molecules collide when all concentrations are 1 moldm ̄³ and on whether the molecules are properly oriented when they collide, T is the temperature, measured in Kelvin, and k is the temperature dependency (rate constant) for the reaction.
By finding the rate equation, we are able to rearrange it and find the rate constant for each temperature. For example, if the rate equation was r=k[A][B], k would be r/([A][B]). Inserting the rate at specific temperatures will give me the rate constant for that particular temperature, allowing one to perform more calculations and analysis.
By taking the natural log of both sides of the equation, we get:
lnk=lnA-(Ea/RT) or lnk=lnA-(Ea/R)x1/T
We can find the activation enthalpy by treating the equation above as a straight line graph equation (y=mx+c), where lnk represents y, lnA represents C, -(Ea/R) represents m and 1/T is x. By plotting 1/T against lnk, we are given a straight line graph, the gradient of which is Ea/R. We can expect this graph to look like the following:
*4
As the gradient is Ea/R, if we multiply this value by the gas constant we are given the activation enthalpy Ea.
Relating this to the activation enthalpy, the Maxwell-Boltzmann distribution graph depicts the various energies of the molecules in a reaction, based on the fact that the same molecules will have equal mass, and as Kinetic Energy = ½mv2, the energy of the particles depends on the velocity at which they are travelling. The shaded area to the right of the straight vertical line that marks the activation enthalpy value shows that amount of reactant molecules that possess enough energy to react, whereas the area on the left shows those that do not.
As is a widely known and used fact, altering the temperature of the components in or surroundings of a reaction can massively affect its rate of occurrence. In general, increasing the temperature for an exothermic reaction will slow the rate, as the system is attempting to get rid of excess energy, and providing thermal energy by increasing the temperature works against this process. Endothermic reactions, on the other hand, often benefit from increasing the temperature, as the name suggests.
For such reactions, we can visualize the effects of increasing the temperature on the Maxwell-Boltzmann distribution curve as “squashing the line downwards”, creating T2. This means the average energy of the molecules is greater, thus there are more with an energy that exceeds the activation enthalpy, so more react in a shorter period of time:
*5
The kinetics-related reason for this is that the thermal energy given to the molecules is used as kinetic energy, meaning they move faster and further for a longer amount of time, so that they are more likely to collide and due to having a greater energy, are more likely to collide successfully.
In many reactions where the activation enthalpy is around 50kJ/mol, increasing the temperature of the system can increase the rate of reaction by 100%. This may be something I consider when my results are obtained and the necessary calculations are completed. The following graph shows this process, with a line at 50kJ/mol, showing how the area under the line depicting T+1 is double that of the other.
Exothermic/Endothermic Reactions
*6
In an exothermic reaction, the total energy given out from the system is greater than that given in, increasing the temperature of the surrounding environment. As the diagram depicts, the enthalpy of the reactants at the start is much greater than that of the products. The system’s enthalpy initially increases as it receives enough energy to reach its activation enthalpy and cause a reaction. The enthalpy change of a reaction such as this will be negative, as the system as a reduced final enthalpy.
In an endothermic reaction, the total energy taken into the system is less than that given out, as could be predicted. Where exothermic reactions often need heat to begin, endothermic reactions will need sustained temperatures in order to react over a period of time. Again the diagram depicts the enthalpy of the system and clearly shows its final enthalpy exceeds its initial enthalpy.
Catalysts
*7
The addition of a catalyst to a reaction will increase the rate of a reaction. Heterogeneous catalysis involves a catalyst in a different physical state as the reactants, usually where the catalyst will be a solid and the reactants either liquid or gas. The process involves the reactants adsorbing onto the surface of the catalyst. As they do this, the bonds within them weaken and break. Following this, the fragmented reactant molecules, due to their proximity, form new bonds between each other and the products are formed. The products then desorb and diffuse form the surface of the catalyst. The Haber process is a particularly prevalent example of this, where ammonia is formed from nitrogen and hydrogen molecules, with a solid iron catalyst.
For every reaction, a suitable catalyst must be selected, as if the reactants do not adsorb onto the surface of the catalyst strongly enough, they will diffuse before they have a chance to react. If they adsorb too strongly, they will not be able to react or diffuse from the catalyst’s surface and will cause poisoning, rendering the catalyst useless. Hence, the perfect catalyst must be used otherwise it may not only have no improvement on the rate of the reaction concerned, but may even hinder the process, whilst wasting energy and resources.
Homogenous catalysis is where the catalyst used is in the same physical state as the reactants, although many of the mechanisms involved in the process of homogenous catalysis are also applicable. The catalysts are often dissolved in a solvent, along with the substrates, where they will react to form the product(s).
Both kinds of catalysis have the same result, in that they increase the reaction rate by offering the reactants an “easier path”. They both reduce the amount of energy necessary to react and thus reduce the activation enthalpy. On the Maxwell-Boltzmann distribution graph, we can see the straight vertical line depicting the activation energy, and the addition of the catalyst would have the effect of moving this line to the left, thus increasing the shaded area beneath the line and the number of molecules that have sufficient energy to react. This is the cause of the increase in initial rate of reaction.
Autocatalysis is a term describing a reaction in which a product works as a catalyst for the same reaction. Consequently, the reaction may initially proceed slowly, using the sulphuric acid as a catalyst, but as more of the particular product is formed, the reaction rate increases. The oxidation of oxalic acid by potassium permanganate is in fact an example of autocatalysis. Its equation is:
*8
2 MnO4-(aq ) + 5 H2C2O4(aq ) + 6 H3O+(aq ) --> 2Mn2+(aq ) + 10 CO2(aq ) + 14 H2O
The Mn2+ ions become the catalyst in this case, aiding the reaction and increasing its rate. Considering this, we can expect the rate to begin slow and then as the Mn2+ is produced, increase rapidly. This behaviour is seen on the following graph.
*9
Without the aid of the mechanism for the reaction, I cannot be sure, but one observation I’ve made is that both the H3O+ and the Mn2+ ions act as catalysts at some point during the reaction, hence it is likely that they are acting as a medium between two negative ions repelling each other, and reducing this repulsion, therefore allowing the reaction to occur more easily.
By reducing this repulsion, the negative ions do not have to over some such a strong force; therefore they need less energy to react, creating an “easier route”. Looking at the diagram below, we can see how the energy required for a reaction to occur with a catalyst is massively less than without.
*10
Method
I will first prepare my workspace, placing an absorbent mat on the desk to ensure minimal mess is made and any dangerous solutions spilled are prevented from spreading and causing a hazard. I will be sure to wear a buttoned-up lab coat to protect myself and my clothes from the materials used, wearing gloves on my hands and goggles to cover my eyes.
The initial stages of the investigation will involve measuring the absorbance of various concentrations of potassium permanganate using the colorimeter. From this I will be able to draw a calibration graph, which will be useful in finding the concentrations of solution throughout my reactions later on, thus allowing me to form graphs from my results and deduce a gradient depicting the rate of reaction. If I find that certain concentrations are too high and have absorbances that measure above two- therefore are literally unobtainable due to the restrictions of the colorimeter- I will not use them, as during a reaction it would be impossible to track the progress.
By using the initial concentration of 1moldm ̄³ of potassium permanganate and diluting to particular degrees depending on the concentration I want to produce, I will obtain several solutions of different concentrations. As the colour of the solution I shall be observing is a vivid violet, I shall set the colorimeter to the complimentary filter green/yellow. I will then proceed to reset the colorimeter with distilled water (absorbance 0), and place samples of each concentration of potassium permanganate in the colorimeter one by one, measuring the absorbance of each. I shall then plot a graph of absorbance against concentration, and use this as a calibration graph.
The next stage will be preparing the rest of my solutions. To make my solutions, I will place a particular amount of potassium permanganate in volumetric flask using a bulb pipette, filling the rest with distilled water until the meniscus reaches the thin line on the neck of the flask, diluting the solution in order to produce different concentrations. The amount of potassium permanganate used will depend on the concentration I intend to produce. To find this concentration, I will use the following formula:
New concentration = old concentration x volume of solution to be diluted
volume of water + solution
As I am looking at how changing different factors in the reaction can affect the reaction rate, I will also make various concentrations of the oxalic acid and sulphuric acid, using the same method. The strongest sulphuric acid I will use is 2 moldm ̄³, so will produce the following concentrations of sulphuric acid:
- 1 moldm ̄³
- 0.5 moldm ̄³
- 0.25 moldm ̄³
- 0.125 moldm ̄³
- 0.1 moldm ̄³
The concentrations of oxalic acid I will use are:
- 0.25 moldm ̄³
- 0.025 moldm ̄³
- 0.0025 moldm ̄³
- 0.00025 moldm ̄³
- 0.000025 moldm ̄³
The concentrations of Potassium permanganate used will be:
- 0.01 moldm ̄³
- 0.005 moldm ̄³
- 0.001 moldm ̄³
- 0.0005 moldm ̄³
- 0.0001 moldm ̄³
These concentrations were carefully selected after I carried out a set of trial runs, including experiments with many different concentrations of each of the solutions. Observing these experiments, I took note of which ones were successful and chose those which would give me appropriate results. This was judged on whether the rate of reaction was reasonably fast but not too fast, whether the rates of reaction were varied enough to differ between and therefore obtain a pattern and whether the concentrations would be safe to use.
For the reaction itself, I will use a 10cm³ bulb pipette to transfer a particular amount of oxalic acid from its volumetric flask to the 100cm³ beaker. I will then use a different bulb pipette of the same size to transfer the same amount of sulphuric acid to the same beaker, ensuring to mix these well. After this I will use another clean bulb pipette to transfer the same volume of a particular concentration of potassium permanganate to the same beaker. It is essential that the bulb pipettes are clean before use in order to avoid contamination and error due to confusion over the amount of the particular solution being measured in the pipette. I will instantly swirl this to mix the solutions, stimulating the reaction, and use a teat pipette to transfer around 5cm³ of the newly mixed solution to a clean cuvette, placing this in the colorimeter and pressing the graph function in order to measure the absorbance every 15 seconds. As the reaction progresses, the solution shall become visibly lighter in appearance and the absorbance values shall decrease. The rate at which it decreases will depict the rate of reaction.
This process must be completed for each concentration of potassium permanganate in order to find the extent to which a varying concentration of the substance affects the rate of its reaction with oxalic acid. To ensure a fair test, the other variables, such as the concentrations of sulphuric and oxalic acid and the temperature of solutions, will remain constant. The experiment must be repeated at least twice for each concentration, so I can find an average and reduce the likelihood or magnitude of errors.
When my results are obtained and organised in a tabulated format, I will use my calibration graph to insert the concentrations of permanganate that correspond with each absorbance value, allowing me to create a scatter graph for each table, plotting time against concentration. Upon achieving this, I will be enabled to find the initial rate of reaction on each graph by drawing a tangent to the line of best fit, and by forming a right-angled triangle and dividing the change in y values by the change in x values, giving the gradient of the line at this particular point:
I will find the rate of reaction for each of my graphs, allowing me to discover how changing the concentration of each of my components in the reaction, or the temperature, affects the reaction rate. I will do this by plotting four more graphs comparing:
- Conc. of Potassium Permanganate and rate of reaction
- Conc. of Sulphuric acid and rate of reaction
- Conc. of Oxalic acid and rate of reaction
- Temperature of solutions and rate of reaction
By manipulating the rate equation and Arrhenius’ equation, I will be able to use my results and graphs to find the activation enthalpy.
Risk Assessment
This section shall include all the potential hazards and risks of my investigation. The dangers presented by the reactants, the products and the processes involved shall be discussed. The information presented has been extracted from hazcards and other sources.
Potassium Permanganate
Fortunately, the potassium permanganate I am to use will not be in its solid form at any time, as in this state it can cause a fire if in comes into contact with combustible materials, and if swallowed is harmful. As a solution however, at concentrations such as mine, below 1 moldm ̄³ that is, it may oxidise the skin slightly but will not be harmful.
Oxalic acid
Although it can react violently with oxidising agents such as potassium permanganate, the concentrations I am using will not be a cause for concern. As for its hazards on its own, it does not present any risks under 0.3 moldm ̄³, and due to my carefully selecting the strongest concentration to be 0.25 moldm ̄³, this will also not be problematic.
Sulphuric acid
Solutions of sulphuric acid cease to be corrosive at concentrations under 1.5 moldm ̄³, and as my strongest concentration is 1 moldm ̄³, I will not have to worry about serious dangers. It is classed as an irritant at my concentrations however, so I must take care to avoid problems and follow certain procedures if they occur. If swallowed, the mouth should be washed out and a glass or two of water is to be drunk, in order to further dilute the solution. Vomiting is not to be induced and medical attention should be sought. If it comes into contact with the eyes, they must be flooded with gently running water for 10 minutes.
Carbon Dioxide
As any carbon dioxide produced in my reactions will be in gas form, I can disregard any risks presented by the chemical in its solid state. It can cause asphyxiation in large quantities or at least a reduction in the amount of oxygen inhaled, so although it is likely the amount of carbon dioxide I am to produce would be enough to cause concern, nonetheless I must ensure to keep the area well ventilated.
Manganese (II)
The Mn2+ ions produces will be in an aqueous solution, so once again the threats it would present as a solid can be disregarded. In solution, it is also only dangerous at concentrations exceeding 1moldm ̄³, which is irrelevant as my products will not be this strong; hence no specific safety measures are to be taken.
Results
Each of the following tables contains the results obtained from the reactions I set up. They depict the changing absorbance and thus the concentration of potassium permanganate, as time progresses. The tables are categorised; the first section containing those that show the results of the reactions with various starting concentrations of potassium permanganate. The next section shows those with different starting concentrations of sulphuric acid, the third- different concentrations of oxalic acid and the fourth-different temperatures. In the sections where they remain constant, the concentrations of potassium permanganate, oxalic acid and sulphuric acid will be 0.001 mol dm ̄³, 0.25 moldm ̄³ and 1 moldm ̄³ respectively. The tables give the average absorbance at each time from the three times each particular reaction was done.
The concentrations were found from the calibration graph previously discussed, where I plotted several concentrations of potassium permanganate solution against the absorbance values they produce in the colorimeter:
The graphs drawn from each of these tables have the same number in blue ink at the corner of the page as the number above of its corresponding table next to the concentration. The graph of the above table (calibration graph) is number 1.
Section One – Potassium Permanganate
0.001 moldm ̄³- Graph 2
0.0005moldm ̄³- Graph 16
0.01 moldm ̄³- Graph 17
0.005 moldm ̄³- Graph 18
0.0025 moldm ̄³- Graph 24
Section 2- Sulphuric acid
0.25 moldm ̄³- Graph
6
0.125 moldm ̄³- Graph 3
0.1 moldm ̄³- Graph 4
0.5 moldm ̄³- Graph 5
1 moldm ̄³- Graph 2
Section 3- Oxalic acid
0.025 moldm ̄³- Graph 15
0.25 moldm ̄³- Graph 14
0.0025 moldm ̄³- Graph 12
0.00025 moldm ̄³- Graph 11
0.000025 moldm ̄³- Graph 13
Section 4- Temperatures
18.00°C- Graph 2
25.00°C- Graph 7
30.00°C- Graph 8
35.00°C- Graph 10
45.00°C- Graph 9
Unlike the concentrations and absorbances depicted, the values of the times are not measured to decimal places. This is because all times were taken on the second, and if they were not, it is due to error; hence inserting any decimal places would be pointless and inaccurate. If decimal places were inserted they would be .00 for all times.
For all the experiments where the variable was the concentrations, as opposed to the temperature, the temperature was kept at a steady 18.00°C, although the temperature of the lab fluxuated somewhat, so the temperature throughout the experiment is unlikely to have remained constant.
On each graph I have drawn a tangent to the curve at a place I deem suitable, allowing me to draw a triangle and find the gradient of the line at that particular point, thus finding the initial rate of reaction. From this I can produce the following tables:
Potassium Permanganate rates-Graph 19
From these, I have been able to draw four rate graphs, plotting the concentration of the component or temperature against the initial rate of reaction, which I will now analyse.
Analysing each rate graph, the order of reaction for each component is clear. The straight, horizontal line on the oxalic acid rate graph shows that the order of reaction for oxalic acid is zero, meaning it will not be included in the rate equation. The rate graphs for potassium permanganate and sulphuric acid, however, both clearly give a positive linear correlation depicting first order for both hence the rate equation is as follows:
r=k[A][B]
By inserting the rate for each temperature into this equation and the concentrations of the reaction’s relevant components (sulphuric acid and potassium permanganate), I can rearrange the equation to find the rate constant for each temperature.
k=r/(AxB)
Using this new equation I can produce the following table:
As was previously mentioned in my plan and explained in more detail in the background chemistry presented, the Arrhenius equation will prove useful to my investigation, and it is at this particular point that I can take advantage of it. By taking the natural log of both sides of the equation, the following equation is produced:
lnk= lnA-(Ea/RT) or lnk=lnA-(Ea/R)x(1/T)
Where once again, k is the rate constant at temperature T, Ea is the activation enthalpy and R is the universal gas constant, a known value. This puts the equation in the form of a straight line graph (y=mx+c), however in this case it is closer to y=c-mx, with lnk as y, lnA as c, -(Ea/R) as m and (1/T) as x. By using the values in the table below, I am able to plot a graph of (1/t) against lnk.
The corresponding graph for this is number is 23.
The graph shows a clear negative correlation, with one point that does not fit the trend and can be counted as an anomaly, probably caused by inaccuracies in measurements at some point. The data is actually derived from the rate of reaction for the reaction at 303K, which is somehow less than the rate of the reaction at 298K, a clear mistake.
As is stated on the graph, the calculated gradient of the line is 6.28x10³ mol-1dm³s-1k-1.
This is the value of the activation enthalpy divided by the universal gas constant, therefore by multiplying this number by 8.314472, I can find the Ea:
6.28x10³x8.314472=52214.88416 Jmol-1
Or
+52.21 kJmol-1
As my calculations have shown, the activation enthalpy of my reaction is around 50kJ/mol. This brings to mind the previously discussed concept of how reactions with activation enthalpies of around this value will double in rate when the temperature of the system is increased by 10kelvin. Observing my temperature rate graph, we see that the rate does more than double as the temperature is increased by 10; at 20°C, the rate is 1.32x10^-6, and at 30°C, the rate is 1.24x10^-7 This may be due to the errors calculated or some other unknown contributing factor.
Evaluation
Considering the overall result of my investigation I would deem it a general success. I managed to derive a rate equation for my reaction, determining the order of reaction for each reactant, and find the activation enthalpy. The equipment I used was all suitable and effective, as was the method. Due to the sensible concentrations of chemicals selected and the precautions I took throughout, there were no accidents that risked the health or well being of me and my classmates.
My experiments provided me with suitable results that allowed me to produce graphs for analysis and deduce further information from these. The pattern of each graph was relatively clear, although there were a few results that seemed to be inaccurate and were disregarded as anomalies. These anomalies could have been caused by a number of things which need addressing. The method and equipment used were theoretically suitable, but not perfect. Where class B equipment was used, class A could have been, reducing errors. The environment in which I was working was also not particularly ideal. On different days the temperature within the room varied, as did the amount of sunlight, hence both the rate of reaction and absorbance readings would have been affected. The colorimeter was also rather temperamental, jumping up and down during experiments, although fortunately it did this throughout the investigation so all runs were affected and taking the average seemed to help this. After time in the sunlight, during use, the solutions of potassium permanganate may have been partially oxidised, reducing the actual concentration of the chemical. Due to a faulty motion sensor that controlled the lights within the room, the intensity of light was not constant.
If given the opportunity to change my investigation I would do so through the employment of the following things:
- Calculating the method of producing solutions with the least tolerances in order to reduce inaccuracies further down the line.
- Using class A containers, again to reduce inaccuracies in my solutions.
- Doing a greater number of experiments, using more concentrations and temperatures over a greater range to find results that are more representative of the reaction I am observing.
- Ensuring my permanganate solutions were always stored in the dark
- Create an environment in which the temperature and light levels were constant, so I new that there was only one variable and could confirm the changes in result were due to the changes I have made to the reactants or system, as opposed to something external.
- Use a more reliable colorimeter as to reduce the likelihood of incorrect readings.
It is also true that any mistakes or inaccuracies in my results may have been caused by qualitative errors, for instance, my judgment when producing solutions, or my reactions when taking recordings at certain times, which is particularly significant for the faster reactions. These errors can be reduced through care and effort, but as a human it is inevitable that these mistakes will be made to a certain extent. The unknown error of the original solutions is another cause of inaccuracies that could not be helped.
Regardless of any errors and mistakes made, I believe the majority of my results and analysis serve as support of the validity and general reliability of my finding. Although my investigation my suffer inaccuracies in specific aspects of its design and results, the conclusion drawn from it can be regarded as valid and justifiable.
