Victor M. S. Gii University of Coimbra, 3049 Coimbra, Portugal Students normally become familiar at an early stage with the oossibilitv of relatine the A W for a chemical reaction to the h v a l u e s of other reactions, providing the equation for the former can be written as the algebraic sum of the equations for the latter (Hess's law). Similarly, they easily grasp the fact that if a chemical equation can be given as a sum (of difference) of two others, 1and 2, the equilihrium constant K for the former reaction is the product (or the quotient) of the equilibrium constants K1 and Kz. At a later stage, they can understand, through the relation AGO = -RT in K, that the multiplication (or division) of K values corresponds to the addition (or subtraction) of AGO values. Unfortunatelv it is m i t e easv for such overations to become mechanical. Similar uncritical approaches to stoichiometric and eouilibrium calculations are also likelv. For instance, it is n& unusual with examples like
+ HzO e HS- + H,O+ HS- + HzO s S2- + H30C
lo-')
(1)
(K2= 1.3 X lo-")
(2)
(Kl = 1.0 X
H,S
Zn + Cuz+s Zn2++ CU which can, nevertheless, be given as a sum of Zn + 2Hf
F?
+
Znz+ H,
.
Let initially 14i = ID(i. By taking only the equation sum, one
hasl~e=lcle=19.=I~.and14.=ID(,,and
The mistake lies, of course, in having considered only the equation sum. This can only be acceptable if reactions 3 and 4 ceased on adding A to D, heing replaced by a direct reaction of A with D, which generates, by a strange coincidence, B, C, E, F. I t is important to make the student realize that this is absurd and that there may be even no direct reaction between A and D. In such a case, the equation sum does not represent one reaction but two separate reactions (normally occurring to different extents). This ought to be contrasted with a direct reaction like
324
Journal of Chemical Education
(6)
Cu2++ H2 s CU+ 2Ht (7) It is noted, however, that eq 5 represents the whole phenomenon only if H7 and H?are not present in sufficient concentration for the competing reactions 6 and 7 to occur. In conclusion, an equation sum can be used safely by itself in stoichiometric and eouilibrium calculations onlv if the intermediates in the separate reactions are a t low steadv-state concentrations and if there are no other eouilibria involving those species. Another example of that situation is provided by the biochemical synthesis of sucrose from glucose and fructose with intervention of ATP: + 2ADP3C6H,206+ C6H,,06 2ATP4- + HzO s C,ZHZZO,I (glucose) (fructose) (sucmse) ~~~
~~~
~
~
+
+ 2H2POi that the student considers IHS1..- = 0 and, accordindv, -. IH@+Ie = 4S21e. S ~ e c i aalerts l are therefore necessarv. One way of doing that is by creating absurd conclusions. For example, consider the two reactions
(5)
4G0 = -37 kJ (8)
This expression can be expressed as the sum of and 2ATP4- + 2H20a 2ADP3- + 2H2POa
4G0 = -60 kJ (10)
However, in contrast to reaction 8, the formation of sucrose in reaction 9 only occurs to a very limited extent. This difference is due to two factors: (1) the favorable AGO value of the hydrolysis reaction of ATP (reaction 10) and (2) the real participation of ATP in reaction 8. That is, reaction 8 does not represent only the simultaneous existence of reactions 9 and 10, hut, rather, it is the overall equation for a coupled sequence which involves reaction of ATP with glucose and with fructose. When factor 2 is neglected in the teaching of ATP as a store or source of energy a t an introductory level, the wrong impression is given that biochemical reactions like reaction 8 are driven by a transfer of energy, or free energy, from reaction 10 as if it were heat. If that were the case, then nature could directly use more efficient reactions than reaction 10, for example the overall reaction in respiration
Acknowledgment The author is grateful to H. Burrows for helpful discussions.
