Page 74 - Battery Reference Book

Spontaneous reaction in electrochemical cells 1/59
it can be seen that a particular process will be possible by Equation 1.23
theoretically -if the reaction quotient Q is less than the
corresponding equilibrium constant K; AF will then AF = -nFE (1.23)
involve the logarithm of a fraction and hence will be so that AF is negative if E is positive. Consequently,
negative. If, however, the arbitrary concentrations are when the e.m.f. of a reversible cell is positive, the cor-
such as to m.ake Q greater than A, the value of AF responding cell reaction will take place spontaneously.
will be positive, and the reaction will not be possible The e.m.f. of a cell and even its sign depend on
under these conditions. the activities, or concentrations, of the reactants and
It should be borne in mind, of course, that a change products of the reaction taking place in the cell: hence,
in temperature may affect the value of the equilibrium the value of the free energy change will vary in
constant to such an extent that a reaction that previ- an analogous manner. This is in agreement with the
ously could not QCCW spontaneously, for a given value conclusions reached above. For many purposes it is
of the quotient Q, can now do so. At some tempera- convenient to consider the free energy change AF'
tures K is less than Q, but as the temperature is altered associated with the reaction when all the substances are
K may becoime greater than Q; the sign of AF will in their standard states of unit activity. The appropriate
thus reverse from positive to negative, and the reaction form of Equation 1.23 is
becomes posisible, when the temperature is changed.
It is of interest to consider the physical significance AFo = -nFE2e11 (1.124)
of the conclusion that a reaction will be able to take
place spontaneously if (2 is less than A, but not if Q where E:e,l is the standard emf. of the reversible cell
is greater than A. A comparison of Equations 1.116 in which the given reaction occurs. The value of E&,!
and 1.119, which define K and Q respectively, shows can be obtained by subtracting the standard oxidation
that when Q is less than K, the arbitrary activities (or potentials of the electrodes constituting the cell, Le.
concentratiorls) of the products are relatively less than
those in the equilibrium state. The occurrence of the
reaction will mean that the amounts of the products
are increased, while those of the reactants decrease where Eoleft and Eorlght are the standard oxidation
correspondingly. In other words, the state of the system potentials of the left-hand and right-hand electrodes,
will tend to move spontaneously towards the state respectively, as given in Table 1.2. The standard free
of equilibrium. On the other hand, if Q is greater energy change of the cell reaction can then be derived
than A, the products will be present in excess of the from Equation 1.124.
equilibrium activities and for the reaction to continue Consider, for example, the Daniel1 cell:
would mean a still greater departure from equilibrium; ZnlZnS04(az,z+ = 1)IICuS04(ac.z+ = 1)ICu = (-0.340)
such a change would never occur spontaneously. In
these circumstances, of course, the reaction would tend for which the reaction is
to take place in the reverse direction. Zn + CU'+ = ~n'+ + cu
Although any reaction accompanied by a decrease
of free energy is theoretically possible, this is no for the passage of 2F. The standard oxidation poten-
indication that the process will actually occur with tial of the left-hand (Zn, Znzf) electrode is +0.761V
measurable speed. In a series of analogous reactions, (Table 1.2), while the standard oxidation potential
the rates at which the processes occur are roughly in of the right-hand (Cu, Cu") electrode is -0.340V;
the order of the free energy decrease, but in general, the standard e.m.f. of the complete cell, E:ell is
for different reactions, there is no connection between thus +0.761 - (-0.340) = 1.101V at 2YC, and by
the magnitude of the decrease of free energy and the Equation 1.124:
rate at which the reaction occurs. For example, at
ordinary temperatures and pressures the free energy AFo = -2 x 96500 x 1.101 = -2125005
change for the combination of hydrogen and oxygen
to form water has a very large negative value, yet the = -212500 x 0.2390 = -50790cal
reaction, in the absence of a catalyst, is so slow that no i.e. -50.79 kcal, at 25°C.
detectable amount of water would be formed in years. Since the standard e.m.f. of the cell, is positive,
The passage of an electric spark or the presence of a the standard free energy change, AF', is negative, and
suitable catalyst, however. facilitates the occurrence of the reaction as written is spontaneous; hence, metallic
a reaction which the free energy change shows to be zinc can react spontaneously with cupric ions zt unit
theoretically possible. activity to produce metallic copper and zinc ions also
As shown. above, a reaction can take place spon- at unit activity.
taneously if it is accompanied by a decrease of free Suppose it is required to determine whether the
energy, i.e. when AF is negative. If the reaction can reaction
be made to take place, for the passage of n fara-
days. in a reversible cell of e.m.f. equal to E, then Cd+2H+(a= l)=Cd'+(a= l)+Hz(latm.)