Adapted from an Exercise used at the University of Kansas by J. M. McCormick
Last Update: August 25, 2008
Tabulated values of reaction enthalpies are always quoted at some fixed temperature, T. Since we can write any reaction as Eqn. 1, where R(T) and P(T) are the reactants and products, respectively, at a constant temperature, T,
| R(T) ¦ P(T) | (1) |
the reaction enthalpy may be written as ΔrH(T) to emphasize that it applies when both the reactants and the products have the same temperature. But what is actually measured in an adiabatic calorimeter under constant pressure is Eqn. 2, where K represents the calorimeter and T1 and T2 are the initial and final temperatures, respectively.
|
R(T1) + K(T1) ¦ P(T2) + K(T2) |
(2) |
Since this is an adiabatic process, the change in enthalpy for Eqn. 2 is zero (ΔH2 = 0).
There are several ways that the reaction actually taking place in the calorimeter (Eqn. 2) could be imagined as occurring. For example, we could conceive of an initial step where the chemical reaction occurs at constant temperature T1, followed be a second step in which the heat released or absorbed in the first step raises or lowers the temperature of the products and the calorimeter to T2, as shown as Eqn. 3a and 3b.
|
R(T1) ¦ P(T1) |
(3a) |
|
P(T1) + K(T1) ¦ P(T2) + K(T2) |
(3b) |
An alternate approach, and one which is more appropriate to the current experiment, is to consider a model where the reactants are heated or cooled from T1 to T2 in an initial step followed by the chemical reaction which occurs at temperature T2. This model is shown in Eqn. 4a and 4b.
|
R(T1) + K(T1) ¦ R(T2) + K(T2) |
(4a) | |
|
R(T2) ¦ P(T2) |
(4b) |
Clearly, the sum of Eqn. 4a and Eqn. 4b is Eqn. 2, and as a result:
| ΔH4a + ΔH4b = ΔH2 | (5) |
In this experiment we will evaluate the enthalpy change for Eqn. 1 at T = T2 by noting that ΔH4b is simply ΔrH(T2). Since ΔH2 = 0, Eqn. 5 can be rewritten as
|
ΔrH(T2) = -ΔH4a |
(6) |
Since Eqn. 4a is simply a heating or cooling process, the enthalpy change for this process can, for small ΔT values, be written as Eqn. 7, where ΔT = T2 - T1 and Cp(R + K) is the heat capacity at constant pressure of the reactants, R, and the calorimeter, K.
|
ΔH4a = Cp(R + K)ΔT |
(7) |
Furthermore, we can write explicitly Cp(R + K) for the case of two reactants, A and B, as
|
Cp(R + K) = mACp(A) + mBCp(B) + Cp(K) |
(8) |
Here mA and mB are the masses of A and B, in grams, and and are the heat capacities of the reactants A and B, respectively, in J·K-1·g-1, or other convenient units. The heat capacities Cp(R + K) and Cp(K) are in J·K-1.1 The heat capacity of the empty calorimeter, Cp(K), is constant from run to run, while the other terms in Eqn. 8 depend on the type and amount of the reactants. In general, the first two terms on the right-hand side of Eqn. 8 can be computed from known data (Table 1) and Cp(K) can be obtained by calibration of the calorimeter. Thus, Eqn. 8 can be evaluated and ΔrH(T2) determined.
Notes
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