2BC Wed. 6-10 PM Daniel WallaceJanuary 28, 2013

Demonstration of Basic Thermochemical Principles

Introduction:The objectives for this lab included calibrating a calorimeter, determining the heats of reaction for both a neutralization and precipitation reaction, observing the effect of varying reactant concentrations on reaction enthalpies, and demonstrating Hess’s law by measuring the heats of reaction for three related reactions.

Calorimeter calibration was carried out using the same method outlined in part 1 of technique lab #9. The calorimeter was then used to measure temperature change during reactions which made possible the calculation of reaction enthalpies. To demonstrate Hess’s law, reaction enthalpies were measured for two reactions and the reaction resulting from the addition of the first two. According to Hess’s law, the sum of the enthalpies of the first two reactions will equal the enthalpy of the third reaction.

Theoretical Basis:Styrofoam cups have very low thermal conductivity, so it is acceptable to assume very little heat escapes from the system over a short time interval if the system is at a relatively low temperature. This assumption means the calorimeter is treated as an isothermal system, so it is also assumed that the heat lost by the hot water is equal to the heat gained by the cold water and calorimeter. This relationship can be written in terms of known variables and the unknown Ccal, which can be solved for with basic operations.

The net ionic equation for the neutralization reaction between sulfuric acid and potassium hydroxide is

H+ (aq) + OH- (aq) → H2O (l) ∆H = -57.35 kJThe net reaction, which is also the standard neutralization reaction between a strong acid and base, has a negative enthalpy, meaning it releases heat to its surroundings. Since water is far more stable than separate hydrogen and hydroxide ions, it is easy to understand that the associated enthalpy is negative. Increasing concentration of the reactants means a greater amount of the reactants are present, so it follows that the heat released increases as concentration increases.The balanced equation for the reaction between sulfuric acid and potassium hydroxide is

H2SO4 (aq) + 2 KOH (aq) → K2SO4 (aq) + 2 H2O (l) ∆H = -111.8 kJ

The precipitation reaction used in part 1 isCa(NO3)2 (aq) + Na2CO3 (aq) → 2 NaNO3 (aq) + CaCO3 (s) ∆H = -5.5kJ

It is not immediately obvious that this reaction should be exothermic. However, the formation of a precipitate means some of the aqueous ions became solid, and since the ions move less freely in a solid, it is reasonable that some energy would be released during this process. The heat of

reaction is relatively small, so except at very high concentrations, the temperature change may be barely noticeable.In demonstrating Hess’s Law, the following three reactions were used:(1) 2 NaOH (aq) + CuSO4 (aq) → Na2SO4 (aq) + Cu(OH)2 (s) ∆H = -54.6 kJ(2) Ba(OH)2 (aq) + Na2SO4 (aq) → 2 NaOH (aq) + BaSO4 (s) ∆H = -19.1 kJ(3) Ba(OH)2 (aq) + CuSO4 (aq) → BaSO4 (s) + Cu(OH)2 (s) ∆H = -73.7 kJ

Enthalpies of reaction were calculated using known heats of formation for each product and reactant in the three reactions. As expected, the heat of reaction for equation (3) is equal to the sum of the heats of reaction of equations (1) and (2), according to Hess’s Law. It is highly likely that the experimental heats of reaction for the three equations above will be very close to their actual heats of reaction due to the difficulty in obtaining an accurate calorimeter calibration. However, the experimental reaction enthalpy of equation (3) should be roughly equal to the sum of the reaction enthalpies of equation (1) and (2), regardless of calorimeter calibration accuracy.

Changes to Procedure:-All 4.0 M samples of reactants in Part 1 of the lab were changed to 3.0 M concentrations.-A reaction was written with incorrect coefficients, coefficients were corrected.-For precipitation reaction, the 2.0 M trial was removed because higher concentrations were necessary to observe a change in temperature.

Observations: Calorimeter calibration -

•The two trials yielded heat capacities that were very close to one another.•Calibration data is more consistent than it was for technique lab #9.

Neutralization reaction - •As expected, temperature change is greater when acid/base samples are more concentrated•Calorimeter heats up, so reaction is exothermic

Precipitation reaction -•As concentration of reactants increases, amount of precipitate after reaction increases•Both the 1.0 M and 3.0 M reactions barely increased the temperature of the system. This is consistent with the small ∆H of the reaction•Reaction is slightly exothermic

Calculations:CCal, Trial 1:TM = 39.0 ˚C TH = 70.6 ˚C TC = 11.3 ˚C∆TC = TM - TC = 27.7 ˚C ∆TH = TM - TH = -31.6 ˚CmC = mH = 50.0 g Cs = 4.184 J˚C-1g-1

CCal = -(mH Cs ∆TH + mC Cs ∆TC) ÷ ∆TC CCal = 29.5 J˚C-1

CCal, Trial 2:TM = 41.8 ˚C TH = 71.6 ˚C TC = 15.2 ˚C∆TC = TM - TC = 26.6˚C ∆TH = TM - TH = -29.8 ˚CmC = mH = 50.0 g Cs = 4.184 J˚C-1g-1

CCal = -(mH Cs ∆TH + mC Cs ∆TC) ÷ ∆TC CCal = 25.2 J˚C-1

Average CCal:(29.5J˚C-1 + 25.2J˚C-1) ÷ 2 = 27.3 J˚C-1

Heat of Neutralization, Trial 1:TKOH = 24.1 ˚C TH2SO4 = 23.9 ˚C TAvg = 24.0 ˚C Cs = 4.184 J g-1˚ C-1

TAvg = TInitial TM = 35.1 ˚C CCal = 27.3 J˚C-1 msol = 150.0 g∆T = TM - TInitial = 11.1 ˚Cq = -(CCal ∆T + msol Cs ∆T) = -7.27 kJ∆H = -7.27kJ ÷ 0.1 mol H2O = -72.7 kJ mol-1

% error = (-72.7 – -111.8) ÷ 111.8 = 35.0%

Heat of Neutralization, Trial 2:TKOH = 22.1 ˚C TH2SO4 = 20.1˚C TAvg = 21.1 ˚C Cs = 4.184 J g-1˚ C-1

TAvg = TInitial TM = 41.7 ˚C CCal = 27.3 J˚C-1 msol = 150.0 g∆T = TM - TInitial = 20.6 ˚Cq = -(CCal ∆T + msol Cs ∆T) = -13.5 kJ∆H = -7.27kJ ÷ 0.2 mol H2O = -67.5 kJ mol-1

% error = (-67.5 – -111.8) ÷ 111.8 = 39.6%

Heat of Neutralization, Trial 3:TKOH = 24.2 ˚C TH2SO4 = 23.7 ˚C TAvg = 24.0 ˚C Cs = 4.184 J g-1˚ C-1

TAvg = TInitial TM = 55.3 ˚C CCal = 27.3 J˚C-1 msol = 150.0 g∆T = TM - TInitial = 31.3 ˚Cq = -(CCal ∆T + msol Cs ∆T) = -20.5 kJ∆H = -7.27kJ ÷ 0.3 mol H2O = -68.3 kJ mol-1

% error = (-68.3 – -111.8) ÷ 111.8 = 38.9%

Heat of Precipitation, Trial 1:TInitial = 18.3 ˚C TM = 18.3 ˚C M = 1.0 mol/L∆T = TM - TInitial = 0 ˚Cq = -(CCal ∆T + msol Cs ∆T) = 0 kJError: 5.5 kJ (% error = 100%)

Heat of Precipitation, Trial 2:TInitial = 18.3 ˚C TM = 23.0 ˚C M = 3.0 mol/Lmsol = 100.0 g Cs = 4.184 J g-1˚ C-1 CCal = 27.3 J˚C-1

∆T = TM - TInitial = 4.7 ˚Cq = -(CCal ∆T + msol Cs ∆T) = -2.23kJ∆H = -2.23kJ ÷ 0.3 mol Ca(NO3)2 = -7.43 kJ mol-1

% error = (-7.43 – -5.5) ÷ -5.5 = 35.1%

Demonstration of Hess’s Law:Calculations cannot be carried out because time expired before this part of the experiment was completed.

Discussion:Two trials were carried out for the calibration of the calorimeter. The first and second trials produced heat capacities of 29.5 J˚C-1 and 25.2 J˚C-1, respectively. These values deviate only slightly from the average heat capacity, 27.3 J˚C-1, so the average can be reasonably used as the calorimeter’s heat capacity for the rest of the experiment. Further trials were not carried out because the first two provided an acceptable heat capacity.

Finding the heat of neutralization for the reaction between sulfuric acid and potassium hydroxide was carried out in three trials. All trials were carried out with the same parameters except for the reactant concentration. Concentrations of 1.0 M, 2.0 M, and 3.0 M correspond to trials 1, 2, and 3. As expected from the theoretical neutralization enthalpy, energy released by the reaction increased as the concentration of reactants increased. This must be true because the change in temperature increased as concentrations increased, and heat released by the reaction is directly related to the temperature increase of the calorimeter. The experimental values for the heat of neutralization had very large percent errors, suggesting the results were inaccurate. However, the percent error was similar across all trials, meaning the procedure produced precise results. Inaccurate, precise results suggest that a source of error affected all three trials in a similar way.

The exothermic reaction between calcium nitrate and sodium carbonate has a very small reaction enthalpy, so the experimental heat of precipitation was very difficult to calculate because the change in temperature is so small. For the first and second trials the reactant concentrations were 1.0 M and 3.0 M, respectively. When the sodium carbonate was added to the calorimeter containing sodium carbonate in trial 1, the temperature unexpectedly decreased slightly. This was unexpected because the process is exothermic, despite releasing only a small amount of energy. It is possible that the newly formed precipitate prevented the solution from mixing evenly,

resulting in poor temperature readings for a short duration. Still, there is no easy way to explain the drop in temperature, especially since the sodium carbonate, added second, was warmer than the calcium nitrate by 1.4 ˚C. The second trial was more reasonable, and did a far better job of calculating the heat of precipitation. Between trial 1 and trial 2, percent error dropped by 64.9%. The increase in accuracy suggests that higher reactant concentrations minimize the impact of experimental error by increasing the amount of heat released by the reaction.

Results for the demonstration of Hess’s Law (part 2) are unavailable because the end of the allotted time for the experiment was reached before the lab was completed. However, based on the results from earlier in the experiment, much can be said about what kind of results would be expected for the reactions that were to be carried out for this part.

As shown in the theoretical basis above, all three reactions that were to be used for the demonstration of Hess’s law are exothermic reactions. Calculating the experimental reaction enthalpies would follow the same procedure as that used to calculate the heats of neutralization in part 1. A significant systematic error affected the calculated heats of neutralization, so this error would likely affect the enthalpy calculations for the three reactions in a similar way. Therefore, we can expect the calculated heats of reaction for all three equations to be smaller than their corresponding theoretical heats of reaction. Since the main error that would affect the results is systematic, not random, the sum of the calculated enthalpies for reaction (1) and (2) would likely be very close to the calculated enthalpy for reaction (3).

Conclusion:Several sources of error had an impact on the results of this experiment. A systematic error caused all experimental heats of neutralization to be offset from the theoretical values by 35-40%. An inaccurately calibrated calorimeter is likely the cause of the systematic error, because it would affect all calculations in the same way. Random errors include the limited accuracy of measuring equipment like beakers and mass balances, which likely had a small impact on the results. It is also worth noting that this experiment assumed that reactant solutions had the same density and specific heat as those of water. Because these assumptions are not actually true, they could have negatively influenced the accuracy of the results.

If this experiment were to be carried out again, it would be beneficial to try to eliminate the systematic error caused by an inaccurate calorimeter heat capacity. Either significantly increasing the number of trials used in calibration or redesigning the calorimeter used in the lab could greatly improve experimental results. Additionally, determining the true density and specific heat of solutions used in the lab could help make calculations more accurate. Seeing as all measuring equipment have limited accuracy, little could be done to eliminate this source of error.

One change to the procedure that could also improve results is increasing the volume of solutions used in reactions. Increasing volume increases the amount of reactants used and thus increases the heat released for each reaction. This would allow the calorimeter to come to equilibrium more quickly, which would reduce the impact of random errors on the data.