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5.2 STANDARD ENTHALPY OF REACTION Section 5.2
Standard Enthalpy of Reaction
For a chemical reaction, we define the standard enthalpy (change) of reaction H°
T
as the enthalpy change for the process of transforming stoichiometric numbers of
moles of the pure, separated reactants, each in its standard state at temperature T, to
stoichiometric numbers of moles of the pure, separated products, each in its standard
state at the same temperature T. Often H° is called the heat of reaction. (Sometimes
T
the symbol H° is used for H°, where the r subscript stands for “reaction.”) The
r T T
quantity U° is defined in a similar manner.
T
For the reaction
aA bB S cC dD

the standard enthalpy change H° is
T
¢H° cH° 1C2 dH° 1D2 aH° 1A2 bH° 1B2
m,T
T
m,T
m,T
m,T
where H° (C) is the molar enthalpy of substance C in its standard state at tempera-
m,T
ture T. For the general reaction [Eq. (4.94)]
0 S a n A i
i
i
we have
¢H° a n H° (5.3)*
T i m,T,i
i
where the n ’s are the stoichiometric numbers (positive for products and negative for
i
reactants) and H° is the molar enthalpy of A in its standard state at T. For example,
m,T,i i
H° for 2C H (l) 15O (g) → 12CO (g) 6H O(l) is
T 6 6 2 2 2
¢H° 12H° 1CO , g2 6H° 1H O, l2 2H° 1C H , l2 15H° 1O , g2
2
6
m,T
2
m, T
6
T
2
m,T
m,T
The letters l and g denote the liquid and gaseous states.
Since the stoichiometric numbers n in (5.3) are dimensionless, the units of H°
i T
are the same as those of H° , namely, J/mol or cal/mol. The subscript T in H° is
m,T,i T
often omitted. Since H° is a molar quantity, it is best written as H° . However, the
T m,T
m subscript is usually omitted, and we won’t bother to include it.
Note that H° depends on how the reaction is written. For
2H 1g2 O 1g2 S 2H O1l2 (5.4)
2
2
2
the standard enthalpy of reaction H° [Eq. (5.3)] is twice that for
T
H 1g2 1 2 O 1g2 S H O1l2 (5.5)
2
2
2
since each stoichiometric number n in (5.4) is twice the corresponding n in (5.5).
i i
Although we can’t have half a molecule, we can have half a mole of O , so (5.5) is a
2
valid way of writing a reaction in chemical thermodynamics. For (5.4), one finds
H° 572 kJ/mol, whereas for (5.5) H° 286 kJ/mol, where 298 stands for
298 298
298.15 K. The factor mol 1 in H° indicates that we are giving the standard enthalpy
change per mole of reaction as written, where the amount of reaction that has occurred
is measured by j, the extent of reaction (Sec. 4.8). A H°value is for j 1 mol. Since
n n j [Eq. (4.95)], when j 1 mol for (5.4), 2 mol of H O is produced; whereas
i i 2
when j 1 mol for (5.5), 1 mol of H O is produced.
2
We want to be able to calculate H° of a reaction from tabulated thermodynamic
data for the reactants and products. The definition (5.3) of H° contains the standard-
T
state molar enthalpy H° of each species at T. However, the laws of thermodynamics
m,T