Page 201 - Physical chemistry understanding our chemical world

168 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Worked Example 4.12 The white of an egg denatures while immersed in water boiling
at its normal boiling temperature of 373 K. What is the value of G at this higher
−1
temperature? Take H = 35 kJ mol .
−1
It does not matter The value of G O at 298 K is +5.7kJ mol , the positive sign
which temperature is explaining the lack of a spontaneous reaction. Inserting values into
chosen as T 1 and which the Gibbs–Helmholtz equation, Equation (4.62), yields
as T 2 so long as T 1
relates to G 1 and T 2 G 373 K 5700 J mol −1 −1 1 1
relates to G 2 . − =+35 000 J mol −
373 K 298 K 373 K 298 K
Note that T is a thermodynamic temperature, and is cited in kelvin. All energies have
−1
been converted from kJ mol −1 to J mol .
G O
373 K = (19.13 J K −1 mol ) + (35 000 J mol ) × (−6.75 × 10 −4 K )
−1
−1
−1
373 K
G O
−1
−1
373 K = (19.13 J K −1 mol ) − (23.62 J K −1 mol )
373 K
O
G
373 K =−4.4 J K −1 mol −1
373 K
so
G O =−4.4 J K −1 mol −1 × 373 K
373 K
and
G O =−1.67 kJ mol −1
373 K
G O has a negative value, implying that the reaction at this new, elevated temperature
373 K
is now spontaneous. In summary, the Gibbs–Helmholtz equation quantifies a qualitative
observation: the reaction to denature egg white is not spontaneous at room temperature,
but it is spontaneous at elevated temperatures, e.g. when the egg is boiled in water.

SAQ 4.10 Consider the reaction in Equation (4.63), which occurs wholly
in the gas phase:
5
3
NH 3 + O 2 −−−→ NO + H 2 O (4.63)
4 2
The value of G r O for this reaction is −239.9kJ mol −1 at 298 K. If the
enthalpy change of reaction H r =−406.9kJ mol −1 ,then

(1) Calculate the associated entropy change for the reaction in
Equation (4.63), and comment on its sign.
(2) What is the value of the Gibbs function for this reaction when the
temperature is increased by a further 34 K?