How does the mass of Manganese (IV) Oxide Catalyst (0.1000g, 0.2000g, 0.3000g, 0.4000g, 0.5000g) affect the natural log of the Arrhenius Constant of the decomposition of Hydrogen Peroxide (H2O2) by measuring the rate constant of the reaction with a pressure sensor at different temperatures and calculating it through the Arrhenius Equation

Throughout my experience as an IB Chemistry student, I learnt that catalysts increase the rate of a certain reaction. In our syllabus, investigating why the rate increases through the introduction of a catalyst has always been done by illustrating the fall in activation energy (E_a). Calculating the exact fall in E_a can be done by various different methods, one of which is through calculating the gradient of the Arrhenius Equation, a method that was taught to me during lessons. However, what piqued my interest was that regardless of the concentration or mass of the catalyst in experiments, the E_a would fall by a constant amount that is specific to the type of catalyst that was used. Therefore, I realised that an increase in rate was instead due to a different factor that was represented by the Arrhenius Constant.

Furthermore, I was also taught that there were multiple variants of catalysts. Namely, homogeneous and heterogeneous catalysts as well as biocatalysts. Out of which, heterogeneous catalysts typically decrease activation energy by the greatest extent and increase the rate of reaction for the decomposition of Hydrogen Peroxide (H₂O₂) by the most significant amount. This was what spurred me to use MnO₂ as the catalyst of choice. During my practical lessons, I largely worked with homogeneous catalysts and this provides me with a unique opportunity to use a different type.

This investigation utilizes varying masses of MnO₂ in the decomposition of H₂O₂. The rate at which H₂O₂ decomposes naturally is slow, meaning that over short periods of time, decomposition of it before it is used in the experiment can be considered to be negligible. It is also practical to investigate the effect of catalysts using these chemicals as both H₂O₂ and MnO₂ are readily available and are relatively safe to use in a school laboratory environment.

The journal article referenced is a study on the decomposition of H₂O₂ in the presence of a biocatalyst (Catalase) and seeks to determine the E_a of this reaction through utilization of the Arrhenius Equation. One value of this article is that the procedure that it uses is fairly similar to this investigation’s approach, with the notable exception of that article measuring rate through the time it takes for gas to evolve, while this investigation instead uses a pressure sensor to measure the initial rise in pressure. This investigation also cross-references the article’s Arrhenius Equation and graph, by checking that the graph obtained in this investigation also has a linear and downward trend as the temperature of the reaction vessel increases.

As mentioned previously, the Arrhenius Constant is not only scarcely taught in Chemistry Lessons, but is largely overlooked in most studies, and the lack of such studies is what this investigation aims to extend on.

Prior to measuring the rate of decomposition for H₂O₂, it is first necessary to comprehend the specific mechanics and chemistry behind how catalysts increase rate. Firstly, catalysts create an alternate energy pathway with a lower activation energy for the particles. This increases the frequency of effective collisions between the particles, thus increasing the rate of reaction. They increase the frequency of these effective collisions by acting as intermediaries which react with the reactants in the elementary step mechanisms but remain chemically unchanged at the end of the reaction. Below is the chemical equation for the decomposition of H₂O₂, followed by a possible mechanism for the decomposition in the presence of MnO₂ catalyst. A possible rate determining (slow) step of the mechanism will be determined from the investigation’s results.

Chemical Equation

2H₂O₂(aq) → 2H₂O(l) + O₂(g)

Possible 3-Step Mechanism

MnO₂(s) + H₂O₂(aq) + 2H⁺(aq) → Mn²⁺(aq) + 2H₂O(l) +O₂(g)

Mn²⁺(aq) + 2H₂O₂(aq) ⇌ Mn(OH)₂(aq) + 2H⁺

Mn(OH)₂(s) + H₂O₂(aq) → MnO₂(s) + 2H₂O(l)

As seen from figure 1, if the proposed 3-step mechanism is taken to be true, each intermediate step will consist of its own E_a, and the net activation energy required for these steps amount to significantly less than the uncatalyzed reaction. However, while E_a falls, it is to be noted that the presence of the catalyst does not affect the enthalpy change of the reaction, as seen in the diagram where ΔH remains constant between both reactions.

Figure 2 shows an example of the Maxwell-Boltzmann Curve when a catalyst is present and absent. As seen, when a catalyst is present and E_a is lowered, the number of particles in the system that possess the minimum amount of kinetic energy to undergo a successful collision is greater, increasing the frequency of effective collisions. Therefore, more particles will react per unit time, increasing the rate of reaction.

The Arrhenius Equation is used for calculating the rate constant of a given rate equation. In this case, Rate = k [H₂O₂] is the given equation, where it is known that this is a first order reaction. Here, the Arrhenius Equation expresses the rate constant as k = \(Ae ^{\frac{−Ea}{ RT}}\), where A = Arrhenius constant, R = 8.31JK^-1mol^-1 and T = Temperature. It is necessary to obtain the values of ln(k) so that a linear graph of ln(k) against \(\frac{1}{T}\) can be plotted, thus the equation is rewritten as ln(k) = \( (\frac{1 }{T} ) (\frac{ −Ea }{R} ) \)+ ln (A). By doing so, the natural log of the Arrhenius Constant ln(A) can be determined, as on a linear graph, ln(A) is the vertical intercept. By finding the experimentally determined E_a using the equation, it can be cross-referenced to theoretical estimates of the expected E_a to see the validity of the experiment. Besides the value of ln(k), the uncertainty of ln(k) is also required to plot error bars on the Arrhenius graph and find the uncertainty of the Arrhenius Constant.

A pressure sensor is used during each repetition of the experiment in order to find the initial increase in pressure. From this value, it can be inputted to the ideal gas formula to find the initial rate of reaction. Next, since the initial concentration of H₂O₂ is known, the rate constant is calculated, and by using the Arrhenius Equation, ln(A) can also be found. As the mass of MnO₂ catalyst increases, it is likely ln(A) will also increase. When ln(A) increases, the graph is shifted upwards, indicating that at any given temperature, the rate constant is larger and therefore the rate of reaction is faster. Furthermore, the constant is partly considered to measure the frequency of collisions between the reactant and the catalyst and having a larger mass of catalyst would logically increase such collisions.

The preliminary stages of my experiment underwent several modifications to measure the rate of decomposition of H₂O₂. A gas syringe was initially intended to measure the time taken for a certain volume of O₂ to be evolved from the reaction. This was similar to the set-up the reference article used, but after some testing, it was found to be impractical and difficult to work. This was due to my usage of a heterogeneous catalyst as compared to a biocatalyst that they used, resulting in the rate at which O₂ was produced to be too quick to measure adequately. Furthermore, using a gas syringe subjects the experiment to human error and bias since there will be some delay to when measuring the time taken. As a result, the approach to measuring rate was refined by using a pressure sensor instead of a gas syringe.

Another problem encountered was finding a set-up that would most accurately measure the initial rate. This problem was attributed to the fact that after pouring H₂O₂ into the reaction chamber that contains the catalyst, it takes about half a second to seal it with a cork (which had the pressure sensor attached to it). In that short amount of time, a fairly significant volume of O₂ would have escaped, greatly affecting the results that were attained. To combat these issues, a modified set-up which is shown in figure 3 below was adopted which ensured no O₂ would escape when the decomposition first occurs.

Independent Variable

The independent variable as mentioned, will be the mass of MnO₂ that is present during the decomposition of H₂O₂. The masses that are used in each trial are 0.1000g, 0.2000g, 0.3000g, 0.4000g and 0.5000g. In order to manipulate the mass, MnO₂ in powdered form is measured using a mass balance, which is relatively accurate as it has an uncertainty of ±0.0010g.

Furthermore, for each mass of MnO₂, the temperature of the reaction chamber is set to 20.0°C, 30.0°C, 40.0°C, 50.0°C and 60.0°C for 1 trial. This is necessary in order to plot the graph for the Arrhenius Equation, which is used to find the change in the Arrhenius Constant. It is to be noted that although this variable is manipulated, it is not the independent variable. To change the temperature, the entire reaction chamber (a conical flask of 250.0cm³ volume) is placed inside a water bath of desired temperature for at least 30 minutes. A thermometer is present in the water bath at all times in order to ensure the temperature remains constant at all times.

Dependent Variable

The dependent variable for this investigation is the initial rate of reaction for the decomposition of H₂O₂. It is relatively easy to measure as O₂ is produced, which affects the pressure of a reaction chamber, and thus a pressure sensor is used to measure the initial change in pressure. In order to achieve a result as accurate as possible, the pressure sensor is also connected to a phone application known as SPARKvue, which is able to graph the change in pressure in increments of 0.05s. As already mentioned, this method is favourable a gas syringe would be filled too quickly. Furthermore, a gas syringe and timer are also subject to human error, this method thereby minimizes such issues.

Control Variables

Controlled variables include the volume and concentration of the H₂O₂ solution, as well as the volume of the reaction chamber. It is necessary to ensure that the concentration of H₂O₂ is consistent throughout all trials as its concentration affects rate and will be required for calculating the rate constant. This is done by taking H₂O₂ of a known concentration from a stock solution. Otherwise, replicates that use the same mass of MnO₂ may have vastly differing initial rates, which will reduce the accuracy of the experiment.

The volume of the reaction chamber must remain constant as the pressure change is dependent on the volume. To do this, all reactions are done in a conical flask that is 250.0cm³ in volume. If not done, the initial volume of O₂ gas produced will have different readings for the initial change in pressure, even if an equal amount of O₂ gas is produced between replicates.

Although volume of H₂O₂ does not affect the rate of reaction, it decreases the volume of the reaction chamber since an increase in volume of the solution results in a decrease in volume for the rest of the reaction chamber. A constant 10cm³ of H₂O₂ solution is thereby measured and injected into the flask by a syringe when the reaction occurs. If not done, this will face the same issue as not keeping the volume of the reaction chamber constant.

Preparation of 0.1765M H₂O₂ Stock Solution

• Using a 50.0cm³ pipette, add 50.0cm³ (±0.1cm³ ) of 6% H₂O₂ (1.765M) solution into the 500.0cm³ volumetric flask
• Fill the 500.0cm³ (±0.5cm³ ) volumetric flask up to the marking with distilled water
• Mix well by shaking
• Place the flask into the cooler

Experimental Procedure to Find Initial Change in Pressure

• Using a mass balance, measure 0.1000g (±0.0010g) of MnO₂ powder
• Pour the MnO₂ powder into the 250.0cm³ conical flask
• Pipette 10.00cm³ (±0.02cm³ ) of H₂O₂ from the stock solution into a test tube and seal with a rubber cork
• Set the temperature of the water bath to be 20.0°C (±0.1°C) (293.15K) and monitor temperature with a thermometer at all times
• Place both the conical flask and sealed test tube into the water bath
• Use the stopwatch to time for 30 minutes to pass
• Using a syringe, suck the H₂O₂ solution from the test tube
• Attach test tube and pressure sensor to a rubber cork (With 2 holes poked through)
• Using the rubber cork, seal the conical flask
• Place plasticine around the edges of the cork and the syringe (Refer to figure 3 for final set-up)
• Push the H₂O₂ solution from the syringe into the conical flask and record the change in pressure (± 2.0kPa) using the pressure sensor and SPARKvue application
• Repeat steps 5-15 to obtain 3 replicates and readings
• Repeat steps 5-16, setting the temperature of the water bath to be 30.0°C, 40.0°C, 50.0°C and 60.0°C (303.15K, 313.15K, 323.15K, 333.15K) on subsequent attempts
• Repeat steps 5-17, using 0.2000g, 0.3000g, 0.4000g and 0.5000g of MnO₂ on the subsequent trials

Qualitative Observations

When the H₂O₂ is inserted into the reaction chamber, there will be a change in the colour of the solution from colourless to grey. This is due to MnO₂ now being present in the solution, but this is not of any significance since it is not indicative of a start or end point of the experiment. A change in the pressure of the reaction chamber is difficult to observe since O₂ gas is both odourless and colourless and H₂O that is produced as a product is also colourless.

Bubbles are produced when the reaction occurs but taking note of this is obsolete since the rate of reaction is already calculated by measuring the pressure change using the pressure sensor.

This calculation is done to determine the rate constant k for the decomposition of H₂O₂ at 20.0°C and in the presence of 0.1000g MnO₂ catalyst. All subsequent calculations are done in similar fashion and the final processed results are compiled in the next section.

Arrhenius Graph with Error Bars and Maximum/Minimum Slopes

Using the replicate for 0.1000g of MnO₂ as an example, its Arrhenius Graph can be plotted, along with its error bars and maximum/minimum slopes. The data for which is taken from the tables in section 3.2.

From here, the natural log of the Arrhenius Constant (ln(A)) can be easily determined as it is the constant of the function. Thus, when (1 / T) = 0, ln(A) can be found, which is seen to be 25.94. Similarly, the uncertainty of ln(A) is determined by considering the ln(A) of both the maximum and minimum slopes. Below are the calculations to find the uncertainty of ln(A).

Absolute Uncertainty = \(\frac{±(28.074-24.412)}{2}\) = ±1.9 (to 2 s. f)

Table of ln(A) and Absolute Uncertainty of ln(A) for Each Mass of MnO₂

Following a similar process as the one done in section 3.3.1, ln(A) and its absolute uncertainty can be found for each mass of MnO₂.

The R² value from the graph under section 3.3.1 is very near 1, indicating that there is negligible random error and thus high precision. However, the error bars for the final processed data is fairly significant, ranging from ±1.4 to ±1.9, meaning that the results may not be accurate. From the results obtained, it can be observed that there is a slight positive and relatively linear correlation between the mass of MnO₂ and the value of ln(A). However, the increase in the constant is seen to be largely marginal, with the difference between the most and least mass of catalyst only being 1.6. This can be attributed to the nature of the function, which is logarithmic. ln(A) only increased slightly as this small increase means the rate constant does not increase much either when more mass of MnO₂ is used. Hence, this agrees with the theoretical understanding of catalysts, as a very small amount is typically needed to increase rate significantly.

The data collected can be cross-referenced to verify its reliability. Firstly, the reference article by Aradhya Bansal agrees with the collected data since the Arrhenius graphs of this experiment and the article yield linear plot-points and is downward sloping. Secondly, by checking the gradients obtained from the various Arrhenius graphs, an E_a between 37kJmol^-1 and 39kJmol^-1 is calculated. This deviates slightly from literary data, which states that the E_a of the decomposition is 35.4kJmol^-1 . There is also the presence of some systematic error as all E_a recorded is higher than the theoretical one, compounding onto the accuracy issue. Therefore, it can be concluded that the collected data is relatively reliable, although not exact.

MnO₂(s) + H₂O₂(aq) + 2H⁺(aq) → Mn²⁺(aq) + 2H₂O(l) +O₂(g) —

Mn²⁺(aq) + 2H₂O₂(aq) ⇌ Mn(OH)₂(aq) + 2H⁺

MnO₂ does not appear in the rate expression, it affects rate mathematically through altering ln(A), and the aforementioned trend states that ln(A) is directly proportional to the mass of MnO₂. However, the increase in ln(A) may be chemically explained from how an increased mass of MnO₂ affects the first elementary step of the reaction. Assuming that the above mechanism holds true, increasing the mass of MnO₂ would increase the frequency of Mn²⁺ ions produced, shifting the equilibrium of the second elementary step to the right. This has the effect of producing more H⁺ ions, which in turn enables the first step to occur more readily. Increasing MnO₂ does not increase rate significantly because in an aqueous solution of H₂O₂, H⁺ ions are only sparingly available from the self-ionisation of water as well as from the partial dissociation of the 0.1765M H₂O₂ solution, largely inhibiting the rate at which the first step can occur unless more H+ ions are introduced. From this, it can be inferred that the first step may be the rate determining step.

Furthermore, the data also seems to suggest that relatively small masses of catalysts would suffice, since when comparing the increase in rate due to mass and temperature, temperature seems to have a more significant role. The reason for this may also tie back to the fact that in the first elementary step, H⁺ ions are in low concentration, and increasing the mass of MnO₂ may not significantly increase the rate since H⁺ ions are the limiting reagent.

In conclusion, the results of the experiment is precise due to the low random error, but is not entirely accurate as there is a rather significant systematic error in both the final data and when cross-referencing the E_a. After the collection and interpretation of data, the direct relationship between mass and ln(A) was better understood. The gradual increase in ln(A) relative to mass shows how while increasing the amount of catalyst present has an effect in increasing rate, this increase diminishes as mass increases. One possible reason for this was found after analyzing a possible reaction mechanism, where it was found that MnO₂ may have been in large excess, thereby not having much effect on increasing the rate and thus ln(A). Therefore, this investigation has not only demonstrated how MnO₂ catalyst affects ln(A) but has also displayed the extent to which MnO₂ alters it.

One strength is that the procedure accounts for the change in temperature during different replicates by not only heating the reaction chamber to the desired temperature, but also heating the H₂O₂ solution separately. Since the decomposition of H₂O₂ in the presence on any catalyst occurs readily, if this step is not done, the H₂O₂ solution would not be the same temperature as the reaction chamber as heat would not have sufficient time to be transferred. Hence, this ensures that the horizontal values obtained on the Arrhenius graph accurately correspond to the experimental data.

Another strength of the procedure is the multiple replicates that were taken for each mass and each temperature, which greatly reduces the chance of any outliers, consequently minimizing any random error. This is evident from the R² value of the various Arrhenius graphs being close to 1, indicating a very strong linear correlation. Hence, the use of replicates helps in raising the precision of the experiment.

There are several limitations that this experiment has, which may have affected the results of the experiment. Firstly, the set-up of a syringe which contains the H₂O₂ solution is flawed in the sense that when the solution is inserted into the reaction chamber, there is a time window of around 0.1s where the full volume of 10cm³ solution has not entered the reaction chamber. This would mean that the initial change in pressure at t = 0s will not be the highest, which goes against the theoretical understanding of rate, giving rise to systematic error. In order to attempt to rectify this, the initial change in pressure is taken to be at the point where the gradient is the largest, although this is still limited as some of the H₂O₂ would have already decomposed and the initial concentration would not be 0.1765M. Since the concentration is no longer 0.1765M, the calculation of rate constant k would not be correct, skewing the results of the experiment. This could be the reason as to why the E_a found from the Arrhenius graphs are consistently higher throughout all masses.

Secondly, while the preparation of the stock solution of H₂O₂ involves storing it in a chilled environment to greatly slow down the natural rate of decomposition, decomposition will still occur when the solution is being heated up to the appropriate temperature in the water bath. Similar to the previous point, this has the effect of affecting the concentration of the solution, which may skew the results of the experiment as well.

Thirdly, the particle size of MnO₂ is inconsistent even though it is meant to be in powdered form. This is due to the ionic structure of MnO₂ which may result in small chunks of the solid being present. Consequently, the inconsistency will affect the surface area to volume ratio of the catalyst even for replicates which use the same mass of MnO₂, which would have likely affected the initial change in pressure. This problem was partly accounted for by repeating multiple trials for each mass and taking its average, as it tries to counteract the random error.

Lastly, the pressure sensor that was used may suffer time lags between recording and feeding the data to the application, leading to systemic error. This is due to the nature of the sensor, which sends the data to the app through Bluetooth.

One possible improvement to minimize the effects of the first limitation is by creating a mechanism that would release MnO₂ into the conical flask and have the H₂O₂ solution present in the reaction chamber itself instead. Doing this helps prevent some of the solution from decomposing before the full amount has been inserted into the reaction chamber, ensuring that the initial concentration remains consistent at 0.1765M as far as possible.

The second limitation could be subverted by heating up two samples of H₂O₂ in separate test tubes for the same amount of time. Afterwards, the second sample undergoes a redox titration against an oxidizing agent such as KMnO₄ in order to find the mols present after heating. From this, a new initial concentration of H₂O₂ can be determined for each temperature it is heated to.

To further account for the third limitation, the MnO₂ can be further pulverized by using a mortar and pestle before pouring it into the conical flask.

As mentioned during the interpretation of the possible rate mechanism of the reaction, H⁺ ions were likely the limiting reagent for the initial first intermediate step. This could open the possibility on doing an experiment about confirming if the proposed reaction mechanism is true. The set-up would be similar, but the reaction chamber would now have a solution containing varying concentrations H⁺ ions alongside the fixed mass of catalyst. A pressure sensor would be used to find the initial increase in pressure which can be used to find the initial rate. A positive trend between the concentration of H⁺ ions and the rate of reaction would indicate that the aforementioned mechanism is true, and the extent to which it increases the rate can be explored as well. This extension may reveal a possible method to increase the effectiveness of a catalyst other than just increasing its mass, since its effectiveness is only marginally increased when a greater mass is used, as shown through finding ln(A) in this report’s investigation.

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