Following the ideas above for the specific heat at constant volume, the
specific heat at constant pressure can be written in terms of the heat divided
by the temperature change, with the heat being equal to the change in
enthalpy. Again, assuming that the changes in enthalpy are incremental,
the expression can be written in terms of a partial derivative, with the
specific heat at constant pressure being equal to the derivative of the
enthalpy with respect to temperature at constant pressure:
(2.29)
Enthalpy changes of biochemical reactions
Many biochemical reactions occur at a constant pressure and the enthalpy
change is equal to heat change during the reaction. The enthalpy change
is determined by the difference in enthalpy between the initial and final
states. By convention, enthalpy changes are reported under what are
termed standard ambient temperature and pressure conditions. For most
of chemistry, the standard state is defined as 1 mol of an object at 1 barof
pressure and at a temperature of 298.15 K. Enthalpy changes in reactions
are generally additive, which allows the enthalpy to be determined for a
complex process by considering the individual steps. For example, the
enthalpy change for a reaction A→Cis simply the sum of the enthalpy
changes for the two stepwise reactions A→Band B→C. Likewise the
enthalpy change for a reverse reaction, for example B→A, has the same
value, but the opposite sign, as the change for the forward reaction A→B.
That is, a reaction that releases heat will absorb heat if reversed.
When systems undergo a reaction, the components may change their
phase. For example, when water is heated at its boiling point it will become
a vapor. The conversion of a substance from one phase to another is called
a phase transition. The phase transition often represents a state change
between a gas, liquid, and solid. Alternatively, the transition can involve
different solid forms; for example, carbon can exist as graphite or diamond
solids.
The energy that must be supplied to the system to cause a phase change
is called the enthalpy of formation. The energy required would depend upon
the conditions, such as temperature and pressure, at which the reaction
occurs. In order to associate a specific enthalpy change with a given reac-
tion, changes are always reported under standard conditions; that is, at
a pressure of 1 bar. For example, when ice melts at 0°C the enthalpy change
is +6.01 kJ mol−^1. The enthalpies associated with the reverse change will
always have the same value but opposite sign. So for water, the enthalpy
change is +6.01 kJ mol−^1 for the ice-to-liquid transition and −6.01 kJ mol−^1
for the liquid-to-ice transition. The value of the enthalpy change is
C
q
T
H
T
C
H
PPT P
== →=
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
Δ
Δ
Δ
∂
∂
38 PARTI THERMODYNAMICS AND KINETICS
