Enthalpy of a Reaction
Enthalpy of a Reaction
❒
Thermochemical
measurements are made either at (a) constant volume or (b) constant pressure. The
magnitudes of changes observed under the two conditions are different.
❒ The
change in internal energy (ΔE): is the heat change accompanying a chemical
reaction at constant volume because no external work is performed.
❒ However
at constant pressure not only does the change in internal energy take place but
work is also involved because of expansion or contraction. In the laboratory
most of the chemical reactions are carried out at constant pressure
(atmospheric pressure) rather than at constant volume. In order to study the
heat changes for reactions taking place at constant pressure and constant
temperature, chemists have introduced a new term called enthalpy.
❒ The
enthalpy of a system is defined as: the sum of the internal energy and the
product of its
pressure and volume. That is,
H =
E + PV
where E is the internal energy, P is the pressure and V is the volume
of the system. It is also called Heat content.
❒ Just
like internal energy, enthalpy is also a function of the state and it is not
possible to measure its absolute value. However a change in enthalpy (ΔH)
accompanying a process can be measured accurately and is given by the
expression.
ΔH =
Hproducts – Hreactants
= Hp
– Hr
❒ Thus
if ΔV be the change in volume in case of a reaction at constant temperature and
pressure, the thermal effect observed will be the sum of the change in internal
energy (ΔE) and the work done in expansion or contraction. That is,
ΔΗ =
ΔE + P × ΔV
❒ Therefore,
while the heat change in a process is equal to its change in internal energy ΔE
at constant volume, it gives at constant pressure the enthalpy change ΔH. That
is,
ΔE =
Heat change in a reaction at constant volume
ΔH =
Heat change in a reaction at constant pressure
❒ For
reactions involving solids and liquids only the change in volume (ΔV) is very
small and the term P × ΔV is negligible. For such reactions ΔH is equal to ΔE.
❒ In
case of gases, however, we must specify whether the reaction has taken place at
constant volume or at constant pressure because the value of P × ΔV is
appreciable. Most of such reactions are, however, studied at constant pressure
and change in enthalpy (ΔH) is involved
Exothermic and Endothermic Reactions
❒ Let
us consider a general reaction at constant pressure,
A +
B → C +
D
❒ If
HA, HB, HC and HD be the enthalpies
of A, B, C and D respectively, the heat of reaction at
constant pressure viz., ΔH is equal to the difference in enthalpies
of the products and the reactants
i.e.,
ΔH =
Hproducts – Hreactants
= (HC
+ HD) – (HA + HB)
❒ The
value of ΔH may be either zero, negative or positive. Where ΔH is zero, the
enthalpies of the products and reactants being the same, the heat is evolved or
absorbed. In case ΔH is negative, the sum of enthalpies of the products is less
than that of the reactants and the difference in enthalpy is given out in the
form of heat.
❒ Such
reactions which are accompanied by the evolution of heat energy are called
Exothermic reactions.
❒ When
ΔH is positive, the enthalpy or heat content of the reactants and an equivalent
of heat is absorbed by the system from the surroundings.
❒ Such
reactions which are accompanied by absorption of heat are called Endothermic
reactions. Thus for an exothermic reaction Hp < Hr and
ΔH = – ve, for an endothermic reaction Hp > Hr and ΔH
= +ve.
Examples of Exothermic and Endothermic Processes
❒ When
trying to classify a process as exothermic or endothermic, watch how the
temperature of the surroundings changes.
❒ An
exothermic process releases heat, and causes the temperature of the immediate surroundings
to rise.
❒ An
endothermic process absorbs heat and cools the surroundings.
Sign of ΔH and ΔE
❒
A negative sign of ΔH or ΔE shows that heat is evolved and the
reaction is exothermic.
❒ A positive
sign of ΔH or ΔE indicates that heat energy is absorbed and the reaction is endothermic.
Calculation of ΔH from ΔE and vice versa
❒ The
enthalpy change of a reaction at constant pressure (ΔH) and internal energy
change (ΔE) are related to each other as:
ΔH =
ΔE + P × ΔV ... (i)
where ΔV is the change in volume due to expansion or contraction
when measurement is done at
constant pressure, P. Though
heat changes of reactions are usually measured at constant pressure, it is
sometimes necessary to carry out the reaction at constant volume as, for
example, in the measurement of heat of combustion in a bomb calorimeter.
❒ The
above relationship can be used, if desired, for the conversion of ΔH into ΔE
and vice versa.
❒ Let
us consider a reaction
aA +
bB → cC
+dD
Change in number of moles
=
No. of moles of products – No. of moles of reactants
= (c
+ d) – (a + b)
= Δn
❒ Let
the volume occupied by one mole of the gas be V. Then, change in volume, ΔV =
change in No. of moles × volume occupied by one mole of the gas.
ΔV =
Δn × V
P ×
ΔV = P (Δn × V)
P ×
ΔV = PV × Δn ... (ii)
But
PV =
RT (for one mole of gas)
Putting RT in place of PV in equation (ii) we get:
PΔV
= RT Δn
Substituting the value of PΔV in equation (i) we get:
ΔH =
ΔE + Δn RT
❒ It
may be pointed out that while determining the value of ΔH, only the number of
moles of gaseous reactants and products are taken into consideration. The value
of gas constant R is taken either in calories or joules per degree per mol and
is 1.987 cal (approximately 2 calories) or 8.314 joules.
Solved Problem
Problem (1): The heat of combustion of ethylene
at 17ºC and at constant volume is – 332.19 kcals. Calculate the heat of
combustion at constant pressure considering water to be in liquid state. (R = 2 cal degree–1 mol–1)
Solution
The chemical equation for the combustion of ethylene is:
Problem (2): The heat of combustion of carbon monoxide
at constant volume and at 17ºC is – 283.3 kJ. Calculate its heat of combustion
at constant pressure (R = 8.314 J degree–1 mol–1).
Solution
Problem (3): The heat of formation of methane at
298 K at constant pressure is – 17.890 kcal. Calculate its heat of formation at
constant volume. (R = 1.987 cal degree–1 mol–1)
Solution
The thermochemical equation for the heat of formation of methane at
298 K at constant pressure is:
Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.
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