1) The standard heat of reaction (ΔH0T) at temperature T can be treated as occurring in three steps: cooling reactants from T to T1, allowing the reaction to occur at T1, and raising products from T1 to T. 2) By adding the enthalpy changes for these three steps, an equation is derived relating ΔH0T to ΔH0T1 and the heat capacities of reactants and products. 3) The heat capacities are expressed as functions of temperature, and the equation is expanded to express ΔH0T as a function of T, involving heat capacity change terms and constants that can be evaluated if ΔH0 is known at one temperature.

1. Advanced Chemical Engineering
Thermodynamics
Presented By: Guided By:
Mosam Patel Prof. Z Z Painter
ME (Chemical)
CHEMICAL ENGINEERING DEPARTMENT
VISHWAKARMA GOVERNMENT ENGINEERING COLLEGE
CHANDKHEDA

2. Effect Of Temperature On Heat Of
Reaction
• Consider the reaction
aA + bB → cC + dD
Here, a, b, c and d are stoichiometric coefficient.
• This reaction may be written as
cC + dD – aA – bB = 0
in which –a, -b, c, d are called stoichiometric numbers
• Denoting the stoichiometric numbers of the species taking
part in a chemical reaction by vi, a chemical reaction in
general may be represented by
 𝑖 𝑣𝑖 𝐴𝑖 = 0………………………………………………(1)

3. • The actual reaction occurring at temperature T, for which the
standard heat of reaction is ΔH0
T, may be treated as occurring
in three steps as in fig 1.

4. • The reactants are cooled from temperature T to T1. The
enthalpy change for this step is
 𝛥𝐻1 =
𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 𝑇
𝑇1
𝑛𝑖 𝐶 𝑃,𝑖 𝑑𝑇 = 𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 𝑇1
𝑇
𝑣𝑖 𝐶 𝑃,𝑖 𝑑𝑇…...(2)
• This reaction is allowed to occur at temperature T1. The
enthalpy change is
 𝛥𝐻2 = 𝛥𝐻 𝑇1
0
………………………………………..(3)
• The temperature of the product is raised from T1 to T in this
step. The enthalpy change is
 𝛥𝐻3 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑇1
𝑇
𝑛𝑖 𝐶 𝑃,𝑖 𝑑𝑇 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑇1
𝑇
𝑣𝑖 𝐶 𝑃,𝑖 𝑑𝑇…….(4)

5. • The standard heat of reaction at temperature T, is obtained by
adding the preceding three equations
 𝛥𝐻 𝑇
0
= 𝛥𝐻1 + 𝛥𝐻2 + 𝛥𝐻3 = 𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 𝑇1
𝑇
𝑣𝑖 𝐶 𝑃,𝑖 𝑑𝑇 +
𝛥𝐻 𝑇1
0
+ 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑇1
𝑇
𝑣𝑖 𝐶 𝑃,𝑖 𝑑𝑇
• The above result can be written as
 𝛥𝐻 𝑇
0
= 𝛥𝐻 𝑇1
0
+ 𝑇1
𝑇
( 𝐼 𝑣𝑖 𝐶 𝑃,𝑖)𝑑𝑇……………………………………(5)
• The summation in the above equation is overall species taking
part in a reaction. Let the heat capacity of the substances be
represented by following equation
 𝐶 𝑃 = 𝛼 + 𝛽𝑇 + 𝛾𝑇2……………………………..(6)

6. • Utilising equation (6), equation (5) can be written as
 𝛥𝐻 𝑇
0
= 𝛥𝐻 𝑇1
0
+ 𝑇1
𝑇
𝛥𝐶 𝑃 𝑑𝑇………………….……………(7)
Where, 𝛥𝐶 𝑃 = 𝛥𝛼 + (𝛥𝛽)𝑇 + (𝛥𝛾)𝑇2……………………………(8)
And
 𝛥𝛼 = 𝑣𝑖 𝛼, Δ𝛽 = 𝑣𝑖 𝛽 , 𝛥𝛾 = 𝑣𝑖 𝛾……………………………(9)
• Equation (5) may be expanded as
 𝛥𝐻 𝑇
0
= 𝛥𝐻 𝑇1
0
+ 𝛥𝛼 𝑇 − 𝑇1 +
1
2
𝛥𝛽 𝑇2 − 𝑇1
2
+
1
3
𝛥𝛾( 𝑇3 −

7. • The constants appearing in the above equation can be
grouped together to a single constant ΔH’, so that we have
 𝛥𝐻 𝑇
0
= 𝛥𝐻′ + 𝛥𝛼𝑇 +
𝛥𝛽
2
𝑇2 +
𝛥𝛾
3
𝑇3…………………(11)
• The constant ΔH’ in the above equation can be evaluated if
the heat of reaction at a single temperature is known.
Equation (11) can be used for the evaluation of the standard
heat of reaction at any temperature T.