To determine the standard enthalpy of formation of Magnesium Oxide using Hess Law.

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International Baccalaureate Chemistry

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International Baccalaureate Diploma Program (IBDP)

Session: May 2015

Chemistry HL Lab Report

Lab Report Title: To determine the standard enthalpy of formation of Magnesium Oxide using Hess’ Law.

Criteria Assessed:

Data Collection and Processing (DCP)
Conclusion and Evaluation (CE)

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International School, Singapore

AIM: To determine the standard enthalpy of formation of Magnesium Oxide using Hess’s law.

INTRODUCTION:

The objective of this experiment was to determine the change in enthalpy when one mole of Magnesium (Mg) reacts with half a mole of Oxygen (O2) to give one mole of Magnesium Oxide (MgO). The balanced chemical equation is as follows: Mg (s) + O2 (g) → MgO (s) ---- ΔHMgO f

The reaction between Magnesium and Oxygen to form Magnesium Oxide is essentially the combustion of Magnesium and since every combustion reaction is an exothermic reaction, this reaction too is an exothermic reaction, i.e. it too will produce heat to the surroundings. In fact, the combustion of Magnesium is highly exothermic as it produces flames whose temperatures reach almost 2500oC (http://physics.stackexchange.com). At such high temperatures, a very bright white light is produced and if directly looked upon for long periods of time, the high content of ultra-violet radiation has the potential to damage unprotected eyes. Moreover, such high temperatures cannot be measured using a common thermocouple (K-type) so they need much more sophisticated setup of Ir-Rh thermocouples in an inert atmosphere. All these factors together make it extremely difficult to calculate the enthalpy of formation of MgO directly.

Swiss-born-Russian scientist, Germain Henri Hess had come up with the idea of calculating the enthalpy of reaction of a certain reaction using an alternate set of stepwise reactions which would add together in such a way that it would give the same reaction. The enthalpy of reaction for each of these reactions can then be added together to give the enthalpy of reaction of the primary reaction (formation of MgO, in this case). This is because he stated that according to the law of conservation of energy, the total enthalpy change of a reaction will depend only on the difference between the enthalpy of the product and the enthalpy of the reactants and not on what path it follows. This is known as Hess’s law.

The alternate set of stepwise reactions that were followed in this experiment to arrive at the value for the enthalpy of formation of MgO(s) are as follows:

Mg (s) + 2HCl (aq.) → MgCl2 (aq.) + H2 (g) ---------- ΔHX
MgO (s) + 2HCl (aq.) → MgCl2 (aq.) + H2O (g) ---------- ΔHY
H2 (g) + O2 (g) → H2O (l) ---------- ΔHH2O = -285 kJ.mol-1

Adding all the three reactions, we obtained the following reaction:

Mg (s) + 2HCl (aq.) + MgCl2 (aq.) + H2O (g) + H2 (g) + O2 (g) MgCl2 (aq.) + H2 (g) + MgO (s) + 2HCl (aq.) + H2O (g)

Mg (s) + O2 (g) MgO (s)

Since reaction 2 was reversed, the sign on the value of ΔHY was also reversed because the amount of heat required to form the reactants back from the products will be the same as the amount of heat given out when the reactants formed the product (in this case, the exothermic neutralization reaction of MgO and HCl). Therefore, to arithmetically calculate the value for the enthalpy of formation of MgO the following equation was then followed: ΔHMgO = ΔHX - ΔHY + ΔHH2O.

Experiment 1 and 2 could be safely and efficiently carried out under the school lab conditions with the objective to fulfill the aim.

To carry out the arithmetic calculations required, values of the reaction enthalpy of the all the three reactions were needed but since the value for ΔHH2O had already been provided to us by the lab in-charge, all that was needed to be determined were the values for ΔHX and ΔHY. These were determined separately by dividing the experiment into 2 parts called part X and part Y where part X was used to determine the value for ΔHX by carrying out reaction 1 and part Y was used to determine the value for ΔHY by carrying out reaction 2.

VARIABLES:

Independent Variables:

Length of Magnesium (For part X): For all the trials, a 3cm strip was cut away from the same roll of Magnesium ribbon. It was ensured that the strip cut was as straight as possible and also, the strip was clean of any contaminants. The strips were weighed each time on the same electronic balance and each time, the mass of Magnesium was approximately the same.
Mass of Magnesium Oxide (For part Y): For all trials, 0.05g of MgO was weighed out using the same electronic balance. The container claimed to contain MgO with only trace amounts of impurities.

Dependent Variables:

Maximum temperature reached: Temperature of the solution was recorded using the same thermometer each time so that no additional systematic errors are introduced.

Table 1: Controlled Variables

APPRATUS AND CHEMICALS:

Table 2: Apparatus required for the experiment.

Table 3: Chemicals required for the experiment.

PROCEDURE:

Setting up the calorimeter – Two Styrofoam coffee cups were taken and one was placed inside the other with a rubber band in between the cups to create an air gap. A lid was placed on top and through the hole, a thermometer was placed through it. Once the calorimeter was setup, it was let aside.

Part X – With Magnesium Strip

Using the ...

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Table 1: Controlled Variables

APPRATUS AND CHEMICALS:

Table 2: Apparatus required for the experiment.

Table 3: Chemicals required for the experiment.

PROCEDURE:

Setting up the calorimeter – Two Styrofoam coffee cups were taken and one was placed inside the other with a rubber band in between the cups to create an air gap. A lid was placed on top and through the hole, a thermometer was placed through it. Once the calorimeter was setup, it was let aside.

Part X – With Magnesium Strip

Using the stock solution of 2M HCl prepared by the lab in-charge, the burette was filled until the 0.00cm3 mark.
Using the burette, 15cm3 of 2M HCl was withdrawn into the calorimeter and was allowed to sit for a minute or two so that its temperature reaches the ambient temperature. In the duration of these few minutes, Magnesium was prepared for reaction using the following two steps.
From the 6cm strip of Magnesium ribbon, a 3 cm strip was cut and wiped with a clean cloth to remove any contaminants.
The 3cm strip of Magnesium was then weighed using the electronic balance. Its mass was noted.
The temperature of the acid was then measured using the thermometer and its reading noted.
The Magnesium was then added to the calorimeter and the lid of the calorimeter was closed as quickly as possible to prevent any heat losses.
Using the thermometer, the mixture was very gently stirred for a few seconds.
Every five seconds, the reading on the thermometer was read as accurately as possible and noted.
For 120 seconds, 24 readings were taken and noted in a pre-made data collection table.
Once 120 seconds were up, the calorimeter was emptied and cleaned so that another trial of the same experiment could be performed.

Part Y – With Magnesium Oxide Powder

The calorimeter was cleaned thoroughly ensuring no chemicals were left behind which would hinder in the reaction in part Y.
Using the burette, 15cm3 of 2M HCl was withdrawn into the calorimeter and was allowed to sit for a minute or two so that its temperature reaches the ambient temperature. In the duration of these few minutes, Magnesium Oxide was prepared for reaction using the following step.
From the MgO powder given to us by the lab in-charge, 0.05g of MgO was weighed out on a petri dish using the electronic balance.
This mass of MgO was added to the 15cm3 of 2M HCl in the calorimeter.
The lid of the calorimeter was closed as quickly as possible to ensure that heat loss through convection currents was minimized.
Using the thermometer, the mixture was very gently stirred for a few seconds.
Every five seconds, the reading on the thermometer was read as accurately as possible and noted.
For 120 seconds, 24 readings were taken and noted in a pre-made data collection table.
Once 120 seconds were up, the calorimeter was emptied and cleaned so that another trial of the same experiment could be performed.

Safety Precautions:

Throughout the experiment, a lab coat was worn so that any spills do not cause damage to clothes or body.
Covered shoes and Safety goggles were worn to avoid damage from spillage of HCl.
The work-table was wiped clean and dried before and after the experiment.

To avoid errors, following precautions were taken:

When using the thermometer, it was made sure that the bulb of the thermometer was completely immersed into the HCl to avoid any systematic and random errors in the temperature readings.
When clamping the burette to the retort stand, it was made sure that the retort stand was not tilted towards any side as this could have introduced systematic errors in the volume readings.
While performing all the experiments, it was made sure that only one person was in-charge of the stopwatch. This is because since different humans have different reaction times, it is important to ensure that the systematic error due to reaction time is the same and is not varying.
While filling up the burette, it ensured that only the person would be in-charge since due to height differences, parallax errors of different magnitudes could be introduced introducing unwanted random errors (inconsistent systematic errors).
Each time the electronic balance was used, it was appropriately tarred to prevent any zero errors.

RAW DATA COLLECTION:

The following tables contain all the raw data that was recorded in the lab while performing the experiment. The temperature of solution in every trial was recorded every five seconds.

Part X, Trial 1:

Table 4: Data Collection: Part X, Trial 1.

Part X, Trial 2:

Table 5: Data Collection: Part X, Trial 2

Part Y, Trial 1:

Table 6: Data Collection: Part Y, Trial 1

Part Y, Trial 2:

Table 7: Data Collection: Part Y, Trial 2

RAW DATA PROCESSING:

For Part X, Trial 1

To obtain an estimation of the maximum temperature reached in the trial, a graph is drawn which shows all the progressing and regressing values of temperature against time. Following that, a best fit line is drawn for all the progressing and then the regressing values of temperature. Whichever point the two lines meet at can safely be assumed to be a good estimate of the maximum temperature reached and how much time had elapsed.

Graph 1: Highest temperature reached in Part X, Trial 1.

For the best estimation of maximum temperature reached, a magnified view of the intersection of horizontal line and y-axis is useful.

Figure 1: Zoomed in view of the y-axis and horizontal line intersection.

From the figure, the value for the maximum temperature reached can be safely estimated to be 40.7oC.

Since the maximum temperature reached by the solution of 15cm3 water has been determined to be 40.7oC and the room temperature at which the solution was at 0s was determined to be 32.4oC, the change is temperature can be given by the following formula:

ΔT (change in temperature) = Final temperature – Initial Temperature

ΔT = 40.7 – 32.4 = 8.3K

The mass of solution of 15cm3 of 2M HCl and Magnesium strip is assumed to be 15g. Also since Magnesium has a negligible heat capacity, its heat capacity is not taken into consideration when calculating the heat released in the solution.

Formula for heat released in the solution → Q=mc.ΔT

Q = 15 × 4.2 × 8.3
Q = 522.9J

The number of moles of MgCl2 produced in this reaction = Number of moles of Mg used

Number of moles of Mg used = = = 0.0021moles
Number of MgCl2 produced = 0.0021moles.

Heat that would be released if 1 mole of MgCl2 would be formed = Standard Enthalpy of Reaction

Standard Enthalpy of reaction calculated for this trial =
ΔHX (Trial 1) = = 249000J = -249kJ.mol-1.

For Part X, Trial 2

Graphical analysis similar to that used in Part X, Trial 1 has been used to determine the maximum temperature reached in the duration of the reaction.

Graph 2: Highest temperature reached in Part X, Trial 2.

Figure 2: Zoomed in view of the y-axis and horizontal line intersection.

From the figure, the value for the maximum temperature reached can be safely estimated to be 40.8oC.

Since the maximum temperature reached by the solution of 15cm3 water has been determined to be 40.8oC and the room temperature at which the solution was at 0s was determined to be 32.2oC, the change is temperature can be given by the following formula:

ΔT = 40.8 – 32.2 = 8.6K

Since total heat released = Q = mc.ΔT

Q = 15 × 4.2 × 8.6 = 541.8J

Number of MgCl2 produced = 0.0021moles

Std. Enthalpy of reaction for this trial = ΔHX (Trial 2) = 258000J = 258kJ.mol-1.

To find the average value for ΔHX, the average of ΔHX (Trial 1) and ΔHX (Trial 2) was taken.

ΔHX = -253.5kJ.mol-1

Therefore, the standard enthalpy of reaction of reaction 1: Mg (s) + 2HCl (aq.) → MgCl2 (aq.) + H2 (g) ------------ ΔHX = -253.5kJ.mol-1

For Part Y, Trial 1

Graphical analysis similar to that used in Part X has been used to determine the maximum temperature reached in the duration of the reaction.

Graph 3: Highest temperature reached in Part Y, Trial 1.

Figure 3: Zoomed in view of the y-axis and horizontal line intersection.

From the figure, the value for the maximum temperature reached can be safely estimated to be 34.6oC.

Since the maximum temperature reached by the solution of 15cm3 water has been determined to be 34.6oC and the room temperature at which the solution was at 0s was determined to be 32.5oC, the change is temperature can be given by the following formula:

ΔT = 34.6 – 32.5 = 2.1K

Since total heat released = Q = mc.ΔT

Q = 15 × 4.2 × 2.1 = 132.3J

Number of MgCl2 produced = Number of moles of MgO used

Number of Moles of MgO used = = 0.0012moles

Number of Moles of MgCl2 used =0.0012moles

Std. Enthalpy of reaction for this trial = ΔHY (Trial 1) = 110250J = 110.25kJ.mol-1.

For Part Y, Trial 2

Graphical analysis similar to that used in Part Y, Trial 1 has been used to determine the maximum temperature reached in the duration of the reaction.

Graph 4: Highest temperature reached in Part Y, Trial 2.

Figure 4: Zoomed in view of the y-axis and horizontal line intersection.

From the figure, the value for the maximum temperature reached can be safely estimated to be 34.05oC.

Since the maximum temperature reached by the solution of 15cm3 water has been determined to be 34.05oC and the room temperature at which the solution was at 0s was determined to be 32.1oC, the change is temperature can be given by the following formula:

ΔT = 34.05 – 32.1 = 1.95K

Since total heat released = Q = mc.ΔT

Q = 15 × 4.2 × 1.95 = 122.85J

Number of moles of MgCl2 produced = 0.0012moles

Std. Enthalpy of reaction for this trial = ΔHY (Trial 2) = 102375J = 102.38kJ.mol-1.

To find the average value for ΔHY, the average of ΔHY (Trial 1) and ΔHY (Trial 2) was taken.

ΔHY = -106.3kJ.mol-1

Therefore, the standard enthalpy of reaction of reaction 2: MgO (s) + 2HCl (aq.) → MgCl2 (aq.) + H2O (l) ------------ ΔHX = -106.3kJ.mol-1

Calculating ΔHMgO

Since the enthalpies of reaction for both reaction 1 and reaction 2 are known, Hess’ law can be applied and the following method can be used for calculating the value for ΔHMgO.

ΔHMgO = ΔHX - ΔHY + ΔHH2O

ΔHMgO = -253.5kJ.mol-1 - -106.3kJ.mol-1 -285kJ.mol-1
ΔHMgO = -253.5 + 106.3 - 285
ΔHMgO = -432.2kJ.mol-1

Therefore, the standard enthalpy of formation of MgO: Mg (s) + O2 (g) → MgO (s) ----------------- ΔHMgO = -432.2kJ.mol-1

Error Propagation:

Total Error = Random Error + Systematic Error

To calculate the total random error percentage, the percentage uncertainty of the smallest reading on each apparatus is added. Also, since the final value of ΔHMgO was computed using the values of ΔHX and ΔHY, the absolute uncertainty of the two values need to be added together to give the absolute uncertainty for the value of ΔHMgO.

Therefore, absolute uncertainty of final value = absolute uncertainty of ΔHX + absolute uncertainty of ΔHY.

Step 1: Calculating absolute uncertainty of the value for ΔHX

Percentage uncertainty =

Table 7: Total Random Error Calculation for Part X

Total random error = 21.14%

Therefore, absolute error = = 49.8

Therefore, ΔHX = -253.5±49.8 kJ.mol-1

Step 2: Calculating absolute uncertainty of the value for ΔHY

Percentage uncertainty =

Table 8: Total Random Error Calculation for Part Y

Total random error = 21.14%

Therefore, absolute error = = 22.5

Therefore, ΔHY = -106.3±22.5kJ.mol-1

Step 3: Calculating total absolute uncertainty of the value for ΔHMgO

Absolute uncertainty of value for ΔHMgO = absolute uncertainty of ΔHX + absolute uncertainty of ΔHY.

Absolute uncertainty of value for ΔHMgO = 49.8 + 22.5 = 72.3

Therefore, ΔHMgO = -432.2±72.3kJ.mol-1

The literature value for the standard enthalpy of formation of MgO is given to be -601.2kJ.mol-1.

Therefore, percentage error in the derived value =

Total error = Total random error + Total systematic error

Total systematic error = Total error – Total random error
Total systematic error = 28.1% - 21.1% = 7.0%

CONCLUSION AND EVALUATION:

It can be concluded that this experiment was successful considering the conditions under which it was performed. The total percentage deviation from the literature value was unimpressively large but at the same time, it should be taken into consideration that it is not possible to perform such experiments require much more sophisticated instruments that those readily available in the school lab. The value for ΔHMgO was determined to be -432.2±72.3kJ.mol-1. This means that according to this experiment, the value of ΔHMgO lies anywhere from -359.9 kJ.mol-1 to -504.5kJ.mol-1. The literature value for ΔHMgO was given to be -601.2kJ.mol-1 therefore the value in the range closest to the literature value (-504.5kJ.mol-1) is still 16.1% off.

The experiment was carried out with the maximum possible care to avoid any errors however, there still were several limitations in the apparatus and several assumptions made that have led to the this high degree of inaccuracy.

Firstly and most significantly, the calorimeter made for the purposes of this experiment was engineered rather unimpressively. Building a perfect calorimeter is practically impossible but refinements to the materials used and design could help in building a more efficient calorimeter. However, under the material and time limitations, this was the best type of calorimeter that could be devised. An example of a more sophisticated calorimeter that could be used is a simple thermos flask which to a large extent minimizes heat loss due to conduction, convection and radiation.

Due to the heat loss from the calorimeter, the value for ΔT in each trial was understated because in each trial some amount of heat was lost which could have been used for generating a higher rise in temperature. Since the value for ΔT is directly proportional to the enthalpy of reaction, an understatement in this value led to an understatement in the final value of ΔHMgO and it is evident from the results of the raw data analysis. Intuitively, lower the value for ΔT, lower the heat released by the reaction.

Another assumption that has led to the underestimation of the final value of ΔHMgO is the assumption that the solution had the same specific heat capacity of water. Clearly, the solution contained Magnesium metal (in part X) or MgO (in part Y) which leads to an increase in the specific heat capacity of the solution. Also inaccuracies in the process of standardization of HCl, if any, could have led to an understatement (or overstatement) of the specific heat capacity of the solution. Since Q = mc.ΔT, a understatement in the value of c would lead to a understatement in the value of Q which in turn, would lead to an understatement in the value of ΔHMgO.

Secondly, since Magnesium is a fairly reactive material, it would not be wrong to say that over time, any piece of Magnesium ribbon would gather some amount of oxide coating on it. The strip of Magnesium used in this experiment might also have gathered a layer of oxide coating on it since it had been sitting in the lab for a reasonably long period. As evident from reaction 2, MgO reacts with HCl much less vigorously as Mg itself and therefore, any presence of oxide on Mg is bound to slow down the reaction. In this experiment, due to presence of oxide on Magnesium, the mass of Mg that reacted would no longer be 0.05g. This means that the heat produced if all 0.05g would be Mg would be greater than that recorded and therefore, the value of Q (heat produced by 0.05g of Mg) is understated.

To overcome this common oxide problem, the strip should be sanded off of its oxide coating using a sand paper. However, sanding the 3cm strip irregularly can also chip off some metal which would further introduce random errors. Therefore, the best way to deal with this problem would be to use freshly produced Magnesium strips for the experiment and after the experiment, store Magnesium under mineral oil to prevent any contact with Oxygen in the air so that it would be still be beneficial if the experiment were ever to be performed again in the future.

Random errors in this experiment were also quite large with the error due to uncertainty in the stopwatch only one being negligible enough. Other than that, 21.1% is not a small error and to reduce the random errors in the experiment, the only solution would be to use more precise instruments such as those stated as follows:

An analytical balance could be used in place of the electronic weighing balance. The electronic weighing balance is quite a precise instrument but since it is being used to measure very small masses, even a small uncertainty of ±0.01g translates to a large percentage uncertainty. Analytical balances have an absolute uncertainty of ±0.001g and that would result in a percentage uncertainty ten times lesser in magnitude.
The burette too could be replaced by a 15cm3 pipette which has an absolute uncertainty of much smaller magnitude. However, since the burette is not giving a very large percentage uncertainty, this improvement to the apparatus can safely be given the least preference. Only after investments in a better calorimeter and an analytical balance have been made, should one think to invest in a 15cm3 pipette.
Lastly, a great improvement to the procedure would be if a data logger software and a thermometer probe would be used to record temperature over time. By using this method, the need for graphical analysis is completely eliminated and with that the need to estimate the maximum temperature is also eliminated. A temperature logger uses a software to log temperature over time so the maximum temperature can be determined more precisely. A temperature logger would also eliminate human errors in the following ways:

Since temperature reading was required every 5 seconds, it was very difficult to accurately read the thermometer so quickly avoiding all possible parallax errors. In the total of 4 trials, 92 thermometer readings have been taken. It is likely that a few of them were taken in a haste where assuming a trend, a reading was estimated. Often times, the reading was taken up to a second later.
Stopwatch readings also had the element of human reaction time and for all 92 readings, this reaction time would differ slightly (on an average, decreasing slightly after each reading because of practice). Using a data logger, the need of a student to keep track of time would be eliminated. This way more groups could be made and rather than spending time on keeping track of time, time could be spent on gaining skills such as making a calorimeter or learning to use a burette etc.

In conclusion, although the error was large, the results obtained demonstrate the applicability of Hess’ law in real life.