Reactions in bioprocesses occur as a result of enzyme activity and cell metabolism.
During reaction, relatively large changes in internal energy and enthalpy occur as bonds between atoms are rearranged. Heat of reaction ΔHrxn is the energy released or absorbed during reaction, and is equal to the difference in enthalpy of reactants and products:
ΔHrxn5 X
products
Mh2X
reactants
Mh ð5:18ị
or
ΔHrxn5X
products
nh2X
reactants
nh ð5:19ị
where P
denotes the sum, M is mass, n is number of moles, and h is specific enthalpy expressed on either a per-mass or per-mole basis. Note that M and n represent the mass and moles actually involved in the reaction, not the total amount present in the system. In an exothermic reaction the energy required to hold the atoms of product together is less than for the reactants; surplus energy is released as heat and ΔHrxnis negative in value.
On the other hand, energy is absorbed during endothermic reactions, the enthalpy of the products is greater than the reactants, andΔHrxnis positive.
The specific heat of reactionΔhrxnis a property of matter. The value ofΔhrxndepends on the reactants and products involved in the reaction and the temperature and pressure.
Because any given molecule can participate in a large number of reactions, it is not feasible to tabulate all possible Δhrxn values. Instead, Δhrxn can be calculated from the heats of combustion of the individual components involved in the reaction.
5.8.1 Heat of Combustion
Heat of combustion Δhc is defined as the heat evolved during reaction of a substance with oxygen to yield certain oxidation products such as CO2gas, H2O liquid, and N2gas.
The standard heat of combustion Δhc is the specific enthalpy change associated with this reaction at standard conditions, usually 25C and 1 atm pressure. By convention, Δhc is zero for the products of oxidation (i.e., CO2gas, H2O liquid, N2gas, etc.); standard heats of combustion for other compounds are always negative. Table C.8 in Appendix C lists selected values; heats of combustion for other materials can be found inPerry’s Chemical Engineers’ Handbook[1]and CRC Handbook of Chemistry and Physics[2]. As an example, the standard heat of combustion for citric acid is given in Table C.8 as21962.0 kJ gmol21; this refers to the heat evolved at 25C and 1 atm in the following reaction:
C6H8O7ðsị14:5 O2ðgị !6 CO2ðgị14 H2Oðlị
Standard heats of combustion are used to calculate the standard heat of reaction ΔHrxn for reactions involving combustible reactants and combustion products:
ΔHrxn5X
reactants
nΔhc2 X
products
nΔhc ð5:20ị
where nis the moles of reactant or product involved in the reaction, and Δhc is the stan- dard heat of combustion per mole. The standard heat of reaction is the difference between the heats of combustion of reactants and products.
5.8.2 Heat of Reaction at Nonstandard Conditions
Example 5.6shows how to calculate the heat of reaction at standard conditions. However, most reactions do not occur at 25C and the standard heat of reaction calculated using Eq. (5.20)may not be the same as the actual heat of reaction at the reaction temperature.
Consider the following reaction between compounds A, B, C, and D occurring at tem- peratureT:
A1B!C1D
The standard heat of reaction at 25C is known from tabulated heat of combustion data.
ΔHrxnat temperature Tcan be calculated using the alternative reaction pathway outlined inFigure 5.6, in which reaction occurs at 25C and the reactants and products are heated
E X A M P L E 5 . 6 C A L C U L A T I O N O F H E A T O F R E A C T I O N F R O M H E A T S O F C O M B U S T I O N
Fumaric acid (C4H4O4) is produced from malic acid (C4H6O5) using the enzyme fumarase.
Calculate the standard heat of reaction for the following enzyme transformation:
C4H6O5!C4H4O41H2O Solution
Δhc50 for liquid water. FromEq. (5.20):
ΔHrxn5ðnΔhcịmalic acid2ðnΔhcịfumaric acid
Table C.8 in Appendix C lists the standard heats of combustion for these compounds:
ðΔhcịmalic acid5 21328:8 kJ gmol21 ðΔhcịfumaric acid5 21334:0 kJ gmol21 Therefore, using a basis of 1 gmol of malic acid converted:
ΔHrxn 51 gmolð21328:8 kJ gmol21ị21 gmolð21334:0 kJ gmol21ị ΔHrxn 55:2 kJ
AsΔHrxnis positive, the reaction is endothermic and heat is absorbed.
or cooled between 25C and T before and after the reaction. Because the initial and final states for the actual and hypothetical paths are the same, the total enthalpy change is also identical. Therefore:
ΔHrxnðatTị5ΔH11ΔHrxn 1ΔH3 ð5:21ị
whereΔH1and ΔH3are changes in sensible heat and ΔHrxnis the standard heat of reac- tion at 25C.ΔH1and ΔH3are evaluated using heat capacities and the methods described inSection 5.4.1.
Depending on the magnitude of ΔHrxn and the extent to which T deviates from 25C, ΔHrxnmay not be much different fromΔHrxn:For example, consider the reaction for respi- ration of glucose:
C6H12O616 O2!6 CO216 H2O
ΔHrxn for this conversion is 22805.0 kJ; if the reaction occurs at 37C instead of 25C, ΔHrxn is 22801.7 kJ. Contributions from sensible heat amount to only 3.3 kJ, which is insignificant compared with the total magnitude of ΔHrxn and can be ignored without much loss of accuracy. With reference toFigure 5.6,ΔH15 24.8 kJ for cooling 1 gmol glu- cose and 6 gmol oxygen from 37C to 25C; ΔH358.1 kJ for heating the products back to 37C. Having opposite signs,ΔH1andΔH3act to cancel each other. This situation is typi- cal of most reactions in bioprocessing where the actual temperature of reaction is not suffi- ciently different from 25C to warrant concern about sensible heat changes. When the heat of reaction is substantial compared with other types of enthalpy change, ΔHrxn can be assumed equal toΔHrxnirrespective of reaction temperature.
A major exception to this general rule are single-enzyme conversions. Because many single-enzyme reactions involve only small molecular rearrangements, heats of reaction are relatively small. For instance, per mole of substrate, the fumarase reaction ofExample 5.6 involves a standard enthalpy change of only 5.2 kJ; other examples are 8.7 kJ gmol21 for the glucose isomerase reaction,226.2 kJ gmol21for hydrolysis of sucrose, and229.4 kJ per gmol glucose for hydrolysis of starch. For conversions such as these, sensible energy changes of 5 to 10 kJ are clearly significant and should not be ignored. Furthermore, calcu- lated standard heats of reaction for enzyme transformations are often imprecise. Being the
A + B (T)
C + D (T)
C + D 25°C A + B
25°C
ΔHrxn
ΔH1 (Heat or cool A + B)
ΔH3 (Heat or cool C + D) ΔH2 = ΔH°rxn
Hypothetical path
(Standard reaction)
FIGURE 5.6 Hypothetical process path for calculating the heat of the reaction at nonstandard temperature.
difference between two or more relatively large heat of combustion values, the small ΔHrxnfor these conversions can carry considerable uncertainty depending on the accuracy of the heat of combustion data. When coupled with usual assumptions, such as constant Cpand Δhm within the temperature and concentration range of interest, this uncertainty means that estimates of heating and cooling requirements for enzyme reactors are some- times quite rough.