Solution Calorimetry
Jenny Lee Petrauskas
Jon Weiss
Lilia Zhahalyak
Chem 309L
Lab #5
10/19/06
Abstract:
The enthalpy changes as a result of the first and second protonations of glycine were determined using solution calorimetry. This was accomplished by measuring the heat absorbed or released when a known amount of glycine was added to hydrochloric acid, sodium hydroxide, and sodium chloride in a calorimeter. Using this data, it was possible to find the enthalpy changes, which were 1,266 cal/mol and 10,936 cal/mol for the first and second protonations respectively. These values were then compared to theoretically calculated enthalpy changes and the percent error was found to be 7.56% and 6.56% respectively.
Introduction1:
Heat effects are an essential aspect to understanding chemical reactions. The study of such effects of is known as calorimetry, and the two most common types are constant volume and constant pressure calorimetry. In this experiment the change in heat during the reaction was manipulated into enthalpy. The acid-base reactions of glycine, create changes in enthalpy that can be used to determine the molar enthalpies of the two stages of glycine proton-transfer, as detailed in Equations 1 and 2, where HGly+- represents the zwitter ion (+H3NCH2COO-).
H2Gly+ = H+ + HGly+- (zwitter ion) (1)
HGly+- = H+ + Gly-(2)
Since the molar enthalpies of the two reactions above (ΔHI and ΔHII) cannot be measured directly, four individual reactions were considered to determine ΔHIand ΔHII indirectly. The first equation is the protonation of glycine as the result of a reaction with a strong acid, as in Equation 3, where the change in enthalpy is denoted ΔHA.
HGly+-(s) + H+→ H2Gly+(aq)(3)
The secondequation is the transition in state from solid to aqueous glycine as the result of a reaction with a salt, as in Equation 4, where the change in enthalpy is denoted ΔHB.
HGly+-(s) → HGly+-(aq)(4)
The third equation is the formation of water from the reaction between glycine and a strong acid, as in Equation 5, where the change in enthalpy is denoted ΔHC.
HGly+-(s) + OH-→ Gly- + H2O (5)
Finally, the last equation is the formation of water from protons and hydroxide ions, as seen in Equation 6, where the heat of formation of water is denoted ΔHD.
H+ + OH- → H2O(6)
The value of ΔHD for the above reaction is -13,340 cal when there is no ionic strength and -13,550 cal when there is 0.5 ionic strength1. Since it was assumed that there was little effect of ionic strength in this experiment, an averaged value of -13,465 cal was used for ΔHD in all calculations.
The four reactions in Equations 3-6 were taken into account in this experiment because their changes in enthalpy are easy to measure in the laboratory and as a result of simple algebra they can be manipulated to result in Equations 1-2, the reactions that are being investigated. Subtracting Equation 4 from Equation 3 yields Equation 1, and consequently the difference in their enthalpies, ΔHI, can be determined by the following equation:
ΔHI = ΔHB– ΔHA(7)
Likewise, subtracting Equations 4 and 6 from Equation 5 yields Equation 2, and thus ΔHII may be found by a similar manipulation reflected below:
ΔHII = ΔHC – ΔHB–ΔHD(8)
The equilibrium constants for the desired two reactions were reported in the literature as least squared fits as in the following equations:
pK1 = -46.7920 + 2378.22T-1 + 16.64 log(T)(9)
pK2 = -16.1083 + 3165.76 T-1 + 6.09 log(T)(10)
Using the thermodynamic relationship in Equation 11, the literature values of ΔHIand ΔHII were calculated as follows, where R was the universal gas constant (1.98721 calK-1mol-1) and T was the temperature (293.55 K). From these equations, the literature values of ΔHIand ΔHII were determined to be 1279.8 cal/moland 10935.7 cal/mol.
d lnK/dt = ΔH/RT(11)
ΔHI = R(2378.22)(2.303)-16.464RT(12)
ΔHII = R(3165.76)(2.303)-6.09RT(13)
Experimental1:
Before beginning the experiment, the Parr 1455 Solution Calorimeter was standardized using tris (hydroxymethyl) aminomethane (Parr; P/N 3421 #CS084; CAS #77-86-1). 0.5009(+/-0.0001) g (4.135 +/- 0.083 mmols) of TRIS weremeasured onto a 126C Teflon Dish and covered with a glass bell. Meanwhile 100.0(+/-0.2)ml of 0.1 N HCl (Fisher Scientific; Lot #062895-24) were carefully measured by weight into a Dewar flask. The flask was placed into the calorimeter, followed by the sealed Teflon dish connected to a glass rod. Once the rotating cell was assembled the motor was begun by setting *101 to 1. The calorimeter was then allowed to come to equilibrium, which was monitored using the Scientific Workshop Program (V 2.3.3; Pasco Scientific; Interface SW500 – 1.0). Using this program, the thermometer was set to 20.25°C and the variance was set at 0.5°C, with the baseline positioned near the bottom of the chart, since the reaction was expected to be exothermic. The program was started and once the system was at equilibrium the reactants were combined by pushing the rod down, and when the calorimeter returned to equilibrium the program was ended. The data acquisition system monitored voltage (millivolts) as a function of time. This is applicable since voltage is linear to temperature when the changes in temperature are small, as in this experiment.
In order to calculate the energy change Q of a system, it is essential to take into account the energy equivalent of the calorimeter and its contents. Thus the resulting thermogram was analyzed to determine the net corrected temperature rise, ΔTC(from the extrapolated values of Tf and Ti). Using this value, the known energy input of the system was determinedfrom the following equation, where QE is equivalent to the energy input (in calories), m is the weight of the TRIS (in grams), and T0.63R is the temperature at the 0.63R point of the thermogram (in kelvins).
QE = m[58.738 + 0.3433(25 - T0.63R)] (14)
Once QEwas determined, it was used to find e, the energy equivalent of the calorimeter (in calories/°C), as in the following equation:
e = QE / ΔTC(15)
The energy equivalent of the empty calorimeter was then calculated by taking the difference between the empty calorimeter and the heat capacity of 100 g of 0.100 N HCl as follows, where e’ is the energy equivalent of the empty calorimeter (in calories/°C):
e’ = e – (100.00)(0.99894)(16)
Once the energy equivalent of the calorimeter was determined, the calorimeter cell was prepared to collect experimental data. First 100.0(+/-0.2) ml of 0.3 N hydrochloric acid was measured by weight into the Dewar flask [prepared by combining 30 ml of1 N hydrochloric acid (Fisher Scientific; Lot #062895-24) in a 100 ml volumetric flask and filled to the mark with distilled deionized water] and 1.5040 (+/- 0.0001) g (20.035 +/- 0.133 mmol) of glycine (Fisher Scientific; Lot #990475) were weighed into the solid sample compartment. The Scientific Workshop Program was again employed, this time using an initial temperature of 25.05°C and a variance of 0.5°C. The baseline was set near the top of the chart since the reaction was expected to be endothermic. The resulting thermogram was then used to calculate ΔHA, the change in enthalpy of a proton-transfer for the reaction in Equation 3 above.
The same procedure was then repeated using 100.0 (+/- 0.2) ml 0.3 N sodium chloride [prepared by combining 1.7518 (+/- 0.0001) g sodium chloride (Acros 99+%; Lot #B011-1766A) in a 100 ml volumetric flask and filling to the mark with distilled deionized water] and 1.5013 (+/- 0.0001) g (19.999 +/- 0.133 mmol) of glycine, at an initial temperature of 20.4°C and a variance of 2°C. The resulting endothermic thermogram was then used to calculate ΔHB for the reaction in Equation 4 above.
Finally the procedure was repeated a third time using 100.0 (+/- 0.2) ml 0.3 N sodium hydroxide [prepared by combining 30 ml of 1 N sodium hydroxide (Fisher Scientific; Lot #063179-24) in 100 ml of distilled deionized water in a volumetric flask] and 1.5037 (+/- 0.0001) g (20.003 +/- 0.133 mmols) of glycine, at an initial temperature of 20.7°C and a variance of 0.3°C. The resulting endothermic thermogram was then used to calculate ΔHC for the reaction in Equation 5 above.
As discussed above, the molar enthalpies of the two stages of glycine proton-transfer can be determined by subtracting the appropriate change in enthalpy values. Thus Equations 7 and 8 were employed to determine the experimental molar enthalpies of the two stages of glycine proton-transfer.
ΔHI = ΔHA – ΔHB(7)
ΔHII = ΔHC – ΔHA – ΔHD(8)
The experimentally obtained values for the molar enthalpies of the two stages of glycine proton-transfer were then compared to the literature values using a percent difference calculation as in the following equation:
% Difference = [Theoretical-Experimental]*100/Theroretical(17)
Results:
The data was collected by plotting voltage as a function of time (Figures 1-4). The correlation between voltage and temperature was a known value for each graph. The calorimeter was first standardized by measuring a reaction with a known change in heat. Tris (hydroxymethyl) aminomethane was reacted with 100 ml of 0.1 N HCl and had a known change in energy of 58.738 cal/g (Figure 1).
Figure 1:Tris Standardization. Each volt represents 0.05 oC.
The heat effects of the reaction of approximately 20 mmols of glycine with 0.3 N HCl, NaCl, and NaOH were then measured (Figures 2-4).
Figure 4:Glycine reacted with HCl: Each volt represents 0.05 oC.
Figure 2:Glycine reacted with NaCl.Each volt represents 0.20 oC.
Figure 3:Glycine reacted with NaOH: Each volt represents 0.03 oC.
Using the graphs above, it was then possible to extrapolate the change in temperature for each reaction, as seen in Table 2 below:
ΔT/Volt (K/V)(+/- 0.05) / ΔV (V)
(+/- 0.007) / ΔT (K)
(+/- 0.007)
Tris / 0.05 / 5.335 / 0.2668
NaCl / 0.20 / -2.550 / -0.5100
NaOH / 0.03 / -2.560 / -0.0768
HCl / 0.05 / -6.600 / -0.3301
Table 2: Change in temperature for each reaction.
The energy equivalent of the calorimeter was then determined using tris (hydroxymethyl) aminomethane, which had a known heat change. The energy equivalent wasfound to be 140.7 cal/ oC. The change in heat and energy was then calculated for each reaction, and tabulated in Table 3 below:
T at .63R(oC) (+/- 0.05) / Q(cal) / ΔH (cal/mol)NaCl / 22.77 / -71.75 / 3588
NaOH / 20.62 / -6.81 / 340.4
HCl / 19.72 / -46.43 / 2321
Water / -13465
Table 3: Calculated change in heat and entropy values, using e= 140.7 cal/ oC.
The data for the reactions were then used to determine the changes in enthalpy for the first and second protonations of glycine, as shown in Table 4:
Protonation / ΔH / Theoretical ΔH / Error / Theoretical pKFirst / 1266 / 1177 / 7.56% / 2.372
Second / 10218 / 10936 / 6.56% / 9.704
Table 4: Change in entropy for the first and second protonations of glycine.
Error Analysis:
Two types of errors were analyzed at the end of the experiment: errors in measured values and errors in calculated values. Measured values in the experiment include measurements made on the balance (accurate to +/- 0.0001 g), 50 ml volumetric pipet (accurate to +/- 0.05 ml), 100 ml volumetric flask (accurate to +/- 0.16 ml), and calorimeter (accurate to 100 mV per degree). Errors were propagated through the following equations, where σ is the error of a measured value.
%σx = (σx/x) * 100(18)
z = x +/- y; σz = √ (σx2 + σy2)(19)
z = x */÷ y; σz= z * √ [(%σx)2 + (%σy/y)2](20)
Discussion:
The heat effects accompanying the acid base reactions of glycine revealed that dissociation of solid glycine in aqueous environment under basic and acidic conditions are endothermic and absorb heat when reacted with 0.3 N HCl and 0.3 N NaOH at an ionic strength of 0.3 N NaCl. The values of the molar enthalpies ∆HI(1266 cal/mol or 1.27 kcal/mol) for the first loss of proton and ∆HII(10218 cal/mol or 1.02E1 kcal/mol) for the second loss of proton of glycine were experimentally measured from the heat change (Q). The values of Q were calculated by using the net corrected temperature change ∆T determined from the reaction thermograms and the energy equivalent, e, of the calorimeter and its contents.
The experimentally determined molar enthalpy values were compared to the theoretical enthalpy values calculated from Equation 9 where ∆HIwas 1177 cal/mol or 1.18 kcal/mol, and from Equation 10 where ∆HIIwas 10936 cal/mol or 1.09E1 kcal/mol.2 The percent differences of the experiment were found to be 7.6% and 6.6% respectively, when experimental molar enthalpy values ∆HI and ∆HIIwere compared to the theoretical values. The magnitude of error obtained upon comparison could be explained by the measurement errors associated with the experimental procedure. Incorrect extrapolation of the baseline for the initial and final temperature values could lead to the erroneous values for the net corrected temperature ∆T and T0.63R. The standardization procedure with TRIS could be considered another source of experimental error, leading to an incorrect value of T0.63R tris, and, consequently, to the experimentally obtained values of QEand the energy equivalent, e.
The study of glycine proton transfer enthalpies ∆HIand ∆HII promotes an understanding of the heat change associated with these acid dissociation reactions. It has to be noted that the calculated enthalpy changes are not the standard values since the experiments were carried out at electrolyte concentration of 0.3 M NaCl, although the effect of ionic strength on the values obtained was assumed to be small.1-2 The experimentally obtained values for the molar enthalpies were reasonably close to the reference values reported by King 2, therefore proving that the employed experimental method provided an effective way to evaluate the molar enthalpies for two stages of proton transferof amino acid glycine under aqueous acid base conditions.
References:
1.)Ramette, R. W. J. Chem. Educ. 1984, 61, 76-77.
2.)King,E. J. J. Am. Chem. Soc.1951,73, 155-159.
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