Kopp’s rule

Kopp s rule Kosher glycerin Kotulskite Kovar... 

A relatively simple example of a group contribution technique is the method for estimating Hquid and soHd heat capacities (159). This method is a modification of Kopp s rule (160,161) which was originally proposed in 1864. Kopp s rule states that, at room temperature, the heat capacity of a soHd compound is approximately equal to a stoichiometric summation of the heat capacities of its atoms (elements). The Hurst-Harrison modified equation is as follows ... 

There are no reliable prediction methods for solid heat capacity as a function of temperature. However, the atomic element contribution method of Hurst and Harrison,which is a modification of Kopp s Rule, provides estimations at 298.15 K and is easy to use ... 

As a further approximation, it may be assumed drat dre elements conform to Neumann and Kopp s rule that dre heat capacities of compounds and elements are about 25Jgatom Consequently the htral temperature, 7j, which is achieved at the reaction front is given by... 

Kopp s rule does not take into account the arrangement of the atoms in the molecule, and, at best, gives only very approximate, ball-park values. 

Some general rules exist, such as that the molal heat capacity (at constant pressure) of any monatomic gas is approximately 5 cal/deg mole, except at very low temperatures. The most useful rule (Kopp s rule) is that the. molal heat capacity of a solid substance is the sum of " its atomic heat capacities ivith the value about 6.2 for all atoms except the light ones, for which values used are... 

The rule of Dulong and Petit, dealing with the relation between the heat capacity of an element and its atomic weight, has been mentioned in Chapter 8. It is closely related to Kopp s rule. 

When the experimental or measured value of Cp for a particular liquid is not available, a fair approximation for Cp near room temperature can be obtained by Kopp s Rule, which states that the heat capacity of a liquid is approximately equal to the sum of the atomic heat capacities of its individual atoms. For the purpose of Kopp s Rule, these individual atomic heat capacities (molar basis) are given in Table 8.5. 

Example 8.4 Using Kopp s Rule for liquids, estimate the Cp for sulfuric acid at room temperature. 

Wien data are not available for the heat capacity of a solid, it can also be estimated by Kopp s Rule however, the values of heat Capacity for each element are different from those used for liquids. Table 8.8 gives heat capacity of the elements for use in Kopp s Rule for solids. Kopp s Rule for solids is usually... 

Table 8.5 Heat Capacity of Elements at 20°C for Kopp s Rule for Liquids...

Table 8.8 Heat Capacity of Elements For Use In Kopp s Rule For Solids At 20°C...

In Chapter 8, along with tables of measured thermophysical data, we saw some fairly simple techniques for estimating these values when experimental results are not available. Among these techniques were Kopp s Rule for the heat capacity of both liquids and solids, and Trouton s ratio for latent heats of fusion and vaporization, along with Kistiakowski s temperature correction for the latter. 

Estimate the heat capacity of a liquid or solid species using Kopp s rule. Estimate the heat of fusion and heat of vaporization of a species using correlations in Section 8.4b. 

Kopp s rule is a simple empirical method for estimating the heat capacity of a solid or liquid at or near 20°C. According to this rule, Cp for a molecular compound is the sum of contributions (given in Table B.IO) for each element in the compound. For example, the heat capacity of solid calcium hydroxide. Ca(OH)2, would be estimated from Kopp s rule as... 

C/.)soiid is not listed in Table B.2, so it must either be found elsewhere or estimated using Kopp s rule. The latter provides a crude approximation but a very reasonable one to make in this case, considering how little this step will contribute to the overall enthalpy change. 

A liquid mixture of 30 wt% acetone and 70 wt% 2-methyl-l-pentanol (C5H14O) is cooled from 45 C to 20 C. Calculate the associated specific enthalpy change in J/g, using Kopp s rule to estimate any heat capacity for which a tabulated value cannot be found. State all assumptions you make. 

Twenty liters of liquid n-propyl benzoate (QH5CO2C3H7, SG = 1.021) and 15 liters of liquid benzene are mixed and heated from 25°C to 75°C. Calculate the required heat input (kJ), using Kopp s rule when necessary. State all assumptions you make. 

Table B.IO Atomic Heat Capacities for Kopp s Rule"...

C (300) = 25.0 cal K" mol is estimated using Kopp s rule. Heat capacities at higher temperature are estimated from... 

For the crystal range 298.15 - 478.9 K, these estimated C values vary from 34.63 to 36.69 cal K fair agreement with the adopted values and were estimated by comparison with ZrCl (cr) and HfCl.(cr) estimated the heat capacity of NbCl based on Neumann and Koppe s rule, C 26.71 + 35.2 x lO T cal K... 

The heat capacity was estimated at 8 cal K mol from comparisons with similar compounds and from Kopp s rule. 

Solids. Only very rough approximations of solid heat capacities can be made. Kopp s rule (1864) should only be used as a last resort when experimental data cannot be located or new experiments carried out. Kopp s rule states that at room temperature the sum of the heat capacities of the individual elements is approximately equal to the heat capacity of a solid compound. For elements below potassium, numbers have been assigned from experimental data for the heat capacity for each element as shown in Table 4.2. For liquids Kopp s rule can be applied with a modified series of values for the various elements, as shown also in Table 4.2. For example, the heat capacity at room temperature of Na2S04 lOHaO would be 2(6,2) + 1(5.4) + 14(4.0) + 20(2.3) = 119.8 cal/(g mol)( C). The heat capacity of coal can be estimated from equations in the Coal Conversion Systems Technical Data Book cited in the supplementary references. Consult Reid or Perry s Handbook fpr tables of heat capacity data for solids. 

TABLE 4.2 Values for Modified Kopp s Rule Atomic Heat Capacity at 20 C [cal/(g atom)(°C)]... 

Estimate the heat capacity (Cp) of acetic acid by (a) Kopp s rule and (b) Pachaiyappan s constants. Compare with the experimental value at room temperature. 

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