The purposes of these three experiments are to determine the heat capacity of a calorimeter and with that data, confirm Hess’s Law and observe enthalpy changes within reactions. By measuring the change in temperature that occurs with the interaction of two different reactants, we were able to determine both the calorimeter constant and the change in enthalpy of a given reaction. The results were rather mixed, as some numbers more closely resembled the theoretical values than others did.
The first experiment is devoted to finding the calorimeter constant for a polystyrene cup. Whenever a reaction takes place inside a calorimeter, some heat is lost to the calorimeter and its surroundings. In order to achieve maximum accuracy, we must know exactly how much heat will be lost, so that the results of the next two experiments will be as correct as possible. The equation used to determine it is a simple manipulation of the overall heat of the reaction equation, which is: Overall Heat = – [(Sp.Ht. hotwater * Mass of water * Change in temperature) + (Sp.Ht. coolwater * Mass of water * Change in temperature) + (Cp calorimeter * Change in temperature)] Since an error is bound to happen during the experimental process, three calculations were done to find an average. This experiment is vital to the success of the following two thermochemistry experiments.
The second experiment, entitled Hess’s Law, is a simple confirmation of said law. To do so, we take three reactions, where one of them is the same as the other two, and measure the heats of reaction for each of them. Hess’s Law states that the heat of reaction of the one reaction should equal to the sum of the heats of reaction for the other two. The three reactions used in this experiment are: (1) NaOH(s) Na+(aq) + OH-(aq)
(2) NaOH(s) + H+(aq) + Cl-(aq) H2O(l) + Na+(aq) + Cl-(aq) (3) Na+(aq) + OH-(aq) + H+(aq) + Cl-(aq) H2O(l) + Na+(aq) + Cl-(aq) In order to find the heat released by each reaction, we used a variant of the overall heat of a reaction equation, which was q = – [Sp.Ht. * m * Change in temp.]. In addition to finding the change in enthalpy, change in entropy was also calculated using theoretical values in given reference tables. Finally, the overall free energy released was calculated using the equation: Change in free energy = Change in enthalpy – (Temperature * Change in entropy). All of this is then used to verify Hess’s Law by calculating the percent error involved in the experiment.
The third experiment, called Thermochemistry: Acid + Base, combines the concepts of the previous two experiments. The main concept is to observe the change in enthalpy that results from the various reactions between strong and weak acids and bases. There were four reactions used in this experiment, and they are:
(1) HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l)
(2) HCl(aq) +NH3(aq) NH4Cl(aq)
(3) HC2H3O2(aq) + NaOH(aq) NaC2H3O2(aq) + H2O(l)
(4) HC2H3O2(aq) + NH3(aq) NH4C2H3O2(aq)
By monitoring the change in temperature that results from the reaction of an acid and a base, it is possible to calculate the overall energy for each reaction, also known as ∆H rxn/mole of limiting reactant. This experimental value can be compared with the theoretical to determine how accurate the experiment was. The lower the percent error, the more accurate we were at calculating the energy involved in each reaction.
In order to do any calculation for energy, we first had to find the calorimeter constant. In order to do that, we first took and weighed a polystyrene cup (our calorimeter) and added approximately 100 g of warm water to it. The actual measurements are recorded in Table 1-1. The mass of the cup with the water in it were recorded to find the exact mass of the water added. Next, a cylinder was weighed, like the cup, and about 48 mL of cool water was added. The total was weighed and recorded in the same table. Afterwards, temperature sensors connected through a LabPro device were suspended in the two containers and the calculator’s DataMate program was used to record temperature over a 90 second time interval. After a few seconds of data collection from the separate liquids, they were mixed together and stirred with the sensors until there was no time left. By using Graphical Analysis, a graph of the data was printed, displaying temperature vs. time. Tangent lines were drawn on the graph in order to determine the initial and final temperatures of the two liquids. The above procedure was repeated two more times for the sake of precision. Finally, we calculated the calorimeter constant using the formula listed in the Introduction section.
Even though we conducted an experiment to find the heat capacity of a calorimeter, we were given a new value for the constant for experiment 2, due to inaccuracy in our results. For the lab called Hess’s Law, we first started by setting up the calculator to collect temperature data again. The procedure is the same as the one used in the last experiment, except that the time interval is set to 4 minutes. Next, we obtain a polystyrene cup to use as our calorimeter and fill it with 100 g of water. The cup is placed within a 250-mL beaker to keep it in a sustained environment. A temperature sensor is placed in the water and is stabilized. Then, we obtained solid NaOH and weighed about 2 grams to the nearest thousandth decimal point. This value is recorded, along with all other data in Table 2-1. Afterwards, data collection begins and after about 15 seconds, the NaOH is added to the water. The resulting solution is stirred for the duration of the time interval and by using Graphical Analysis a graph is produced. This procedure is repeated twice more for 0.5 M HCl in place of water for one trial, and then 1.0 M HCl and 1.0 M NaOH solution for the third trial. All of the measurements are recorded in the table mentioned above.
For the final experiment, the procedure is very similar to its predecessors. We began by initializing the LabPro and DataMate to collect temperature data over time (this time it is a 180 second interval). First, we measure as close as we can to 50 g of a base of our choice in a 100-mL graduated cylinder. A temperature sensor is placed in the cylinder. Next, we weighed 100 g of a chosen acid in the calorimeter. The calorimeter is placed in a 1000-mL beaker for stability and a temperature sensor is submerged in the acid. After the sensors have a chance to equilibrate, we started to collect data. When about 15 seconds have passed, we poured the base into the calorimeter with the acid and stirred for the duration of the time with both sensors. Then, when time was up, we used Graphical Analysis to print the resulting temperature vs. time graph. This processed is repeated three more times until every combination of strong and weak acids and bases is used.
The data we recorded for the first experiment appears to be accurate, though drawing tangent lines to find final and initial points has its inherent inaccuracy. Using the formula discussed in the introduction, our equation turned out like the following:
0 = – [(47.166 g * 4.184 J/g°C * 16.561 °C) + (98.874 g * 4.184 J/g°C * -9.4139 °C) + (Cp calorimeter * -9.4139 °C)]
Cp calorimeter = -66.522 J/°C
The average of the three obtained values is as simple as adding them all together and dividing by three, the number of values, which looked like this: (-66.522 + 348.619 + 225.669)/3 = 169.255 J/°C. This number is much higher than the default value we were given for the next lab, which was only 15.0 J/°C.
For the Hess’s Law experiment, the numbers looked much better. The first thing we did with the data was solve for the change in temperature, which was just final temperature minus initial temperature. The result gave us something like this: 23.9 °C – 19 °C = 4.9 °C. Second, we calculated the heat released by each equation, which is shown as this: q = – [Sp.Ht. * m * ∆t]
q = – [4.18 J/g°C * 99.524 g * 4.9 °C]
q = -2.038 kJ
Then, the heat lost to the calorimeter was calculated using the formula q = – [Cp * ∆t]. From that, we found that q = – [15.0 J/°C * 4.9 °C] = -0.0735 kJ. Next, the total ∆H was found by adding both values of q above, which just equals -2.1115 kJ. In order to find ∆H/mol NaOH, we had to find how many moles were used in each reaction based on the mass of NaOH weighed and recorded in Table 2-1. The format for finding the number of moles looked like the following: 2.0810 g NaOH * (1 mol NaOH / 40 g NaOH) = 0.052 mol NaOH. This value is used to divide the ∆H to find the ∆H/mol NaOH value, which equaled -40.606 kJ/mol. Using the ∆H of Reaction 2 as the theoretical value, and the combined ∆H values of Reactions 1 and 3, we can find out our percent error, which is shown below as:
% error = abs ((theoretical – experimental) / theoretical) * 100
% error = abs ((79.56 – 94.87) / 79.56) * 100
% error = 19.24 %
The above values can all be found on Table 2-1. The above process was repeated with data collected from the whole class, which yielded a 14.47 % error. Finally, using theoretical numbers, we calculated ∆H, ∆S, and ∆G for reaction 2. For the first two, a similar equation of sum of products minus sum of reactants equals ∆H and ∆S respectively. ∆G is calculated using the formula in the introduction, which looked like ∆G = -98.8 – 298(0.0580) = -116.062 kJ/mol.
With the data collected in the third experiment a multitude of calculations were carried out. All of the following data can be found in Table 3-1. First, we solved for ∆H rxn, which is the same as the overall heat equation described in the introduction. The calculation looked liked the following:
∆H rxn = – [(4.184 J/g°C * 98.781 g * 4.35 °C) + (4.184 J/g°C * 48.5133 g * 4.0 °C) + (15.0 J/°C * 4.35 °C)
∆H rxn = -2.68 kJ
Next, we needed to calculate the limiting reactant for each reaction, which was just the reactant that yielded the least product. The method for determining it is like so:
98.781 g HCl * (1 mol HCl / 36 g HCl) * (1 mol NaCl / 1 mol HCl) * (1 g NaCl / 1 mol NaCl) = 2.744 g NaCl
48.5153 g NaOH * (1 mol NaOH / 40 g NaOH) * (1mol NaCl / 1 mol NaOH) * (1 g NaCl / 1 mol NaCl) = 1.213 g NaCl Then, we take the ∆H rxn above and divide it by the moles of limiting reactant, which we discovered above (since each solution is 1.0 M, the moles used is the number of grams divided by 1000). This new ∆H rxn / moles of limiting reactant is the experimental value to be
compared to the theoretical value obtained with given numbers. Comparing these two values using the % error equation above, the % error of one of the reactions comes out to be just 1.25%. The rest of the numbers can be observed in Table 3-2. This concludes all of the calculations that were involved in all of the experiments.
The results of this experiment were a mix of both very accurate and nowhere close. For the first experiment, the values for the calorimeter constant were very imprecise, ranging from negative values to ten times greater than the theoretical 15.0 J/°C. This is most likely due to a series of miscalculations and human error. In experiment two, the numbers were far more favorable, with a 19.24 % error for our data and a 14.47 % error for the entire class. This number still seems too high to justify the verification of Hess’s Law and should probably be redone with more care in consistently measuring reactants, but other than that, the experiment was completed well enough. The results for the final experiment are also quite mixed. While some experimental values had only a 1.25 % error, others were grossly erroneous with about 65.1 % error. The most inaccurate data was the ones collected for the reaction of a weak acid and a strong base, which yielded an obviously flawed 300 % error. For the results that were inaccurate, the source of error was most likely to due a miscalculation on my part, possibly in the calculation of the theoretical values, or the experimental for that matter. Much more care must be taken when repeating this lab, for the possible errors are numerous. The purpose of these three labs were to observe the nature of heat and reactions, which the experiments do rather nicely. The procedures described do an excellent job describing the purpose of each step, though they are easy to do incorrectly. In the end, the experiments yielded mediocre results, a mixed bag of incredibly accurate to just very wrong. Thermochemistry is indeed a rather elusive topic, but these experiments make it much more tangible.