Notes

Based on the graphs and experiments that were conducted, it is reasonable to conclude that all of the trials went as expected according to the class averages of all trials. The trial with one the highest productions of hydrogen gas was the increased surface area experimental condition, which had a final amount, after 300 seconds, of 3.82 moles. This trial can be explained by the idea that increasing the surface area of a substance will result in it being able to collide more and produce effective reactions as it covers a greater distance, as defined by the concept of collision theory. Rivaling the increased surface area trial is the trial with the agitation factor implemented. After 300 seconds, this trial produced around 3.68 moles of Hydrogen gas. However, the trial had a class average of 3.90 moles at 280 seconds. The reason for this could be because there is only one trial that reached 300 seconds and the rest of the trials had filled the graduated cylinder in its entirety before 280 seconds, telling us that this is a possible source of error as our graduated cylinders were not big enough to conduct the specific experiment and that it most likely, when given enough space, would have produced more moles of hydrogen gas than an increased surface area. This aligns with the notion of collision theory as agitating/stirring the experiment allowed for the particles to be dissolved quicker than initially, resulting in more particles colliding with each other and an increase in reaction as compared to the controls. The trial with the lowest amount of produced moles of hydrogen gas was the trial that focused on reducing the temperature of the experiment with a total of 2.11 moles of Hydrogen gas produced. This aligns with collision theory as because there was a decrease in temperature and since temperature is the average measure of kinetic energy, this means that there was a reduction in kinetic energy. Since there was a reduction in this amount, it meant that the particles were moving slower than before, resulting in less collisions and a decrease in reaction rate as compared to the controls. Furthermore, the trial which incorporated a reduction in concentration from a 0.6 molar solvent to a 0.3 molar solvent resulted in a decrease in reaction rate as compared to the controls. This makes sense because there was a decreased amount of particles in the solvent that could react with the solute, resulting in a very high decrease at 1.02 moles of Hydrogen gas produced. Finally, the class average control in this experiment taken from 2 different controls was, at 300 seconds, around 3.15 moles. This was very similar with control 1 and 2, with only a 0.08 difference in moles between the two.
When we turn to the calculation aspect of this lab, we first started by finding the conversion factor between the amount of moles given for however many mL of H2 were present by using the ideal gas law. This came out to be 4.09Vx10-5 , this was the basis of getting moles for the entire experiment. After this, we found our individual reaction rate as well as the class average reaction rate and compared them using percent error, which we did for every single trial. Firstly, for trial number 1, our data gave us a reaction rate of 8.47x10-6 mol/s while the class average was 1.08x10-5 mol/s. Trial number two gave us a reaction rate of 1.36x10-5 mol/s, compared to the class average of 1.32x10-5 mol/s, we got a percent error of 3%. On the third trial, we got a reaction rate of 6.73x10-6 mol/s and the class got a reaction rate of 7.03x10-6 mol/s, this ended up giving us a percent error of 4.5%. The fourth trial gave our group a reaction rate of 2.86x10-6 mol/s, compared to the class average, which was 3.40x10-6 mol/s, the percent error ended up being 16%. For trial 5, our data gave us a reaction rate of 9.9x10-6 mol/s and the class average came out to 1.03x10-5 mol/s. This then subsequently gave us a percent error of 3.9%. Finally, for trial 6 we got a reaction rate of 1.25x10-5 mol/s and the class got a reaction rate of 1.27x10-5 mol/s, this resulted in a percent error of 2%.
Our assumptions concerning how each trial would rank on reaction rate were correct. Trials that had conditions that collision theory states would increase the reaction rate were fast, such as trial 2 and 6, which were agitation and increased surface area. On the other hand, we had assumed trials 3 and 4 were going to be much slower because of the lowered temperature and decreased concentration, things both stated in collision theory to affect reaction rate, in which we were correct. Finally, the controls were both in the middle of these 4 trials, which we had assumed and which also makes sense due to the fact that nothing is changing for an increase or decrease in reaction rate.
After this, we compared both of the controls to each other and found the average of them both for use later in the lab. When comparing them, we found that they had a 5% error between them, which can be explained by outside factors affecting the experiment later in period, such as the volumetric flask not being a constant temperature for both control trials. Next, we averaged both reaction rates to get the control average, which was 1.06x10-5 mol/s. We then compared control one to the control average and found that they had a 2% error margin.
The next steps we took were finding the reaction rates (mol/s) for the rest of the trials and attributing them a factor of change compared to the control average. The first trial got a factor of change of 1.02, indicating a 2% increase from the control average. Next, the second trial got a factor of change of 1.25, which is a 25% increase, we can then conclude that agitating the experiment increased its reaction rate by 25%. For the third trial, we found that it had a factor of change of 0.663, which means that the decrease in temperature caused an approximately 34% decrease in reaction rate. Similarly, the fourth trial, got a factor of change of 0.321, meaning it was a 68% decrease from the control average. The fifth trial gave us a factor of change of 0.972 , a 3% decrease of reaction rate. Finally, the last trial gave us a factor of change of 1.20, which is a 20% increase of reaction rate when the surface area was increased.
Now, we move on to the rate law calculations, we used the rate law formula, the ideal gas law as well as the secant method to determine the predicted and observed instantaneous reaction rate of the control average and trial 4 (lower concentration) at 20s and 200s. To do this, we had to find the instantaneous reaction rate (mol/l*s) of the values below and above 20 and 200s. Once we did this, we were able to use the secant method to find the observed instantaneous reaction rate of 20 and 200 seconds. We found that for trial 4 we got an observed reaction rate of 4.8x10-4 mol/L*s at 20 seconds and 2.4x10-4 mol/L*s at 200s. For the control average section, we got an observed reaction rate of 2.02x10-3 mol/L*s at 20 seconds and 7.00x10-4 mol/L*s at 200 seconds. Considering we were to find a concentration with trial 4 as well as the control average, we used a slightly different procedure for both as the molarity of the hydrochloric acid was different (0.30M and 0.60M). For trial 4, we would minus the reaction rate of 20s and 200s, which was 7.8x10-3 mol/L and 0.0826 mol/L by the initial concentration of 0.30 mol/L to give us the real concentration of 0.29 mol/L and 0.22 mol/L respectively. We did the same thing for the control average section, only changing the initial concentration to 0.60 mol/L, this gave us a concentration of 0.56 mol/L at 20s and 0.38 mol/L at 200s. Using this information, we were able to find the K of both sections by using the observed instantaneous reaction rate at 20s. Using this K and the concentration calculated, we were able to find each predicted instantaneous reaction rate. For trial 4, this was 4.8x10-4 mol/L*s at 20 seconds and 2.8x10-4 mol/L*s at 200 seconds. This resulted in a percent error of 0% and 0.1x102% respectively. For the control average, we got a predicted instantaneous reaction rate of 2.0x10-3 mol/L*s at 20 seconds (the calculation picture forgot the x10-3) and 9.2x10-4 at 200 seconds. This resulted, due to significant figures, with the percent errors of 0% and 24%.
We realize that both 20 second reaction rates had a 0% reaction rate and both 200 seconds had above 10% error. We believe that this is due to the fact that we found the k with the observed instantaneous reaction rate at 20 seconds for each, which is susceptible to human error. If we had been given a K value, this would not have been an issue.
When considering the instantaneous reaction rates at 20 seconds and 200 seconds for both sections, we found that it made sense that each 20 second instantaneous reaction rate was faster than its counterpart at 200 seconds. Unless an experiment is interfered with, the instantaneous reaction rate will usually decrease over the course of time due to the fact that lots of particles have already reacted with each other.

According to the observed graphs from the experimental results, we observed that the data collected resulted with something we expected according to the class averages and our knowledge of collision theory and reaction rate. Starting with a control trial, we used the data collected to compare the results with the trials which had specific experiment conditions which varied results. The first control trial averaged 78.9 mL of hydrogen after 300s. The second control trial averaged 75.2 mL, averaging 77.1 mL from both trials. Both control groups had similar results, with only a small difference of 1.8 mL or 0.08 mol in between them.

To begin, the trial that incorporated agitation produced an Class average of approximately 96.9mL of hydrogen gas after 300 seconds. This aligns with collision theory, as agitation facilitates quicker dissolution of particles due to the movement of the flask during the experiment, leading to increased collisions between the particles and reaction rates compared to the control trial.

Moving on, the trial that focused on reducing the temperature of the experiment resulted in a lower production of hydrogen gas, with only a class average of 51.5 ml of hydrogen produced. This outcome aligns with collision theory as well, as the reduction in temperature decreases the average kinetic energy of particles, leading to slower movement and fewer collisions, thus reducing the reaction rate which caused less production of hydrogen in the experiment.

The trial that produced the one of the highest amounts of hydrogen gas was the one where we increased the surface area of the magnesium by converting it into powder, yielding a final class average of 93.4 mL of hydrogen after 300 seconds. However, this result does face some inconsistencies due to the fact that many of the results for the groups in the class reached 100mL of hydrogen produced before the 300 second mark. This was a problem since the graduated cylinder only read to that amount which caused the data in the table to be not filled out accurately, which can explain possible percent errors. Despite this fact, we can explain the high results since enhancing the surface area allowed for more effective reactions due to increased collision opportunities among particles when turning the magnesium into powder which again reinforces the concept of collision theory.

On the other hand, the trial involving a reduction in concentration from a 0.6 molar HCl to a 0.3 molar solvent resulted in a decreased reaction rate compared to the controls, producing only a class average of 24.9 mL of hydrogen gas. This can be logically explained by the reduced number of particles available for reaction due to the decreased concentration of the solute in the solvent. Reducing the concentration of HCl caused fewer HCl molecules to be available to react in the solution which is why the rate the hydrogen gas is produced decreased because there are fewer collisions between HCl molecules and other reactants. Once again this aligns with the principles of collision theory.

Group Data vs Class Data:
When it comes to comparing the data we collected with the Class average data and calculated the average reaction rate and then calculated percent error. For the first control #1 trial, our average reaction rate was
1.06x10-5 mol/s while the class averaged 1.08x10-5 mol/s being only 0.9% error. For the agitation trial, we received 1.32x10-5 mol/s and the same was for the class average which gave us a 0% error. The reduced concentration trial we got 3.97x10-6 mol/s and the class average was 3.40x10-6 mol/s resulting in a percent error of 17%. This can possibly be explained by the potential subtle differences in concentration by small decimals which can impact the results and cause them to vary. For the temperate reduction trial we got 6.13x10-6 mol/s and the class got 7.03x10-6 mol/s with a percent error of 13%. This could be explained by the small differences in temperatures for individual groups experiments which were done at different times with different conditions (ex. room temperature). For our second control trial, we got 1.05x10-5 mol/s while the class averaged 1.03x10-5 mol/s being only 2% error. For the last trial with increased surface area, we got 1.36x10-5 mol/s while the class averaged 1.27x10-5 mol/s being only 7% error. This can be explained by possible differences in measuring digital scales measuring the Mg that could have slight differences which would impact our results as well as human errors since there were multiple data sets being used.
Once again, according to factors that influence reaction rate and collision theory, our results made sense when there was an increase of reaction rate compared to the control when agitated the flask during the experiment and increasing the surface area of the solvent which created more opportunities for particles to react and faster. The same goes for how the reaction rate decreased when we decrease the temperature and the concentration of HCL for the experiment which brought less collisions between the particles since they were slower and less concentrated.

For the calculations, a conversion factor was calculated using PV=nRT in order to calculate how many moles there were from the amount of hydrogen produced in mL, which resulted in 4.09x10-5 V. This was then used to calculate the average reaction rate per trial for the class data average and the individual group data.

When comparing the reaction rate average for the 2 controls trials, it resulted in 1.06x10-5 mol/s and the percent error was only 2%. This can be explained by the subtle changes in temperature and pressure of the environment since both trials were conducted at different times in a room filled with multiple chemical experiments occurring.
When it comes to the factor of change between the average reaction rate of the trials and the control average data of the class after 300s, we concluded many interesting results. Agitation trial had the highest factor of change being 1.25 while the reduced concentration had 0.312. The other trial which had an increase from the control average was the surface area trial having a 20% increase. The temperature reduction trial had a factor of change of 0.663 being a decrease from the control. These numbers once again can be explained by the concept of collision theory and factors that affect reaction rate (previously explained).

Another crucial calculation we made was the concentration of control 1 and 2 and the lowered concentration trial using moles after 300s based on class average data and the 20mL of HCL used per trial. They resulted with 0.323mol/L for control #1, 0.315 mol/L for control #2 and 0.102 mol/L for the reduced concentration. This showed us how changes in concentration can greatly affect how fast reactions happen.

Rate Law Mathematical predictions
Using the mathematical equations and calculations using rate law, the conversion factor with the ideal gas law, as well as the secant method, we were able to calculate a measured and predicted value for instantaneous reaction rate. This was done for the control average and the lower concentration trial which had a HCL concentration of 0.60M and 0.30M, at 20s and 200s. By using instantaneous reaction results from the secant method for values 20s and 200s, we used rate law to solve for a K value at 20s and made predictions using this value for 200s and 20s, this was done for each the low concentration and control average calculation. For the 20s of the control average, we got 2.02x10-3 for measured and 2.0x10-3 for the predicted value resulting in a percent error of 0. For 200s for this, we got 7.00x10-4 for the measured value and 9.2x10-4 for the expected value with a high % error of 24. For the lowered concentration trial, we got 4.8x10-4 for both 20s observed and predicted resulting in a percent error of 0. For 200s, we got 2.4x10-4 observed and 2.8x10-4 predicted with percent error of 1 x 10 %. Based on the graph, we can see that the predictions were fairly similar to observed for 20s trials with being around 0% error, but for 200s the results had a higher source of error due to the fact the K was solved using human measured data which can include errors. Some things that we observed from this is that the reaction rate was slower at 200s than 20s because as the reaction progresses, reactant concentrations decrease, leading to fewer collisions and a slower rate.

One last thing to note is that some of the high percent errors can be explained by the different times that the individual groups did the lab experiments which could have most likely had different conditions of pressure and temperature which could have impacted the results. Similarly, the slight differences in human measures when looking at the graduated cylinder can impact results. A last thing that can influence the results would be possible not 100% efficient/high quality equipment which would obviously help with the experimentation data.