Investigation of hess law

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ContentsSection A: Introduction2Section B: Analysis3Qualitative data3Raw data3Data processing3Limiting reagent4Enthalpy change5Section C: Evaluation8Systematic error8Random error9Overall evaluation9Section D: Conclusion10Section E: Bibliography11

Section A: IntroductionThis experiment was designed to investigate Hess Law, which states:[The enthalpy change] for a specific reaction is equal to the sum of [enthalpies] of reaction for any set of reactions which in sum are equivalent to the overall reaction [1]That is, enthalpy change is a state function in which the pathway of the reaction doesnt matter; only the difference between the initial and final values is significant. This is useful for determining the enthalpy change of reactions that are either impractical or impossible to determine experimentally under certain conditions.In this investigation, I determine the enthalpy changes of reacting potassium hydrogen carbonate and potassium carbonate with hydrochloric acid and calculate their sum to find, according to Hess Law, the enthalpy of reaction of the thermal decomposition of anhydrous potassium hydrogen carbonate into potassium carbonate. Hess Law applies here because the thermal decomposition of anhydrous potassium hydrogen carbonate forms the same reactants from the same products as the sum of the reactions of potassium hydrogen carbonate and potassium carbonate with hydrochloric acid, so the overall energy change should be the same regardless of the number of steps.

Section B: AnalysisQualitative dataReactionObservation

1. K2CO3 + 2HCl -> 2KCl + H2CO3Cup exterior feels hot (exothermic)

Cup exterior feels hot (exothermic)

2. KHCO3 + HCl -> KCl + H2CO3Cup exterior feels cold (endothermic)

Cup exterior feels cold (endothermic)

Table B.1: Qualitative observations of chemical reactionsRaw dataSubstanceMass( 0.0005g)

Anhydrous potassium carbonate (K2CO3)3.000

2.556

Potassium hydrogen carbonate (KHCO3)3.543

3.620

Table B.2a: Quantitative measurements of solid reactantsSubstanceVolume( 0.5 cm3)Concentration[footnoteRef:1](mol dm-3) [1: This value was taken from the manufacturers packaging, so it is assumed that this quantity will have zero uncertainty.]

Hydrochloric acid (HCl)302

Table B.2b: Quantitative measurements of non-solid reactantsInitial temperature of acid( 0.05C)Final temperature of solution( 0.05C)

21.828.0

21.627.1

21.713.4

22.413.4

Table B.3: Temperature of acid at start and solution at endData processingFirst, we must determine the number of moles of potassium carbonate and potassium hydrogen carbonate. This is done using the formula:

I will demonstrate my method in performing this calculation using the first trial of reacting potassium carbonate with hydrochloric acid. I will not show the other calculations, but their results will be stated in Table B.4.

Uncertainty

Calculation

SubstanceMass( 0.0005g)Molar mass[footnoteRef:2] kg mol-1) [2: Molar mass is a value calculated by combining values from the periodic table, so it is assumed that molar masses will have zero uncertainty.]

Moles(moles)Uncertainty

K2CO33.000138.210.0217 = 0.0005

2.5560.01850.0196% = 0.0005

Average K2CO32.7780.02010.0360% = 0.001

KHCO33.543100.120.03540.0141% = 0.0005

3.6200.03620.0138% = 0.0005

Average KHCO33.5820.03580.0279% = 0.001

SubstanceVolume( 0.05cm3)Concentration(mol cm-3)Moles[footnoteRef:3] [3: ]

( 0.0001 mol)

HCl3020.06

Table B.4: Calculated amount of reactants in molesSubstanceInitial temperature of acid( 0.05C)Final temperature of solution( 0.05C)Change in temperature[footnoteRef:4]( 0.10C) [4: ]

Anhydrous potassium carbonate21.828.06.2

21.627.15.5

Average:5.85

Potassium hydrogen carbonate21.713.4-7.3

22.413.4-9.0

Average:-8.15

Table B.5: Temperature changeLimiting reagentIn order to determine the limiting reagent in my reactions, I will use the average masses and average number of moles. The masses were 2.778g and 3.582g for K2CO3 and KHCO3 respectively.K2CO3 + 2HCl 2KCl + H2CO3

Mass2.778

Molar mass100.12

Moles0.02010.06

Table B.6: Limiting reagent of potassium carbonate and hydrochloric acidK2CO3 and HCl react in a 1-to-2 ratio, so only 0.0402 moles of HCl are needed. Thus, in this reaction, the potassium carbonate is the limiting reagent and the HCl is in excess.Applying a similar process to the potassium hydrogen carbonate reaction:KHCO3 + HCl 2KCl + H2CO3

Mass3.582

Molar mass138.21

Moles0.03580.06

Table B.7: Limiting reagent of potassium hydrogen carbonate and hydrochloric acidKHCO3 and HCl react in a 1-to-1 ratio, so only 0.0358 moles of HCl are needed. Thus, in this reaction, the potassium hydrogen carbonate is the limiting reagent and the HCl is in excess.Enthalpy changeIn order to investigate Hess law, I must now calculate the molar enthalpy change of the two reactions and compare how the enthalpy from the Hess cycle compares to the reference value of enthalpy for the decomposition of potassium hydrogen carbonate. ReactionMass of heated solution[footnoteRef:5] [5: Here, in order to simplify calculations, I assume that the density and specific heat capacity of hydrochloric acid is the same as that of water.]

(g)Moles of limiting reagent(mol)Specific heat capacity5(J K-1 mol-1)Temperature change(K)

1. K2CO3 + HCl300.02014.1795.85

2. KHCO3 + HCl300.03584.179-8.15

Table B.7: Summary table on reactants for calculating molar enthalpyThe equation for molar enthalpy is as follows:

I will now calculate the molar enthalpy of reaction 1:

= = = 0.06851192754 (3s.f.) = 2.50

Uncertainty

J mol-1 Calculation

Calculation

I will also do the same for the molar enthalpy of reaction 2: = = (3s.f.) = 1.19

Uncertainty

Thus, the molar enthalpy of reaction 1 is -36.5 kJ mol-1 2.50 and the molar enthalpy of reaction 2 is +28.5 kJ mol-1 1.19.

Diagram B.1: Hess cycle showing two pathways between products and reactants

According to the Hess cycle in diagram B.1, the enthalpy change for the decomposition of potassium hydrogen carbonate into potassium carbonate should be equal to twice the enthalpy change of reaction two plus negative one times the enthalpy change of reaction one. That is:

= kJ mol-1

Uncertainty

-1

Calculation

Thus, according to Hess Law, the overall enthalpy change of this reaction is as follows:H = + 93.5 3.69 kJ mol-1 The reference value [3] [4] for the enthalpy change of the decomposition of potassium hydrogen carbonate into potassium carbonate is:H = + 92 kJ mol-1My value for H is between 89.81 and 97.19 kJ mol-1, so the reference value is well within my uncertainty range.

Section C: EvaluationMy percentage error for the final value of the enthalpy change of thermal decomposition of potassium hydrogen carbonate into potassium carbonate was quite low, at 1.63%. Though it could be argued that this was due to the lack of systematic errors in my procedure and the lack of random errors, I believe that it was because the opposite directionalities of my errors cancelled each other out, leading to a low percentage error.The equation I used to calculate molar enthalpy was:

My errors manifest themselves most obviously in values such as T and specific heat capacity. Below, I will outline the reasons I believe this is so.Systematic errorTemperature change (T)Perhaps the biggest weakness in my methodology was the way I decided to measure temperature change. I did so by conducting the reaction in a polystyrene cup and measuring the initial and final temperature of the substance using a thermometer. The largest source of error is the heat lost to the environment through the sides of the polystyrene cup. In my qualitative observations (table B.1), I note that the cup was either cold or warm to the touch during the reaction. This shows that the polystyrene cup is a poor insulator, because I very quickly felt the temperature change of the reaction, meaning that large amounts of heat energy were escaping and entering the system. As heat energy was transferred from the system into the surroundings (outside the polystyrene cup) rather than the thermometer, my value for final temperature was too low, making my value for molar enthalpy too low.To deal with this, I could have insulated the polystyrene cup using a piece of fabric, used a better insulated calorimeter (such as a vacuum flask or thermos), or used a cooling curve of temperature against time to extrapolate an estimate for the amount of heat lost.Specific heat capacity (C)In footnote 2, I stated that I assumed the specific heat capacity of 2M hydrochloric acid to be the same as that of water. As a result, the specific heat capacity I used in my calculations resulted in systematic error. I could have used research to find a reference value for the specific heat capacity of 2M HCl to use in my calculations instead of the specific heat capacity of water. Using the Internet, I found it to be 3.89 J K-1 mol-1 at 20C [5]. The value I used instead was 4.179 J K-1 mol-1, so my value for C would have made my calculated molar enthalpy slightly too high. Note that the direction of this error is opposite to the direction of the error in temperature change.Mass (m)In footnote 2, I stated that I assumed the density of 2M hydrochloric acid to be the same as that of water. I then used this density to calculate a value for the mass of substance being heated, which resulted in a systematic error. I could have fixed this in one of two ways:1. Use a reference value for the density of 2M HCl. The value I found was 1.030 g ml-1 at 25C [6], only slightly higher than the 1.000 g ml-1 I actually used. This would have made my actual value slightly lower than the reference value.

2. Instead of measuring the volume and finding a value for the density to calculate mass, I could simply measure the mass of the acid. First, Id measure the mass of the containing beaker or calorimeter, then tare the scale before pouring in my roughly measured 30cm3 of acid. The second method is preferable for several reasons. Firstly, it avoids making assumptions that lead to inaccuracies and deviations from the actual value. Secondly, it uses fewer variables and calculations, leaving less possibility of error. Thirdly, it involves a minimal number of steps where the acid is transferred from one container into another, making the value for mass or volume more accurate. Finally, the electronic balances used in my method are much more precise (smaller increments, measures up to 3 decimal places) than measuring cylinders (larger increments, leaves room for human measuring errors such as parallax).Random errorIt is difficult to tell the extent of the random error from my experiment and my calculations, because I only conducted two trials of each reaction (two data points each), so it is difficult to determine how grouped the data is. Furthermore, as I did not calculate separate molar enthalpy values for each of my trials, it is even more difficult to determine exactly how large my random error was. Thus, my methodology could have included the following changes to reduce random error and increase precision:1. More readings: conducting more trials of each reaction would reduce the effect of random errors, anomalies, and outliers, making the data more precise. Better still, I perform several trials and then eliminate the highest and the lowest values before calculating an average, reducing the effect of outliers. Theoretically, the more trials conducted the better, but realistically, perhaps 4 trials is enough to eliminate anomalies.

2. Larger volumes of all reactants involved (scaled in proportion to account for the limited amount of limiting reagent) would not reduce the absolute error of each measurement. However, a larger measurement with the same amount of absolute error makes for a much smaller percentage error, making the propagated uncertainties in multiplication and division smaller and thus making the data more closely grouped, reducing random error and increasing precision.Overall evaluationMy temperature change caused my final value for the molar enthalpy of the reaction to be lowered significantly, while my specific heat capacity and mass values caused the molar enthalpy value to increase and decrease slightly. Thus, combining the magnitudes and directionalities of my systematic errors, my value should have been lower than the reference value. However, it was actually higher by 1.63%. I can assume that this discrepancy between expected and experimental value was due to the random errors inherent in the apparatus and myself.

Section D: ConclusionI have conducted a given procedure to investigate Hess Law. Applying Hess Law in my calculation of the enthalpy change on the thermal decomposition of potassium hydrogen carbonate into potassium carbonate gave me +93.5 kJ mol-1, a value that was only 1.63% off the reference value of +92 kJ mol-1. From the data, I would conclude that Hess Law indeed holds true and allows us to predict theoretical values from empirical values and vice versa.However, in my evaluation, I examined my methodology and found evidence both to show that the systematic errors led to a lower value, but also that the random errors counteracted the directionality of the systematic errors and with greater magnitude, making my final value higher than the reference value. As such, while the data support a strong conclusion, I would argue that the evidence I collected, analyzed, and presented is tenable at best somewhat reliable but insufficient to support such a conclusion.

Section E: Bibliography[1] http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Thermodynamic_Cycles/Hess%27s_Law[2] http://www.iun.edu/~cpanhd/C101webnotes/matter-and-energy/specificheat.html[3] https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CDEQFjAD&url=https%3A%2F%2Fchemistryatdulwich.wikispaces.com%2Ffile%2Fview%2FTopic%2B6%2BUsing%2BHess%2BLaw%2Bsodium%2Bhydrogen%2Bcarbonate.doc&ei=4K07VemmGuS4mAWtlYHwBA&usg=AFQjCNH5YBgA81B1RdhsnfE-pgXaIGZLOw&sig2=xbslV9BJ-BiygFvZvfIBJQ&bvm=bv.91665533,d.dGY&cad=rja[4] http://www.markedbyteachers.com/international-baccalaureate/chemistry/determination-of-potassium-hydrogen-carbonate-into-potassium-carbonate.html[5] http://www.laney.edu/wp/cheli-fossum/files/2011/08/14-Heats-of-Rxns.pdf[6] http://www.sigmaaldrich.com/catalog/product/fluka/653799?lang=en&region=HK