Before I changed my method I was trying to measure initial rate. The reaction slows down with time, so to get an accurate value for the initial rate, the reaction should be measured for as short a time as possible, allowing for an accurate time and volume measurement. I should have been measuring only the first 20% of the reaction, say. Since I was using excess magnesium and 20cm3 1.00 mol dm-3 HCl, the total quantity of H2 gas produced during the reaction was 0.01 moles, which has a volume of 240cm3. I was collecting up to 80 cm3 hydrogen, which means I was collecting more than 20% of the hydrogen produced in the reaction: this can not be assumed to be an accurate measure of the initial rate.
This problem is solved in the improved, continuous method because I am collecting all the gas except for the part lost in the first few seconds. From the gas volume, we can calculate the concentration of reactants remaining at each time interval. The amount of gas lost is the difference between the volume of hydrogen produced for the known quantity of reactants, and the final amount of hydrogen collected in the reaction.
I measured the total gas collected as the reaction progressed at the following times after putting a stopper on the boiling tube: 0, 5, 10, 15, 20, 25, 30, 35, 40, 50, 60, 70, 80, 90 and 600 seconds. As 15 readings in total were taken for each test, I was able to get a good curve because each measurement is an accurate average for the mid point of its range. After 40 seconds, measurements were made at 10 second intervals, rather than 5 seconds, because by this time, the rate of reaction was slow enough so that there was little change in the volume of gas collected, so a 10 second average would be sufficiently accurate. A reading after 600 seconds was taken, because by this amount of time a negligible amount of gas was being evolved and the reaction had almost come to a stop. The experiment was carried out 5 times.
Quantities
It is important that the magnesium metal I am using is in excess during the reaction.
In 0.30g of magnesium there are 0.3/24 = 0.0125 moles. At the highest concentration of HCl(aq) that was used in the experiment, 0.20 mol dm-3, there are 0.2×0.025 = 0.005 moles of HCl(aq). 2 moles of HCl(aq) react with 1 mole of magnesium, so 0.025 moles of HCl are needed for 0.0125 moles of magnesium. I am using 0.005 moles of HCl, so the magnesium is 0.025/0.005 = 5 times in excess.
This shows that at all times the magnesium is in a large excess.
ObservationsWhen the magnesium was added to the hydrochloric acid in the boiling tube, the reaction mixture started to fizz: bubbles of a colourless, odourless gas were being produced on the magnesium grains. The boiling tube warmed up during the experiment indicating that the reaction was exothermic.
Results
The results are tabulated below.
The results show that as the reaction proceeds, the amount of gas produced decreases during successive time intervals. Therefore the rate of reaction decreases.
The concentration of HCl can be determined from the volume of H2 according to:
[HCl] = 0.20 mol dm-3 – 2×moles of hydrogen produced / 0.025dm3
This allows me to plot a graph of time against concentration using the mean measurements.
The gradient on this time vs. concentration graph equals minus the rate of reaction. This is further corrected for the initial gas lost below.
The total gas produced in this reaction can be worked out theoretically. The magnesium is in excess so the moles of HCl consumed controls the moles of gas produced.
2HCl(aq) + Mg(s) → MgCl2(aq) + H2(g)
25cm3 of 0.20 Molar HCl was used in all the experiments, which is (0.025×0.2) = 0.005 moles HCl. Therefore 0.0025 moles hydrogen gas should have been produced. This is (0.0025×24000) = 60cm3 of gas. The mean amount of gas produced in my 5 tests after 600 was 57.6cm3, so an upper limit of 2.4cm3 was lost at the beginning of my experiments.
We can use this value to correct all of my results because this is an average volume that is missing from all of them. This would shift all of the points on my graph down so that the curve tends towards a concentration of zero, except the point at zero time. That is how the curve should be because there is no clear end point to this reaction, since the reaction rate is always decreasing but never reaches zero. The corrected graph and table are shown below.
The rate is calculated by dividing each change in [HCl] by the time interval.
To determine the order of reaction, the half-life on the time vs. concentration graph can be measured. The half-life is the time taken for the concentration to half. If consecutive half-lives are constant, then the reaction is of 1st order. If the consecutive half-lives are increasing, then the reaction is 2nd order or greater. As shown on the graph of time against concentration, the consecutive half-lives (t1=15s, t2=29s, t3=54s) for my experiment are increasing. Therefore I must use a different method for determining the order of reaction.
Logarithms involving concentration and reaction rate can be used to produce a graph from which we can work out the order and rate constant of reaction.
Rate = k[HCl]n ,
where k is the rate constant, and n is the order of the reaction. If we take the logarithm of both sides of this equation then we get:
log rate = n log[HCl] + log k .
In the graph below of log[HCl] vs. log(rate), the gradient of the line produced will be the order of the reaction, and the y-intercept will be the logarithm of the rate constant.
From this graph the order of the reaction is 1.98 and the rate constant is 100.426 = 2.67 mol-1 dm3 s.
1.98 is sufficiently close to 2 for me to draw the conclusion that the reaction is of 2nd order with respect to concentration of HCl, since there are significant sources of error in my experiment.
Sources of error
The reaction between HCl and magnesium is exothermic. This means that as the reaction proceeds, heat is produced. Temperature is a factor affecting the rate of reaction: the rate is faster as temperature increases. This means that despite my efforts to make the experiment a fair test, concentration was not the only factor influencing my results, there was also the increasing temperature of the reaction mixture. I repeated the experiment twice more to measure the temperature increase. The mixture went from 23°C to 30°C and 31°C on each test. From the results of the second part of this investigation, we can estimate the error as a factor of the rate.
Using the Arrhenius equation, k = Ae-Ea/RT. k is the rate constant of the reaction and R is the gas constant. The activation energy for this reaction is 18kJ mol-1 as calculated on page 16. We have two temperature values, 296K and 303.5K, and we can calculate the ratio of the corresponding rate constants.
K1/K2 = e-Ea/R ( 1/T1 – 1/T2)
K1/K2 = 1.18
This means there is a increase in rate by a factor of 1.18 during the reaction at room temperature. The temperature increases continuously as the reaction proceeds, so on the graph of log(rate) vs. log [HCl] , the line will be unaffected at the maximum [HCl], but will be shifted by around log 1.18 at minimum [HCl]. This would translate to an error in the gradient of the line, which is the order of the reaction, of (log 1.18)/0.8 ≈ 0.1.
The time taken for me to attach the bung to the boiling tube after the magnesium powder was introduced to the hydrochloric acid was not constant. In each reaction it varied, and therefore when I started measuring the gas produced in each individual experiment, the starting concentration was not exactly the same as it was for the others. This was compensated for by taking the measurement at 600 seconds to represent the completed reaction.
I was taking measurements of gas volume from the small graduations on the scale of the inverted measuring cylinder while the amount of gas was constantly increasing. Therefore, there was certainly some human error involved. My readings were always being rounded to the nearest cm3, so there could be an error of ± 0.5cm3. Besides this, I must take into account the fact that I could not have always been taking the readings at the exact time I should have. There was always some unknown time gap between the time for the measurement on the stopwatch, and the time when I actually took the reading. I estimate that at any reading there could have been a 1 second error.
Mechanism
Since I have shown the reaction to be of second order, the rate equation with respect to HCl(aq) concentration is:
Rate = 2.67×[HCl(aq)]2
A possible pathway for the reaction is proposed on the Nuffield Advancing Chemistry website. For the reaction to occur, first the hydrogen ions need to reach the surface of the magnesium solid. If the kinetic energy of the particles is great enough, an electron will leave the magnesium atom and reduce H+ to H. Two hydrogen atoms will combine to form H2 gas. Then the oxidised magnesium ion will leave the surface of the piece of magnesium metal.
If my results are correct and the reaction is second order with respect to HCl, the rate limiting step must be one in which two hydrogen ions/atoms are involved. The only candidate for this in the pathway above is the joining of two hydrogen atoms. However I believe that the first part of the reaction is likely to be the slowest step in the reaction because it requires the hydrogen ion to randomly diffuse to the surface of the magnesium metal. This would only produce a first order dependence on concentration since only one hydrogen ion is involved. The pathway is therefore not confirmed by my results.
Limitations
If I had time I would have liked to use a gas syringe to collect the hydrogen from the boiling tube. This would eliminate the need to place in end of the delivery tube in the gas collector, so there would be no gas lost in any of the experiments. In this way I could obtain a much more accurate set of results, and therefore a more accurate figure for the order of reaction and rate constant.
The temperature of the reaction mixture rose by 7.5°C during the reaction. Because increasing temperature raises the rate of reaction, this affected my results. The increase in temperature could be reduced by having the boiling tube containing the reaction mixture in a water bath maintained at room temperature. This would help to dissipate the heat created by the exothermic reaction, so that it has less of an effect on the rate of reaction that I was measuring.
As the reaction progresses, the volume of the grains of magnesium decreases. This also decreases the surface area for reaction on which the rate of reaction depends, so this causes an inaccuracy in my results. I would have been able to obtain a more accurate set of results if I could use magnesium powder with larger grains (greater volume:surface ratio and less affected by the experiment). Furthermore, I would increase the excess that the magnesium is in, so that the progress of the reaction would have less effect on the relative surface area for reaction that there is.
Activation energy - Temperature
Problem
To find the activation energy of the reaction between hydrochloric acid and magnesium.
Background Information
Rates of reaction are dependent on temperature. Reactant particles are constantly moving towards each other and colliding in ways that can break and form bonds. Increasing temperature increases the kinetic energy these particles have, so at higher temperature they move faster, which increases the force with which they collide, making a reaction more likely.
For a collision which results in a reaction, the kinetic energy possessed by the colliding particles must be more than a certain minimum energy, Emin, otherwise bond breaking will not take place and the reaction will not start.
In a reaction system the particles will have a range of energies, as shown by the diagram below. By increasing the temperature (T2) the proportion of particles with the necessary activation energy to react (EA) is increased, thus the rate of reaction increases.
The dependence of rate on temperature is given by the Arrhenius equation:
ln(rate of reaction) = ln(collision rate) – EA/R × (1/T)
where k is the rate constant of the reaction, R is the gas constant 8.31 J K-1 mol-1, EA is the activation energy of the reaction in J mol-1, and T is the temperature in Kelvin.
To determine the activation energy, a graph of ln(rate) vs 1/T must be plotted. The gradient of the graph is –EA/R.
To do this, I must carry out an experiment where I vary the temperature of the reaction mixture and measure the rate of the reaction for each of these temperatures, keeping all other variables, as discussed on page 1, constant.
Preliminary tests.
This reaction is exothermic. This could affect my results because as the reaction proceeds, the temperature rises and the reaction rate will increase accordingly. I chose to use a large volume, 100cm3 of HCl to minimise the change of temperature. I carried out a preliminary test to measure how large the temperature increase would be. I found that when carrying out the reaction at room temperature, there was no measurable change in temperature from 23°C using the method described below.
Method
I intend to find the rate of reaction at different temperatures by measuring the amount of time it takes for a small amount of magnesium powder to react completely with an excess of HCl. The reaction ends when the powder disappears and no more bubbles are produced.
It is necessary to keep the hydrochloric acid in a large excess so that the concentration of acid does not vary. 100 cm3 of 0.20 mol dm-3 HCl(aq) is 0.02 moles of HCl. 2 moles of HCl react with 1 mole of magnesium, so for a 5 times excess of HCl, I need 0.01 moles of magnesium, which is 0.048 grams. I rounded this value up to 0.050 grams of magnesium because it was easier to measure accurately on the microgram scale.
- Set up the apparatus shown in the diagram above
-
Heat 100cm3 0.20 mol dm-3 hydrochloric acid to the desired temperature using a Bunsen burner
- Place a thermometer in the beaker and record the temperature as the initial temperature of the reaction mixture
- Add 0.050g magnesium powder to the beaker and start the stop watch
- Observe the reaction and stop the stop watch when there is no more visual reaction activity in the beaker.
- Note the time taken for the reaction to complete
Repeat this procedure using other temperatures for the reaction mixture.
Tests
Test were carried out for temperatures of 23, 30, 40, 50, 60 and 70°C. This is a wide range of temperatures and should be sufficient for obtaining a good graph in order to calculate the activation energy.
A low concentration of acid was used so that the reaction rate was low, therefore the heat produced by the reaction was kept to a minimum, and the reactions last a long time so my results are as accurate as possible.
I repeated each experiment once, so that it would be easier to spot any anomaly that would otherwise affect my results.
Results
Results are shown in the table and graph below. The average rate of reaction is found by taking the inverse of the time for the reaction to reach a point where there is no visual sign of a reaction taking place. The rate units are arbitrary, but not necessary for calculating the activation energy.
My results show that as the temperature of the reactants increases, the time taken for the reaction to finish decreases. None of the results are anomalous, which suggests this method to be highly accurate.
Analysis
The graph appears to be very linear. However it must be a curve as no matter how high the temperature is, the reaction still takes a period of time to complete.
To determine the activation energy for the reaction, a different graph must be used as discussed in the background information on page 11.
The gradient of this graph is –EA/R. R is the gas constant, which is 8.31 J K-1 mol-1.
From this graph the activation energy is 18kJ mol-1, to two significant figures.
Sources of error
The method I used to determine the activation energy of the reaction between hydrochloric acid and magnesium is very simple, and has few sources of error. My measurement of magnesium powder was correct to 2 significant figures (0.050 grams). My measurements of the hydrochloric acid volume were correct to 3 significant figures (25.0cm3) and the concentration was correct to 3 significant figures.
The main source of error however is judging when the reaction is complete. As the reaction progresses, there is less and less visual activity, until suddenly there is no magnesium left. It is difficult to judge exactly when that point is. Therefore I estimate that on any of my tests there could be an error of up to ±2 seconds.
As well as being heated up by the exothermic nature of the reaction, the reaction mixture will cool down as the reaction proceeds if it is at a temperature higher than that of its surroundings. This would have affected my results much more than the heat produced by the reaction, as the volume of HCl was very large. Therefore my results must be inaccurate due to the reduction in rate of reaction due to the falling temperature of the reactants at starting temperatures.
Limitations
More accurate readings would have been obtained if I was able to control the change in temperature over the course of the reaction. This would be possible if I could place the beaker in which the reaction takes place inside a water bath which is maintained at the desired temperature for the reaction. The water bath would receive some of the heat produced by the exothermic reaction, and also it would warm up the reaction mixture as if its temperature falls. Ideally the water bath should be large, for maximum heat capacity, and the reaction mixture small, to allow maximum heat exchange.
Visually judging when the reaction is complete is a method that always has a margin of error due to human error. This was estimated at about ±2 seconds. I could have instead timed how long it took the reaction to produce a certain amount of hydrogen gas, say 50cm3, and taken the inverse of this time to find a rate. This would eliminate the problem of being uncertain when to stop the stopwatch.
Nuffield Advanced Chemistry, Students Book p242.
Nuffield Advancing Chemistry website: www.chemistry-react.org/go/Tutorial/Tutorial_4425.html
Nuffield Advanced Chemistry Student Book, p257
![The Effect of Concentration on the Rate of Reaction between Magnesium [Mg] and Hydrochloric acid [Hcl]](https://mbt-essays-prod-public.s3.eu-west-1.amazonaws.com/934664/listing/934664_1.jpg)
