The Application of Hess's Law in Coffee-Cup Calorimetry

1. Introduction In the study of Thermochemistry, reactions are quantitatively analyzed to determine the amount of heat that has been transferred, whether released or absorbed, between the system and its surroundings. Such data is important in realizing the properties of different types of reactions along with the elements and compounds of which they are comprised. However, it can be difficult to derive the exact enthalpy in a reaction when multiple processes occur simultaneously. A method to circumvent this problem is outlined in Hess’s Law which was established in 1840. Hess’s Law states that the steps taken to determine the enthalpy of a reaction do not matter because the end results will be the same. This is the principle used for both parts of this experiment.
In Part I of the experiment, two different reactions are performed to determine the enthalpy of formation for magnesium oxide. One reaction will involve only Mg, and the other will involve MgO – both will react with 1M HCl. Using the change in heat for both of these reactions, the enthalpies can be determined. With the use of Hess’s Law, the enthalpies of both reactions along with the enthalpy of water can be used to determine the enthalpy of formation for magnesium oxide. Such reactions will take place in a coffee-cup calorimeter which is made up of two Styrofoam cups and a top. It is assumed that the insulation provided by the cups will suffice in retaining the heat within the reaction so that an accurate reading can be derived. This assumption is essential to the accuracy of the results in both Part I of the experiment as well as Part II.
Part II of the experiment will be used to test the accuracy of this experiment against Hess’s Law. Two separate reactions will be induced: the first will be the reaction between 2M NaOH and 2M HCl; the second will be between 2M NaOH and 2M NH4Cl. Once the data is collected from these reactions, the enthalpies can be calculated and Hess’s Law can be used to determine the enthalpy of a third reaction: the reaction between 2M HCl and 2M NH3. In order to test the accuracy of Hess’s Law – or the inaccuracy of the experiment – the third reaction will be performed, the data will be collected, and the enthalpy will be determined. This experiment will yield a greater understanding of the laws of thermodynamics and the challenge of testing them. 2. Experimental In starting Part I of the experiment all materials were obtained, which included a 250mL and 600mL beaker, a 50mL graduated cylinder, two Styrofoam cups, a plastic cover for the cups, a sample of Mg and MgO, and 1M HCl. Other required instrumentation necessary in performing this experiment was a computer and a Vernier LabPro interface along with a temperature probe which measured the temperature changes in the solution over the course of the reactions. Before beginning the experiment, batteries were put into the LabPro interface and the LabPro was set-up on the computer using the Logger Pro Program. The interface system was set-up to collect one sample of data every second for 570 seconds. Once the LabPro was on, which is confirmed by three blinking LED lights, and ready, the procedure could then proceed. The procedure began with the taring of two weighing dishes followed by the weighing of both the Mg and MgO samples on the weighing dishes in order to calculate the weight of the samples alone. Once the weights of the samples were know, the coffee cup calorimeters were prepared. In order to reduce contamination and error, the Styrofoam cups were washed, weighed, and placed into the 250mL beaker. Being that this experiment requires a closed system, a top for the Styrofoam cups was needed with a hole in the center to allow the temperature probe to pass through. Using the 50mL graduated cylinder, exactly 25.00mL of the 1M HCl was measured and poured into the calorimeter (HCl must be handled carefully because it is corrosive and toxic if inhaled).
Once the HCl is poured, the temperature probe was placed into the acid through the hole allowing the LabPro to measure the temperature for 4.5 minutes. At 5.0 minutes the magnesium metal was placed into the calorimeter with the HCl aqueous solution where the LabPro continued recording the temperature until the yellow LED light ceased blinking, which was roughly 4 minutes (the reaction between HCl and Mg metal produces H2 gas which is flammable, it is best to combine the compounds under a hood and to avoid sparks). The LabPro was then taken to the computer to present the data in a graph in the form of Temperature (˚C) versus Time (s). In the meantime, the temperature probe was placed in the 600mL beaker that was filled with 400mL of deionized water for 2 minutes for cleansing purposes. It is important to watch the time carefully during the experiment to preserve the condition of the probe; if the temperature probe is submerged in the HCl for more than 10.0 minutes, it can be damaged.
Once the data was collected, the final solution along with the calorimeter was weighed. The solution was then discarded into the appropriate labeled receptacle and preparations began for the second task of Part I. Such preparations included washing the Styrofoam cups for the calorimeter, making sure that the probe was clean, and restarting the LabPro interface. Once completed, the preceding procedures were followed for the reaction involving the magnesium oxide sample and the HCl aqueous solution. The procedure for only Part I will be revealed in this section, however, the results of Part II will be analyzed in the Results and Discussion portion of this report.

3. Results and Discussion In order to calculate the enthalpy of formation for magnesium oxide – which is the purpose of Part I – a few other calculations must precede. First off, the mass of the samples must be measured in order to calculate the number of moles. The method we used to determine the masses of the Mg and MgO samples is shown in Table 1:
Table 1: Masses of Mg and MgO samples mass of mass of sample + (mass sample + dish) -
Sample weighing dish weighing dish (mass weighing dish) Mass of Sample
Mg 5.122g 5.371g 5.371g – 5.122g 0.249g
MgO 5.122g 5.276g 5.276g – 5.122g 0.154g
Once the masses of the two samples were calculated, the number of moles for each sample could be determined; this was done by multiplying the mass of each sample by 1 mole over the samples molecular weight. Through this formula, we calculated that our sample of Mg contained 6.336 X 10-3 moles and our sample of MgO contained 6.178 x 10-3 moles. With the number of moles calculated, we then needed only one more value to utilize the enthalpy formula, which is derived from the heat transfer formula. The heat transfer formula determines the amount of heat that has been transferred within a reaction and also shows the direction in which it has been transferred. If the “q” value (heat transfer in Joules) is negative, then it indicates that heat has been released from the system into the surroundings, which makes it an exothermic reaction. Conversely, if the “q” value is positive, then the heat has been absorbed into the system from the surroundings – making it an endothermic reaction. The heat transfer formula is shown in equation 1 below:
Eq. 1 q = - (mass of mixture x specific heat capacity of water x Δ temperature (K))
The mass of the Mg/HCl mixture was recorded being 24.999g. The specific heat capacity of water is given and its value is 4.184JK‾¹g‾¹ (1). The last value needed to calculate the heat transferred is the change in temperature (ΔT), which can be determined by subtracting the intial temperature from the final temperature of the reaction. Such data was recorded by the LabPro interface and probe and was put on a graph. Figure 1 is the graph for the Mg/HCl reaction which shows the temperature change over the course of the reaction. What the graph demonstrates is a large increase in temperature indicating that the system is releasing a great deal of energy, which defines an exothermic reaction. Using equation 2 (below), the ΔT would equal 51.73(˚C) – 22.95(˚C) = 28.78(˚C).
Eq. 2 ΔT = T(final) – T(initial)
The ΔT value in the heat transfer formula is represented in the units of Kelvin (K). Even though the measured temperature levels would disagree between Celsius and Kelvin, the ΔT value will be consistent because they do rise and fall by the same factor – there is no calibration necessary; therefore, the ΔT of this experiment, as measured in Celsius, can be used in the heat transfer formula. Once we gathered all of the necessary data, we used equation 1 which is represented below: q = - (mass of mixture x specific heat capacity of water x Δ temperature (K)). q = - (24.999g x 4.184JK‾¹g‾¹ x 28.78K) q = - 3010.268 J
The results of the formula confirm is that the Mg/HCl reaction was an exothermic reaction which is indicated by the negative symbol.
Next we determined the heat transfer for the MgO/HCl reaction. The weight of the MgO/HCl mixture was recorded as being 26.071g. As Figure 2 shows, the initial temperature in the reaction was 30.56(˚C) and the final temperature was 23.14(˚C). Using equation 2, the ΔT for this reaction would result in the following: 30.56(˚C) – 23.14(˚C) = 7.42(˚C). Now, the heat transfer formula can be used to determine the amount of heat transferred within the MgO/HCl; the calculation follows: q = - (mass of mixture x specific heat capacity of water x Δ temperature (K)). q = - (26.071g x 4.184JK‾¹g‾¹ x 7.42K) q = - 809.381 J With the values from the mole calculations and heat transfer for the Mg and MgO reactions, the enthalpy of such reactions can be calculated and then be used to find the enthalpy of formation for MgO. The enthalpy is calculated with the units J/moles. Table 2 shows the method in which the enthalpies for the Mg and MgO reactions were discovered.
Table 2: The Enthalpy for Mg and MgO reactions

Number of Enthalpy J to kJ
Sample Heat Transfer (J) moles Calculation conversion Enthalpy Mg -3010.268 J 6.336E-3 mol -3010.268 J . .001 kJ - 475.105kJ/mol 6.336E-3 mol 1 J
MgO -809.381 J 6.178E-3 mol -809.381 J . .001 kJ - 131.010kJ/mol 6.178 E-3 mol 1 J Using the newfound enthalpy values for Mg and MgO, we applied Hess’s Law to derive the enthalpy of formation for MgO. One other value must also be incorporated into this equation which is the enthalpy of formation for liquid water; that is equal to – 285.967 kJ (2). In order to find the enthalpy of formation for MgO, we used the two reactions that we had performed, along with the enthalpy of formation of water, to cancel out all repeating terms until we were left with the equation 3 (the formation reaction of MgO):
Eq. 3 Mg(s) + ½O2(g) à MgO(s)
In order to cancel out like terms, one of the terms must be a reactant, and the other must be a product. If there is a repeating term that is only represented on one side of the reactions, one of the reactions can be reversed or “flipped” so that the reactants become the products and the products become the reactants. However, if this is done then the sign of the enthalpy value must also be switched between positive and negative – which is then switching the forward reaction between exothermic and endothermic. This idea is expressed through the thermodynamic cycle and allows us to narrow all three reactions down to one, which was the formation reaction for MgO (3). Table 3 (below) shows the formation reaction of water as well as both of the reactions as they occurred in the experiment before we utilized the principle of the thermodynamic cycle: Table 3 Eq.1) Mg(s) + 2HCl(aq) à MgCl2(s) + H2(g) ΔH = -475.105kJ
Eq.2) MgO(aq) + 2HCl(aq) à MgCl2(aq) + H2O(l) ΔH = -131.01kJ
Eq.3) H2(g) + ½O2(g) à H2O(l) ΔH = -285.967kJ

In the table above there are four repeating compounds that need to be canceled out in order to be left with the formation reaction of MgO. As stated earlier, in order to cancel out terms they must be on opposite sides of the equation. Three of the repeating terms all appear on the same sides of the equation. So, in order to cancel out these terms Equation 2 must be reversed and, subsequently, its enthalpy value must also be switch to a positive value. Table 4 below demonstrates this idea, and shows the reactions in their final forms in which like terms can be canceled, and the enthalpy of formation value for MgO can be found. This enthalpy value is found by adding up the enthalpy values of the three reactions. Table 4 illustates this further. Table 4 – Determining the Enthalpy of Formation for MgO
Eq.1) Mg(s) + 2HCl(aq) à MgCl(s) + H2(g) ΔH = -475.105kJ
Eq.2) MgCl2(aq) + H2O(l) à MgO(aq) + 2HCl ΔH = +131.01kJ Eq.3) H2(g) + ½O2(g) à H2O(l) ΔH = -285.967kJ Mg(s) + ½O2(g) à MgO(s) ΔH = - 630.062 With the completed formation equation for MgO, and a new value for its enthalpy, we now know that the formation of MgO is a exothermic reaction. When comparing the values between the ΔH(f) of water and the ΔH(f) of magnesium oxide, it is clear that in order to form one mole of MgO, the reaction releases twice the amount of heat as the amount of heat released when forming one mole of water. The theoretical value of the enthalpy of formation for MgO was given to be -601.8 kJ/mol. The data that our experiment collected resulted in the value -630.062 kJ/mol. In order to find the accuracy of this experiment and to prove the effectiveness of Hess’s Law, the percent error equation can be used which is represented in equation 4 below: Eq. 4 % actual value - theoretical value Error = theoretical value X 100
After using our actual value that was calculated and the theoretical value that was provided, we used the percent error formula and revealed a 4.70% discrepancy between the values.
The data received satisfied the purpose of the experiment for Part I. By performing two reactions and using the values for another, Hess’s Law was applied to find the enthalpy of formation for MgO. Our value for ΔH(f) of MgO was determined through only one process, Hess’s Law, but, Part II of the experiment is used to see the differences in data between the use of Hess’s Law and the actual values determined through performing the actual reaction.

4. Conclusion The procedures of both Part I and Part II of this experiment provided us with a great deal of information. In Part I of this experiment, the objective was to apply Hess’s Law to discover the enthalpy of formation for MgO, by using the enthalpy values from two other reactions. We were able to carry out this process and recorded a value that differed from the given value by 4.70%. Considering the amount of areas that were subject to incurring error, we were satisfied with our result.
Possible areas for error include the insulation for the reaction. Even though many accept Styrofoam cups as being good insulators, the fact is that they still allow heat to escape, whether it’s through the cup or through the imperfect seal at the top of the cup. Another factor that could have skewed the results is the lack of the ability to stir the reaction. A great catalyst for the reactions performed is stirring; however, because the calorimeter had to be sealed, the cup had to be carefully shaken, and could not produce the results that a stirred reaction could have. Human error also played a role in the slight offset of our results compared to the given values. Our calculations relied heavily on accurate data. When we measured the mass of our samples on the weighing dish it was accurate, but, some of the sample may have stayed on the weighing dish when we poured the sample into the calorimeter, lessening the true amount of sample actually reacting. Since each value affects the calculations and many of the calculations affect other calculations, a small degree of human error can have a large impact.
If another were to duplicate this experiment or perform some variation of it, the amount of error can be reduced. If one were to spend more time in the laboratory to perform these procedures, more attention and effort could be spent in making a tighter sealed top for the calorimeter and in handling of all samples and solutions. However, this experiment – as it was – did produce accurate results.
In Part II of this experiment the results were very precise, though it was performed under the same conditions as Part I. The procedure of Part II was designed to test the accuracy of Hess’s Law and to affirm its reliability. When Hess’s Law was used to calculate the enthalpy of the third reaction, it differed from the enthalpy value determined from performing the actual reaction by 0.52 kJ/mol. The percent error calculated for this part of the experiment using equation 4 was 0.97%.
What both parts of this experiment did was confirm the validity of Hess’s Law and provide comfort in its efficiency. In the application of Hess’s Law in coffee-cup calorimetry, the principles of heat flow in reactions and using their reverses in the thermodynamic cycle became animated and clear. The reassurance of the accuracy of Hess’s Law will allow confident analysis in studying the enthalpy values for reactions. 5. References
1. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 308.
2. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 322.
3. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 319.

References: 1. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 308. 2. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 322. 3. Siska, P. In University Chemistry; Conley, K.; Leung, L.; Smith, J.; Pearson, Benjamin Cummings: San Francisco, CA, 2006; p. 319.