Measuring Heats of Reaction

The heat capacity will depend on whether the process is constant-pressure or constant-volume. We will assume a constant-pressure process unless otherwise stated. 

So far we have introduced the concept of heat of reaction and have related it to the enthalpy change. We also showed how to display the enthalpy change in a thermochemical equation, and from this equation how to calculate the heat of reaction for any given amount of substance. Now that you have a firm idea of what heats of reaction are, how would you measure them  

we need to look at the heat required to raise the temperamre of a substance, because a thermochemical measurement is based on the relationship between heat and temperature change. The heat required to raise the temperature of a substance is called its heat capacity. 

Heat is required to raise the temperature of a given amount of substance, and the quantity of heat depends on the temperature change. The heat capacity (C) of a sample of substance is the quantity of heat needed to raise the temperature of the sample of substance one degree Celsius (or one kelvin). Changing the temperature of the sample from an initial temperature t, to a final temperature tf requires heat equal to 

Suppose a piece of iron requires 6.70 J of heat to raise the temperature by one degree Celsius. Its heat capacity is therefore 6.70 J/°C. The quantity of heat required to raise the temperature of the piece of iron from 25.0°C to 35.0°C is 

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Since AH is proportional to the area of the DTA peak, one ought to be able to measure heats of reaction directly, using the equation 7.1.22. Indeed we can and such is the basis of a related method called Differential Scanning Caloiimetiy (DSC), but only if the apparatus is modified suitably. We find that it is difficult to measure the area of the peak obtained by DTA accurately. Although one could use an integrating recorder to convert the peak to an electrical signal, there is no way to use this signal in a control-loop feed-back to produce the desired result. 

Consequently, if the reaction enthalpy is unknown for a given process, the quantum yield must be determined from other measurements. Conversely, if the reaction enthalpy is known, then the quantum yield for the photochemical reaction can be measured. PAC has been used to obtain quantum yields for excited state processes, such as fluorescence, triplet state formation, and ion pair formation and separation. In systems in which competitive reactions occur, care must be taken to accurately account for the partitioning. For example, if a reactive intermediate yields two products, then the measured heat of reaction is the sum of the two individual heats of reaction multiplied by their respective yields. Consequently, there are three unknowns, the partitioning and the individual heats of reaction. Two of them must be known to properly evaluate the third. 

The design and operation of solution calorimeters is an extensive topic. Reference (125) reviews modem calorimetry and identifies earlier discussions. The thermometric titration type of calorimeter has been perfected during the past fifteen or twenty years. It is especially useful for measuring heats of reaction that take place in several steps. The availability of advances in thermometry has had a major effect on calorimetry. 

DSC measures the amount of heat released by a sample as the temperature is increased or decreased at a controlled uniform rate, and so can investigate chemical reactions and measure heats of reaction for phase changes (Figure 2.30). 

Calorimeters are devices that measure heat of reactions (enthalpy change). In the adjoining figure, a bomb calorimeter is shown. It is so called because the reaction occurs in a steel container at the center of the calorimeter, that is known as a bomb . The bomb is inserted in another container filled with water and isolated. The compound is then inserted in a bomb and ignited by electricity. The heat released by the combustion of the compound in the bomb warms up the water. In other words, the heat produced by the combustion of the compound is absorbed by the bomb and the water. For this reason. 

Arnett and Hofelich measured heats of reaction of a variety of alcohols with SbF5/FS03H in sulfuryl chloride fluoride to form their respective carbocations at constant temperature (-40 °C). In this superacid medium there were no ion-pair complications126 and hence reliable calorimetric data were obtained for various cyclopropyl and phenyl substituted cations. The heats of reaction for the formation of tricyclopropylcarbinyl cation (-59.2 kcalmol ), trityl cation (-49.0 kcalmol1) and ferr-butyl cation (-35.5 kcalmol1) show that the relative order of the stabilization of the cationic center is cyclopropyl >... 

A calorimeter is a device that insulates a reaction from the external environment. It can be used to measure heats of reaction. 

We can use specific heat calculations to measure heats of reaction. 

You have thus calculated the desired heat of reaction, which could not be measured directly, from two measurable heats of reaction. 

While activation energies have been published for many isocyanate/ alcohol reactions, relatively few reports have been made of the heat of reaction. Bayer [136] reported a heat of reaction of 52 kcal mole , or 26 kcal equiv", for the hexamethylene diisocyanate/1,4-butanediol reaction. Lovering and Laidler [137] measured heats of reactions for the butyl alcohol isomers with several aromatic isocyanates. Values ranged from 18.5 to 25 kcal equiv . ... 

I See the Saunders Interactive General Chemistry CD-ROM, Screen 6.10, Heat Transfer Between Substances, and Screen 6.1 8, Measuring Heats of Reaction Caiorimetry. 

A coffee-cup calorimeter (Figure 15-3) is often used in laboratory classes to measure heats of reaction at constant pressure, q, in aqueous solutions. Reactions are chosen so that there are no gaseous reactants or products. Thus, all reactants and products remain in the vessel throughout the experiment. Such a calorimeter could be used to measure the amount of heat absorbed or released when a reaction takes place in aqueous solution. We can consider the reactants and products as the system and the calorimeter plus the solution (mostly water) as the surroundings. For an exothermic reaction, the amount of heat evolved by the reaction can be calculated from the amount by which it causes the temperature of the calorimeter and the solution to rise. The heat can be visualized as divided into two parts. 

In 1949/1950 Iliceto and Malatesta28 reported the heat of reaction 13 of aqueous acetone (27a) and NaHS03 to form sodium 2-hydroxy-2-propanesulphonate (27b) as 12.7 kcalmol-1. We have earlier suggested (see Section II.C) that the difference between the heat of formation of an aqueous solution of XCH2S03Na and of XMe is nearly a constant, ca 203 2 kcal mol - From AHf( q, i-PrOH), we would predict that the heat of formation of the aqueous sulphonate is — 76 + (— 203) = — 279 kcal mol-1. From AHf(lq, Me2CO), AHf(aq, NaHS03) and the measured heat of reaction 13, we find a value of - 59.3 + (- 207.1) + (- 12.7) = - 279.1 kcal mol - ... 

Based on the known heats of formation for NaOH(aq), NaCl(aq), NaBr(aq), Nal(aq), and ZrCUCcr), the author studied the heats of formation of ZrBr4(cr), Zrl4(cr). He used two independent methods the dissolution of the Zr-halides in excess NaOH solutions and dissolution in H2O. Molar ratios of Zr-halide to the aqueous medium were always 1/1500. Corrections of the measured heats of reactions for Hf contents of 1.7% in Zr phases were determined but were found to be within the error of the method. The solid Zr halide samples were prepared by halogenation of metals (X = Br, I) or carbides (X = Cl). The Zr/X ratio in these phases was not analysed for X = (Br, I), but literature data were invoked to show that the ratio is A. For the iodide, the Zr content in the solid was analysed to be within 0.05% of the theoretical value of IZ. 

From the reported molar ratio Zr-halide/water we can calculate a molality of 0.037 m in Zr. Based on the present evaluation of the available hydrolysis and polymerisation data it cannot be accepted that monomeric species are formed, but polymeric species or colloids have to be considered to be dominant. The reported Af//° for ZrOOH of - 1132.6 kJ-moP is therefore not retained in the review. In contrast, by comparison of the measured heats of Reaction (A.3) both for X = Cl (with known values for Af//° (ZrCU, cr, 298.15 K)) with those for X = (Br, I), the unknown data for AfH° (ZrX4, cr, 298.15 K) can be determined reliably even if the stoichiometry of the dissolved or colloidal hydrolysed species is not known. The results for Reaction (A.3)... 

The thermodynamic parameters for the formation of several metal-cyanide complexes, among others those of Ni(CN)4 , have been determined using pH-metric and calorimetric methods at 10, 25 and 40°C. In case of nickel(II), the thermodynamic data were determined by titration of Ni(C104)2 solutions with NaCN solutions. The ionic strength of the solutions were 1 < 0.02 M in all cases. The Debye-Huckel equation, related to the SIT model, was used to correct the formation constants to thermodynamic constants valid at 7 = 0. Since previous experiments indicated that the dependence of A,77° in the ionic strength in dilute aqueous solutions is small compared to the experimental error, the measured heats of reaction (A,77 = - 189.1 kJ mol at 10°C A,77 ,= -183.7 kJ mol at 40 C) were taken to be valid at 7 = 0, but the uncertainties were estimated in this review as 2.0 kJ moT. From the values of A,77 , as a function of temperature, average A,C° values were calculated. 

If any of the reactants or products of the calorimetric reaction are gaseous, it is necessary to conduct the reaction in a sealed bomb. Under this condition the system is initially and finally in a constant volume rather than being under a constant pressure. The measured heat of reaction at constant volume is equal to an energy increment, rather than to an enthalpy increment ... 

When performing such DoEs, the use of automated laboratory reactors is highly recommended. In addition to having recipe capabilities and agitation and temperature controls, they also have data acquisition and analysis modules. Eor example, the Mettler Toledo RCI (reactor calorimeter) is an automated laboratory reactor capable of measuring heats of reaction. Such measuranents are important in mechanistic investigations and safety evaluations. We also believe that after the development chemist, reaction calorimetry is the development engineer s best Mend. 

Before turning to these topics in more detail, some of the experimental methods which are currently being used to measure heats of reaction will be briefly described. Recent developments in experimental methods have been reviewed by Skinner< and the details of techniques used in combustion calorimetry, in particular, have been very fully described in Sxperimenfai Thermochemistrp K What follows here is intended, therefore, to give only an idea of the types of apparatus which have been used to obtain the data presented in subsequent chapters ... 

For many polymerization reactions the entropy changes have been either measured or calculated, and from these, combined with the measured heats of reaction, the free energies of polymerization can be calculated. From these data it is possible to determine the extent to which polymerization occurs, and the relative influence of the heat and entropy effects on the reaction equilibrium. 

Heat of reaction for the main and other side reactions. All main and side reactions that could occur in the reaction mixture should be identified, and the heat of reaction of each one of these reactions should be estimated. There are a number of techniques available for measuring heat of reaction, including calorimetery, plant heat and energy balances for processes already in operation, analogy with similar chemistry, literature sources, supplier knowledge, and thermodynamic estimation techniques. 

From the measured heat of reaction of Ph2Hg with iodine, and with Hgl2 28, 76), and Smith s value 160) for AH (Phi, liq) = 27.36 0.5 kcal/mole, the value AH (Ph2Hg, c) = 66.7 + 1 kcal/mole is derived. 

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