Change in enthalpy can occur as a result of:
1. Temperature change 2. Change of phase 3. Mixing or solution 4. Reaction
In the remainder of this section we will consider enthalpy changes associated with (1), (2), and (3). We will then consider how the results are used in energy balance calculations.
Processes involving reaction will be discussed inSections 5.8 through 5.11.
5.4.1 Change in Temperature
Heat transferred to raise or lower the temperature of a material is called sensible heat;
change in the enthalpy of a system due to variation in temperature is called sensible heat change. In energy balance calculations, sensible heat change is determined using a property of matter called the heat capacity at constant pressure, or just heat capacity. We will use the
H2O2 35°C
O2 + H2O 35°C
O2 + H2O 25°C H2O2
25°C
Actual path ΔH
ΔH2 ΔH1
(Cool reactant)
ΔH3
(Heat products)
(Reaction at 25°C)
Hypothetical path
FIGURE 5.2 Hypothetical process path for calculation of enthalpy change.
symbolCpfor heat capacity; units forCpare, for example, J gmol21K21, cal g21C21, and Btu lb21 F21. The term specific heat capacity or specific heat is sometimes used when heat capacity is expressed on a per-unit-mass basis. Values for heat capacity must be known before enthalpy changes from heating or cooling can be determined.
Tables C.3 through C.6 in Appendix C listCp values for several organic and inorganic compounds. Additional Cpdata and information about estimating heat capacities can be found in references such as Perry’s Chemical Engineers’ Handbook [1], CRC Handbook of Chemistry and Physics[2], andInternational Critical Tables[3].
There are several methods for calculating enthalpy change using Cpvalues. When Cpis approximately constant, the change in enthalpy of a substance at constant pressure due to a change in temperatureΔTis:
ΔH5MCpΔT5MCpðT22T1ị ð5:12ị
whereM is either mass or moles of the substance depending on the dimensions of Cp, T1 is the initial temperature, and T2 is the final temperature. The corresponding change in specific enthalpy is:
Δh5CpΔT5CpðT22T1ị ð5:13ị
EXAMPLE 5.1 SENSIBLE HEAT CHANGE WITH CONS TANT Cp What is the enthalpy of 150 g formic acid at 70C and 1 atm relative to 25C and 1 atm?
Solution
From Table C.5 in Appendix C, Cp for formic acid in the temperature range of interest is 0.524 cal g21C21. Substituting into (Eq. 5.12):
ΔH5ð150 gị ð0:524 cal g21C21ị ð70225ịC ΔH53537:0 cal
or
ΔH53:54 kcal
Relative toH50 at 25C, the enthalpy of formic acid at 70C is 3.54 kcal.
Heat capacities for most substances vary with temperature. This means that when we calculate the enthalpy change due to a change in temperature ΔT, the value of Cp itself varies over the range ofΔT. Heat capacities are often tabulated as polynomial functions of temperature, such as:
Cp5a1bT1cT21dT3 ð5:14ị
Coefficientsa, b, c, anddfor a number of substances are given in Table C.3 in Appendix C.
Sometimes we can assume that the heat capacity is constant; this will give results for sensible heat change that approximate the true value. Because the temperature range of interest in bioprocessing is often relatively small, assuming constant heat capacity for some materials does not introduce large errors. Cpdata may not be available at all tem- peratures; heat capacities such as those listed in Tables C.3 through C.6 are applicable only at a specified temperature or temperature range. As an example, in Table C.5 the heat capacity for liquid acetone between 24.2C and 49.4C is given as 0.538 cal g21C21, even though this value will vary within the temperature range.
One method for calculating sensible heat change when Cp varies with temperature involves use of the mean heat capacity, Cpm. Table C.4 in Appendix C lists mean heat capacities for several common gases. These values are based on changes in enthalpy relative to a single reference temperature,Tref50C. To determine the change in enthalpy for a change in temperature from T1 to T2, read the values of Cpm at T1 and T2 and calculate:
ΔH5M
ðCpmịT2ðT22Trefị2ðCpmịT1ðT12Trefị
ð5:15ị
5.4.2 Change of Phase
Phase changes, such as vaporisation and melting, are accompanied by relatively large changes in internal energy and enthalpy as bonds between molecules are broken and reformed. Heat transferred to or from a system causing change of phase at constant tem- perature and pressure is known aslatent heat. Types of latent heat are:
• Latent heat of vaporisation(Δhv): the heat required to vaporise a liquid
• Latent heat of fusion(Δhf): the heat required to melt a solid
• Latent heat of sublimation(Δhs): the heat required to directly vaporise a solid
Condensation of gas to liquid requires removal rather than addition of heat; the latent heat evolved in condensation is 2Δhv. Similarly, the latent heat evolved in freezing or solidification of liquid to solid is2Δhf.
Latent heat is a property of substances and, like heat capacity, varies with tempera- ture. Tabulated values of latent heats usually apply to substances at their normal boiling, melting, or sublimation point at 1 atm, and are called standard heats of phase change.
Table C.7 in Appendix C lists latent heats for selected compounds; more values may be found in Perry’s Chemical Engineers’ Handbook [1] and CRC Handbook of Chemistry and Physics[2].
The change in enthalpy resulting from phase change is calculated directly from the latent heat. For example, the increase in enthalpy due to evaporation of liquid massM at constant temperature is:
ΔH5MΔhv ð5:16ị
EXAMPLE 5.2 ENTHALPY OF CONDENSATION
Fifty grams of benzaldehyde vapour is condensed at 179C. What is the enthalpy of the liquid relative to the vapour?
Solution
From Table C.7 in Appendix C, the molecular weight of benzaldehyde is 106.12, the normal boiling point is 179.0C, and the standard heat of vaporisation is 38.40 kJ gmol21. For condensa- tion, the latent heat is238.40 kJ gmol21. The enthalpy change is:
ΔH550 g106:12 g1 gmol
ð238:40 kJ gmol21ị5 218:09 kJ
Therefore, the enthalpy of 50 g benzaldehyde liquid relative to the vapour at 179C is218.1 kJ.
As heat is released during condensation, the enthalpy of the liquid is lower than the enthalpy of the vapour.
Phase changes often occur at temperatures other than the normal boiling, melting, or sublimation point; for example, water can evaporate at temperatures higher or lower than 100C. How can we determine ΔH when the latent heat at the actual temperature of the phase change is not listed in property tables? This problem is overcome by using a hypo- thetical process path as described in Section 5.3.2. Suppose a liquid is vaporised isother- mally at 30C, but tabulated values for the standard heat of vaporisation refer to 60C.
As shown inFigure 5.3, we can consider a process whereby the liquid is heated from 30C to 60C, vaporised at 60C, and the vapour cooled to 30C. The total enthalpy change for this hypothetical process is the same as if vaporisation occurred directly at 30C.ΔH1and ΔH3are sensible heat changes, which can be calculated using heat capacity values and the methods described inSection 5.4.1.ΔH2is the latent heat at standard conditions calculated using Δhv data available from tables. Because enthalpy is a state property, ΔH for the actual path is the same asΔH11ΔH21ΔH3.
Liquid 30°C
Vapour 30°C
Liquid 60°C
Vapour 60°C Actual path
ΔH
ΔH2 ΔH1
(Heat liquid)
ΔH3 (Cool vapour)
(Vaporisation)
Hypothetical path
FIGURE 5.3 Process path for calculating latent heat change at a temperature other than the normal boiling point.
5.4.3 Mixing and Solution
So far we have considered enthalpy changes for pure compounds. For anideal solution orideal mixtureof several compounds, the thermodynamic properties of the mixture are a simple sum of contributions from the individual components. However, when compounds are mixed or dissolved, bonds between molecules in the solvent and solute are broken and reformed. In real solutions, a net absorption or release of energy accompanies these pro- cesses, resulting in changes in the internal energy and enthalpy of the mixture. Dilution of sulphuric acid with water is a good example; in this case, energy is released.
For real solutions, there is an additional energy term to consider in evaluating enthalpy:
theintegral heat of mixing or integral heat of solution,Δhm. The integral heat of solution is defined as the change in enthalpy that occurs as one mole of solute is dissolved at constant temperature in a given quantity of solvent. The enthalpy of a nonideal mixture of two compounds A and B is:
Hmixture5HA1HB1ΔHm ð5:17ị
whereHAis the enthalpy of compound A,HBis the enthalpy of compound B, andΔHmis the heat of mixing.
Heat of mixing is a property of the solution components and is dependent on the tem- perature and concentration of the mixture. As a solution becomes more and more dilute, an asymptotic value ofΔhm is reached. This value is called the integral heat of solution at infinite dilution. When water is the primary component of a solution,Δhm at infinite dilu- tion can be used to calculate the enthalpy of the mixture. Heats of solution and heats of solutions at infinite dilution for selected aqueous systems are listed in Perry’s Chemical Engineers’ Handbook [1], CRC Handbook of Chemistry and Physics [2], and Biochemical Engineering and Biotechnology Handbook[4].
EXAMPLE 5.3 HEAT OF SOLUTION
Malonic acid and water are available separately at 25C. If 15 g malonic acid is dissolved in 5 kg water, how much heat must be added for the solution to remain at 25C? What is the solu- tion enthalpy relative to the components?
Solution
The molecular weight of malonic acid is 104. Because the solution is very dilute (,0.3% w/w), we can use the integral heat of solution at infinite dilution. From handbooks,Δhmat room temper- ature is 4.493 kcal gmol21. This value is positive; therefore the mixture enthalpy is greater than that of the components and heat is absorbed during solution. The heat required for the solution to remain at 25C is:
ΔH515 g1 gmol104 g
ð4:493 kcal gmol21ị50:648 kcal
Relative to H50 for water and malonic acid at 25C, the enthalpy of the solution at 25C is 0.65 kcal.
In biological systems, significant changes in enthalpy due to heats of mixing do not often occur. Most solutions in fermentation and enzyme processes are dilute aqueous mix- tures; in energy balance calculations these solutions are usually considered ideal without much loss of accuracy.