Variation Of Heat (Or Enthalpy) Of Reaction With Temperature
Heat of Reaction or Enthalpy of Reaction
❒
The
heat of a reaction is simply the amount of heat absorbed or evolved in the
reaction.
❒ We also
know that the amount of heat absorbed or evolved at constant temperature and
pressure is called enthalpy. Therefore the amount of heat change during a reaction
at constant temperature and pressure may also be called enthalpy change. Its
value depends upon the number of moles of the reactants which have reacted in
the given chemical reaction.
❒ Heat
of reaction may be defined as: the amount of heat absorbed or evolved in a
reaction when the number of moles of reactants as represented by the balanced
chemical equation change completely into the products.
❒ For
example, the heat change for the reaction of one mole of carbon monoxide with 0.5
mole of oxygen to form one mole of carbon dioxide is – 284.5 kJ. This means
that 284.5 kJ of heat is evolved during the reaction and is the heat of reaction.
It can be represented as:
❒ It
is very important to note that heat of reaction varies with the change in
temperature.
❒ we must mention the temperature at which the
reaction is taking place. It is also convenient for comparison to fix up some
temperature as standard or reference.
❒ According
to the conventions prevalent in thermodynamics, the temperature of 298 K under
a pressure of one atmosphere has been fixed as the standard state.
❒ The
heat change accompanying a reaction taking place at 298 K and one atmospheric
pressure is called the standard heat change or standard enthalpy
change. It is denoted by ΔHº.
Variation Of Heat (Or Enthalpy) Of Reaction With Temperature
❒ The
heat of reaction changes with change in temperature of a gas due to variation
in its specific heat. The equations representing the variation of heat change
of reaction with temperature are known as Kirchoff’s equations.
❒ At
constant volume, the heat of reaction, ΔE, is given by the relation:
ΔE =
E2 – E1
where E1 and E2 are the internal energies of
the reactants and products.
❒ Differentiating
this equation with respect to temperature at constant volume, we get:
But we have already seen that:
where (Cv)2 and (Cv)1 are heat capacities of
the products and reactants respectively.
So, Change in heat of reaction at constant volume per degree
change in temperature is equal to the difference in heat capacities at constant
volume of products and reactants.
❒ Integrating
the above equation between temperatures T1 and T2, we
have:
where ΔE2 and ΔE1 are heats of reaction at
temperatures T2 and T1 respectively.
❒ Similarly,
at constant pressure the heat of reaction ΔH is given by the reaction:
ΔH =
H2 – H1
where H2 is the heat content (enthalpy) of the products
and H1 being that of the reactants.
❒
Differentiating with respect to temperature at constant pressure,
we have:
❒ According
to the equation, we have:
where (CP)2 and (CP)1 are
the heat capacities of products and reactants respectively.
or d (ΔH) = ΔCP × dT
❒ Change
in heat of reaction at constant pressure per degree change of temperature is
equal to
difference in heat capacities of products and reactants at constant
pressure.
❒ Integrating
the equation between temperature T1 and T2, we have
❒ The
relations (2), (3), (5) and (6) were first derived by Kirchoff and are called
Kirchoff’s equations.
❒ These
equations may be used for calculating heat of reaction at a given temperature
when it is known at some other temperature and when the heat capacities of
products and reactants are known.
Solved Problems
Problem (1): The heat of reaction:
½ H2
+ ½ Cl2 → HCl
at 27ºC is – 22.1 kcal. Calculate
the heat of reaction at 77ºC. The molar heat capacities at constant pressure at
27ºC for hydrogen, chlorine and HCl are 6.82, 7.70 and 6.80 cal mol–1 respectively.
Solution:
Problem (2): The heat of reaction:
N2
+ 3H2 → 2NH3
at 27ºC was found to be –21.976 kcal. What will be the heat of
reaction at 50ºC ? The molar heat capacities at constant pressure and at 27ºC for
nitrogen, hydrogen and ammonia are 6.8, 6.77 and 8.86 cal mol–1
degree–1.
Solution:
Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.
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