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THE EFFECT OF TEMPERATURE ON THERMODYNAMIC VARIABLES 167

denaturing involves the rearrangement of bonds – in this case, of
This argument here has
hydrogen bonds. For convenience, in the discussion below we say
been oversimplified
that bonds change from a spatial arrangement termed ‘1’ to a dif-
because the reaction
ferent spatial arrangement ‘2’.
is thermodynamically
From everyday experience, we know that an egg will not dena-
irreversible – after all,
ture at room temperature, however long it is left. We are not saying you cannot ‘unboil an
here that the egg denatures at an almost infinitesimal rate, so the egg’!
lack of reaction at room temperature is not a kinetic phenomenon;
rather, we see that denaturation is energetically non-spontaneous
◦
at one temperature (25 C), and only becomes spontaneous as the Some reactions are
temperature is raised above a certain threshold temperature, which spontaneous at one
◦
we will call T (critical) (about 70 C for an egg). temperature but not
at others.
The sign of the Gibbs function determines reaction spontaneity,
O
so a reaction will occur if G is negative and will not occur if
O
G is positive. When the reaction is ‘poised’ at T (critical) between
The temperature de-
O
spontaneity and non-spontaneity, the value of G = 0. pendence of the Gibbs
O
The changes to G with temperature may be quantified with
function change is
the Gibbs–Helmholtz equation: described quantita-
tively by the Gibbs–
G O G O 1 1 Helmholtz equation.
2 1 O
− = H − (4.62)
T 2 T 1 T 2 T 1
O
where G is the change in Gibbs function at the temperature T 2 The word ‘pseudo’
2
O
and G is the change in Gibbs function at temperature T 1 .Note derives from the Greek
1
how values of T must be expressed in terms of thermodynamic stem pseudes meaning
‘falsehood’, which is
temperatures. H is the standard enthalpy of the chemical pro-
often taken to mean
cess or reaction, as determined experimentally by calorimetry or
having an appearance
calculated via a Hess’s-law-type cycle. that belies the actual
The value of H r for denaturing egg white is likely to be nature of a thing.
quite small, since it merely involves changes in hydrogen bonds.
For the purposes of this calculation, we say H r has a value of
−1
35 kJ mol . Denaturing albumen
Additionally, we can propose an equilibrium constant of reaction, is an ‘irreversible’
although we must call it a pseudo constant K (pseudo) because we can- process, yet the deriva-
not in reality determine its value. We need a value of K (pseudo) in tions below assume
order to describe the way hydrogen bonds change position during thermodynamic re-
denaturing. We say that K (pseudo, 1) relates to hydrogen bonds in the versibility.In fact,
complete reversibility
pre-reaction position ‘1’ (i.e. prior to denaturing) and K (pseudo, 2)
is rarely essential; try
relates to the number of hydrogen bonds reoriented in the post-
to avoid making calcu-
reaction position ‘2’ (i.e. after denaturing). We will say here that
lations if a significant
K (pseudo) is ‘1/10’ before the denaturing reaction, i.e. before boiling
extent of irreversibility
the egg at 298 K. From the van’t Hoff isotherm, K (pseudo) equates is apparent.
−1
to a Gibbs function change of +5.7kJ mol .