A GRAPHICAL METHOD OF TEACHING THE THERMOCHEMISTRY OF HIGH TEMPERATURES* ALPREDSTANSPIELD, MCGULUNIVERSITY, MONTREAL, CANADA
I have for many years used the late Prof. J. W. Richards' "Metallurgical Calculations" as a basis for my instruction in this subject and whenever possible 1 employ diagrams, drawn on the blackboard, to make the meaning clearer. In Chapter IV, "TheTbennochemistty of Highl'emperatures," Richards considers the amount of heat produced or absorbed by a chemical reaction a t a high temperature, and also the amount of heat produced or absorbed if we start with the reagents cold and finish with the products hot, or vice versa. Originally I used a simple rectangle, ABCD, Figure 1, in which A represents the reagents a t 0°, B represents the reagents a t to, C the products a t to, and D the products a t 0'. Temperature is shown by the vertical ordinate, but heat is not represented quantitatively. In passing from A to D, we have the heat of the reaction a t 0°, and from B to C the heat of the reaction a t t o ; from A to B the heat absorbed by the reagents in passing 1 D A from 0 to to, and from D to C the heat absorbed FIGURE 1.-THE TEERMOby the products from 0 to to. C ~ M I S T R Y OP HIGH TEMThe diagram serves to show that we can pass PEKATURSS. A QUALITATIVE from one state to another by either of two rptes, ~ ~ , " , " " , " , " ~ ~ ~ : N O BTHE SOP the heat production or absorption being the same in each case. Thus, in passing from A to D, we may pass directly, ohtaining the heat of the reaction a t 0°, or we may go from A to B, lending to the system the heat required to raise the reagents from 0 to to, then from B to C obtaining the heat of the reaction a t to, then from C to D giving out the heat contained in the products a t to. As the heat produced by either route is the same, we find that: Heat in reagents (0' - to) + Heat of reaction at Heat of reaction at 0' = t o + Heat in products (0" - to).
oA
{
,,. ".
Heat of reaction at
1
t'
=
Heat of reaction at 0' + Heat in reagents (OD - to) - Heat in products (OD - t o ) .
The diagram also shows very simply how to obtain the heat that is produced or absorbed, in passing from A to C or from B to D. The diagram shown in Figure 1 can he made entirely quantitative, * Presented before the Fifty-fifth General Meeting of the American Electrachemical Society, held at Toronto, Canada, May 27.28, and 29, 1929. 43
JOURNAL OF CHEMICAL EDUCATION
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JANUARY, 1930
by using the horizontal ordinate to represent heat; any heat given out by the system being represented by distances to the right, and any heat absorbed by the system by distances to the left, as in Figure 2. Here, A represents the reagents a t 0°, AD is made equal to the heat of the reaction a t 0' (supposed to be positive) and D represents the products a t 0". Making AE equal to t o , EB equal to the heat in the reagents from 0 to to, and PC equal to the heat in the products from 0 to t o , then B represents the reagents a t t o , C represents the products a t to, and BC equals the heat of reaction a t to.
Heat of renction a t 1" =
+
Hmt o l reaction a t 0 ' Heat in reagent5 (0 - I D ) - Heat in pnrlucts (0 - 1').
If wc start with the reagents at 0' and end with the products a t t o , the heat-given out by the system will be equal to EC. If we start with the reagents a t t D and end with the products a t O", the heat given out will be equal to BE. When drawn in this way, the four-sided figure representing the cycle of changes hecomes an oblique figure, whose opposite sides need not be I I 1A Hcmtofreastion .t 0. Q I' equal. Moreover, the sloping 0-Heatobsorbod 0 Heatgiven out sides are not even straight FIOW 2.-THE ~ H E R M ~ ~ ~ E M I OP ~ T HIGH R Y lines, as the specific heat TEMPERATURES. A QUANTITATIVB RBPRESEN-varies with the temperature, TATION O F THE CYCLE OF CHANGES but a t any temperature the horizontal distance between the lines is equal to the beat of reaction.
-
CO
+ L/p02
=
CO?
+
As a definite example, the reaction CO '/202 = C02 is plotted in Figure 3 for temperatures between 0" and 3000° C., using the heats of formation of CO and COz given in the International Critical Tables, Vol. V, 1929, and the specific heats of gases under constant pressure given by Partington and Shilling.' Taking A as the zero point, AD is made equal to the heat of the reaction a t 0'; the line AB is plotted so that its horizontal distance from AE a t any temperature, t o , is equal to the heat confrom 0 to to; the line DC, in the same way, shows the tent of CO '/%02 heat in C02 from 0 to to. The heat of reaction a t any temperature,
+
' Partingan and Shilling, "SpecificHeats of Gases," London, 1924.
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TEACHING OF ELECTROCHEMISTRY C
eat of
Reaction a t
t'---
45 F
-----
to, is clearly shown by the diagram, which also shows the amount of heat that results from the reaction starting with the reagents a t one temperature and finishing with the products a t some other temperature. It will be noticed that the heat of reaction is nearly constant, but decreases slightly a t high temperatures. In the case of an endothermic reaction, the equation Heat of reaction at t o =
+
Heat of reaction at 0' Heat in reagents (0 - H v t in products (0 - to)
-
to)
46
JOURNAL OF CHEMICAL EDUCATION
JANUARY, 1930
still holds if we are careful to use the minus sign in expressing the heat of reaction. When, however, we show this graphically, as in Figure 2, we find that D represents the reagents a t 0°,DA the negative heat of reaction a t 0°,A represents the products a t 0°, and the words "reagents" and "products" must be interchanged; also, as we are now thinking of the heat absorbed by the reaction, we must reverse the signs in the equation, which becomes: Hest absorbed by reaction at to =
Heat absorbed by reaction at O D - Heat in reagents (0" - 1) Heat in products (0 - t o ) .
+
The diagram is in effecta thermal equation, and the position of "reagents" and "products" is determined C E by the exothermic or endother; mic nature of the reaction. As, therefore, we cannot draw the B I diagram to suit the equation, II we are obliged to write the equation to suit the diagram; I thus we cannot write:
7
4
I
!4
i 5
+ C = Fe + CO - 37,610
because we shall find FeO
i,
b u C
I
$
t
0"
FeO
I
+
C on the right-hand side of the diagram, and therefore we must write it: Fe
+ CO = FeO + C + 37,610
That is to say, we must write From~ 5.-AT ANY TEMPERATURE, P, THE all equations that are HO~~ZONT INTERCEPT. AG PH, IS THE HEAT exothermic from left to right. GIVENOUT BY THE REACTION AT THATTEMPERATURE It may occasionally happen that a reaction is exothermic a t 0' and endothermic a t some other temperature. We would write such an equation in view of the heat of reaction a t 0'; the curves AB and DC would cross a t some point, and above this temperature the reaction would obviously be endothermic. If it were possible to follow this convention in writing equations, the chemical equation would have gained in value, as i t would show a t a glance, although only qualitatively, in which direction the reaction resulted in the production of heat. *Heat
absorbed
0
Heatgiven out-
The reduction of zinc oxide by carbon is endothermic, and the equation must therefore be reversed, as in Figure 4. The broken line AB shows
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47
the heat content of Zn, plus the heat content of CO, a t each temperature. The steps SM and LV show respectively the heat of liquefaction of the zinc a t 419.4' C., and of its vaporization a t 907'C. In the condensation of zinc from a cooling mixture of CO and zinc vapor, condensation would begin a t some lower temperature (that is, below 907") and would continue over a range of temperature, so that there would be a curve instead of the horizontal line V L Z In plotting this diagram, the writer took the specific heats of ZnO and CO from the International Critical Tables, and also the heats of fusion and vaporization of zinc, but was obliged to use Richards' values for the specific heats of solid, liquid, and gaseous zinc. In Figure 5 the lines AB and DC of Figure 2 have been extended until C is to the left of A. The point G, where DC cuts AE, gives the temperature resulting from the reaction, if we begin with tbe reagents a t 0 ' and if no heat leaves the system. Starting with the reagents a t any particular temperature, shown by the point P, the horizontal intercept PH is the heat given out by the reaction a t that temperature, that is isothermally, while the vertical intercept P T is the rise of temperature produced by the reaction without loss of heat, that is, adiabatically. Standeld, T h e Electric Furnace," 1914, p. 331.
