subject chemistry paper no and title 10: physical
TRANSCRIPT
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
Subject Chemistry
Paper No and Title 10: Physical Chemistry- III (Classical
Thermodynamics, Non-Equilibrium
Thermodynamics, Surface chemistry, Fast kinetics)
Module No and
Title
6, Thermochemistry and Hessβs law
Module Tag CHE_P10_M6
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
TABLE OF CONTENTS
1. Learning outcomes
2. Introduction
3. Change in thermodynamic quantities during a chemical reaction
3.1 Change in internal energy of a chemical reaction
3.2 Change in enthalpy of a chemical reaction
4. Relation between the enthalpy at constant volume and enthalpy at constant pressure
5. Enthalpy of a chemical reaction
6. Determination of enthalpies of a reaction
7. Kirchhoff equation: Variation of enthalpy of reaction with temperature
8. Flame and explosion temperatures
9. Hessβs law
10. Extension of Hessβs law
11. Application of Hessβs law
12. Summary
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
1. Learning Outcomes
After studying this module you shall be able to:
Depict the change in thermodynamic quantities during a chemical reaction
Derive the relation between enthalpy at constant pressure and enthalpy at
constant volume
Know about Kirchhoff equation
Learn about Flame and Explosion temperature
Learn about Hessβs law of constant heat summation
Know how Hessβs law is extended to find entropy and free energy change
Know the applications of Hessβs law
2. Introduction
The branch of chemistry which deals with the energy changes involved in chemical reaction
is called thermochemistry. It is the study of energy and heat associated with chemical
reactions. Thermochemistry focuses on the energy changes, primarily on the systemβs energy
exchange with its surroundings. Thermochemistry can predict the quantities of reactants and
products during the course of the reaction. It is also useful in prediction of the spontaneity of
the reaction. It merges the concepts of thermodynamics with the concept of energy in the
form of chemical bonds. The quantities like enthalpy, heat capacity, entropy, free energy,
heat of formation are mainly calculated through this. According to thermochemistry, the
change in energy which occurs in chemical reaction is mainly because of the change of bond
energy, i.e., it results from the breaking of bonds in the reactants and formation of new bonds
in products.
Thermochemistry is based on two laws:
Lavoisier and Laplaceβs law: This law states that the change in energy
accompanying any transformation is equal and opposite to change in energy
accompanying the reverse process.
Hessβs law: This law states that the change in energy accompanying any
transformation is same whether the process occurs in one step or many steps.
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
Lavoisier, Laplace and Hess have also done investigation on specific heat and latent
heat.
3. Change in thermodynamic quantities during a chemical reaction
3.1 Change in internal energy of a chemical reaction
Consider a chemical reaction during which the temperature and volume is kept constant, i.e.,
dV=0. Thus, work done (w) is also equal to zero as w=PdV. Therefore, equation of the First
law (viz., U = q + w) becomes:
U = vq β¦(1)
where vq stands for the heat exchanged at constant volume.
Let UR be the internal energy of the reactants and UP be the internal energy of the products,
thus change in internal energy will be
ΞU= UP β UR = qv β¦(2)
3.2 Change in enthalpy of a chemical reaction
The heat exchanged at constant pressure is known as the enthalpy change. Suppose pq be the
heat exchanged during a chemical reaction which is occurring at constant pressure. Therefore,
pH q β¦(3)
Let HR be the enthalpy of the reactants and HP be the enthalpy of the products, thus change in
enthalpy will be
ΞH = HP β HR = qP β¦(4)
Thermochemistry enables us to predict the amount of heat that would be evolved or absorbed
in a process without actually performing a tedious set of experiments in the laboratory. The
energy changes for the processes which are not feasible experimentally can also be calculated
through thermochemistry.
Sign convention:
Reactions in which heat is absorbed by the system are called endothermic reactions. In
such reactions HP > HR, so ΞH is positive. Since the energy of the system also increases by
the absorption of heat thus ΞU is also positive in endothermic reactions. While the reactions
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
in which heat is evolved, are called exothermic reactions. In such reactions HP < HR so ΞH
is negative. In such reactions ΞU is also negative.
4. Relation between enthalpy at constant volume (qv) and enthalpy at
constant pressure (qp)
The relation between ΞH and ΞU is given by:
H U P V β¦(5)
where ΞV is the volume change taking place in a reaction.
Since vq U and pq H , therefore we can write equation (5) as
p vq q P V β¦(6)
Now writing the above equation in simplified manner;
For n moles of an ideal gas,
PV = nRT β¦(7)
Suppose n1 be the number of moles for gaseous reactants and n2 be the number of moles of
gaseous products. Let n2 > n1. Thus increase in the number of moles is given by 2n β 1n =
gn . The corresponding increase in volume ( V ) will be given by (V/n) gn . Therefore,
g gP V P(V / n) n RT n β¦(8)
Thus, gP V RT n β¦(9)
Substituting equation (8) in equation (6),
p v gq q n RT β¦(10)
In the above equation gn stands for the difference between the number of moles of
gaseous products and gaseous reactants.
5. Enthalpy of a chemical reaction
Standard Enthalpy change of a reaction is defined as the enthalpy change of reaction
determined at 25ΒΊC and at 1atm pressure and is denoted by ΞHΒΊ
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
Considering various enthalpy changes:
(a) Enthalpy of formation
The enthalpy of formation can be defined as the amount of heat exchanged at constant
temperature and pressure during the formation of one mole of the substance from its
constituent elements in their standard states. It is represented by ΞfH. Its unit is kJ molβ1.
For example, the enthalpy of formation of CO2 is equal to the enthalpy change for the
following reaction
C(s) + O2(g) β CO2(g) ΞfH = β393.5 kJ molβ1
π»2(π) + 1
2π2(π) β π»2π(π) ΞfH = -285.830 kJ mol-1
π»2π(π) β π»2(π) +1
2π2(π) ΞfH = +285.830 kJ mol-1
(b) Enthalpy of combustion
It is defined as the enthalpy change that takes place when one mole of a substance is burnt
completely in the presence of oxygen at a given temperature and pressure. It is denoted by
ΞcH and the unit is kJ molβ1. The combustion is always an exothermic process.
For example, combustion of methane
CH4(g) + 2O2(g) β CO2(g) + 2H2O(l) ΞcHΣ©(298 K)= β890 kJ molβ1
πΆ2π»6(π) +7
2π2(π ) β 2πΆπ2(π) + 3π»2π(π) βπ»Β°(298 πΎ) = β1560 ππ½ πππβ1
(c) Enthalpy of solution
The amount of heat exchanged when 1 mole of solute is dissolved in a sufficient amount of
solvent at a specified temperature and pressure is known as enthalpy of solution.
For example,
HCl (g) + 10 H2O(l) β HCl.10H2O(aq) ΞH = β69.01 kJ molβ1
HCl (g) + 40 H2O(l) β HCl.40H2O(aq) ΞH = β72.79k J molβ1
These values of ΞH show the general dependence of the heat of solution on the amount of the
solvent. As more and more solvent is used the value of heat of solution changes. As the
amount of the solvent increases the resulting solution becomes more dilute and ultimately it
becomes so dilute that further addition of solvent produces no enthalpy change. This solution
is known as infinitely dilute solution.
(d) Enthalpy of Sublimation
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
It is the amount of enthalpy change to convert one mole of a solid to vapor state at a given
temperature and pressure.
H2O (l) β H2O(g) ΞsubHΣ©(298 K)= 50.0 kJmolβ1
(e) Enthalpy of Fusion
It is the change in enthalpy to convert one mole of a solid to its liquid state at a given
temperature and pressure.
H2O (s) β H2O(l) ΞfusHΣ©(298 K)= 6.0 kJ molβ1
(f) Enthalpy of Atomization
It is the amount of heat required to convert one mole of a substance into its constituent atoms
in the gaseous state.
C(graphite) natomizatio
C(g) βaH(C) =716.68 kJmolβ1
H2(g) natomizatio
2H(g) βaH(H)= 436 kJ molβ1
6. Determination of Enthalpies of reactions
Enthalpies of reactions at 25ΒΊC can be determined if ΞHΒΊf values of the reactants and products
involved in the reactions are known as
ΞHΒΊ = Ξ£ΞHΒΊf (products) - Ξ£ΞHΒΊf (reactants) β¦(11)
By convention, ΞHΒΊf values for the elements in their standard states are taken as zero.
7. Kirchhoff Equation: Variation of Enthalpy of reaction with
Temperature
The change in enthalpy of any physical or chemical process varies with temperature at
constant pressure. The effect of temperature on the enthalpy can be understood as follows:
Consider a reaction,
aA + bB cC + dD
The enthalpy change for the above reaction will be:
products reac tan ts C D A BH H H (cH dH ) (aH bH ) β¦(12)
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
Differentiating equation (12) with respect to temperature, keeping pressure constant
C D A B
P P P PP
H H H H( H)c d a b
T T T T T
β¦(13)
Since, P PC ( H / T)
Therefore, equation (13) can be written as
[π(βπ»)
ππ]
π= β πΆπ (πππππ’ππ‘π ) β β πΆπ(πππππ‘πππ‘π )
P, C P, D P, A P, B PP
( H)cC dC aC bC C
T
β¦(14)
where PC = Sum of heat capacities of products β Sum of heat capacities of reactants.
Equation (14) is known as Kirchhoff equation. This equation states that the variation of H
of a reaction with a temperature at constant pressure is equal to PC of the system, i.e.,
P P[ ( H) / T] C β¦(15)
Rearranging the above equation,
Pd( H) C dT β¦(16)
Similarly, the dependence of enthalpy on temperature at constant volume is given by,
V V[ ( H) / T] C or Vd( U) C dT β¦(17)
If the temperature range is small, then change in heat capacity is given by, (assuming
heat capacities are not dependent on temperature)
T T T2 2 2
P PT T T1 1 1
d( H) C dT C dT or 2 1 P 2 1H H C (T T )
β¦(18)
Similarly,
2 1 V 2 1U U C (T T ) β¦(19)
If the temperature range is not small then the heat capacities will vary with temperature.
Thus it is convenient to express the heat capacity as a power series in Temperature (T) i.e.
2PC T T β¦(20)
where , and are constants for a given species. Similarly,
PC = = 2T T ...... β¦(21)
Substituting equation (21) in equation (15) and integrating between T1 and T2, we get
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
T T2 2 2
T T1 1
d( H) ( T T )dT β¦(22)
Or,
2 2 3 32 1 2 1 2 1 2 1
1H H (T T ) (1 / 2) (T T ) (T T )
3 β¦(23)
Equation (23) is the integrated Kirchhoff equation.
8. Flame and Explosion Temperatures
The combustion of a gaseous fuel in air occurs so rapidly that the heat produced during
combustion does not get enough time to dissipate into the surroundings. Thus, combustion
process is found to be equivalent to an adiabatic process. The entire amount of heat produced
is used up to heat the gases which are produced during combustion. Maximum flame
temperature is defined as the maximum temperature attained by the flame zone (containing
the resultant gases) due to the heat evolved by the combustion of the fuel under adiabatic
conditions at constant pressure. On the other hand, if the combustion is carried out under
adiabatic conditions at constant volume, the maximum temperature attained is called
maximum explosion temperature.
Kirchhoff equation is used to calculate the maximum flame temperature for an isobaric
adiabatic process. This is done as follows,
Pd( H) / dT C or Pd( H) C dT β¦(24)
Integrating the above equation gives,
Tf
PTi
d( H) C dT or P f iH C (T T ) β¦(25)
In the above equation PC is assumed to be constant that is why it is taken outside the
integral sign. Thus, if the values of H , PC and the initial temperature iT are known then
the final temperature fT (maximum flame temperature ) can be calculated.
9. Hessβs law
Hessβs law was established by the Russian chemist German H. Hess in 1840. This law is
known as Hessβs law of constant heat summation. This law states that the amount of heat
evolved and absorbed in a process, including a chemical change, is the same whether the
process takes place in one or several steps, i.e., total change in enthalpy does not change
during the course of the reaction. Thus Hessβs law is also known as principle of conservation
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
of energy. The change in enthalpy does not depend on the path taken from the initial to the
final state ( i.e. enthalpy is a state function). Reaction enthalpy changes can be determined by
calorimetry for many reactions. It is of particular utility in calculations of the heat of
reactions which are difficult for practical calorimetric measurements. The overall energy
needed for a chemical reaction can be determined by Hessβs law.
Hessβs law states that the enthalpy change (i.e., heat of reaction at constant pressure) in a
chemical reaction does not depend on the path between the initial and final states of the
system. That is the overall change in enthalpy is same during a chemical change of a reaction
regardless of the number of steps through which the reaction has been taken place. For
example, for a change from reactant to product that can take place in four steps or a single
step, the total enthalpy change will be same.
Single step process:
Reactant β Product ΞH
Multiple step process:
Reactant βA ΞH1
A βB ΞH2
B β C ΞH3
Cβ Product ΞH4
According to Hessβs law
ΞH = ΞH1 + ΞH2 + ΞH3 + ΞH4
This can also be shown by following diagram:
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
This generalization means that enthalpy of the reaction depends only on the initial reactants
and the final products and not at all on the intermediate products that can be formed.
Thus, enthalpy change which cannot be measured directly is calculated by Hessβs law. If the
net enthalpy change of the reaction is negative, then the reaction is said to be exothermic;
positive value for enthalpy change corresponds to endothermic reactions.
Hessβs law states that changes in enthalpy are additive. Thus for a single reaction change in
enthalpy ΞH is given by:
π₯π»πππππ‘πππΒΊ = β π₯π»π(πππππ’ππ‘π )
ΒΊ β β π₯π»π(πππππ‘πππ‘π )ΒΊ
where ΞHf stands for the enthalpy of formation and superscripts ΒΊ represent standard state
values. The above equation is the combination of two reactions. These are:
Reactants β Elements
π₯π»ΒΊ = β β βπ»π(πππππ‘πππ‘π )Β°
Elements β Products
βπ»Β° = β βπ»π(πππππ’ππ‘π )Β°
10. Extension of Hessβs law
The changes in entropy and in Gibbs free energy can also be calculated by applying the
concepts of Hessβs law. The Bordwell thermodynamic cycle is an example of such an
extension which takes advantage of easily measured equilibria and redox potentials to
determine experimentally inaccessible Gibbs free energy values.
Thus the change in free energy can be determined by:
βπΊπππππ‘πππΒ° = β βπΊπ(πππππ’ππ‘π )
Β° β β βπΊπ(πππππ‘πππ‘π )Β°
But entropy can be measured as an absolute value thus entropy of formation is not required,
simply absolute values of entropy are used.
βππππππ‘πππΒ° = β βππππππ’ππ‘π
Β° β β βππππππ‘πππ‘π Β° Ext
11. Applications of Hessβs law
Hessβs law of constant heat summation is useful in the determination of enthalpies of the
following:
Calculation of enthalpies of reactions
Determination of enthalpy changes of slow reactions
Calculation of enthalpies of formation
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
Enthalpy of formation of reactive intermediates
It helps in determining the lattice energies of ionic substances by building Born-Haber
cycles if the electron affinity to form the anion is known
Exercise:
The heat of dissociation per mole of a gaseous water at 18ΒΊ C and 1 atm is 241750 J,
calculate its value at 68ΒΊ C. Data given are:
πΆπ(π»2π) = 33.56; πΆπ(π»2) = 28.83; πΆπ(π2) = 29.12 π½πΎβ1πππβ1
Solution: The dissociation reaction is:
π»2π (π) β π»2(π) + 1
2π2(π) βπ»Β°(291 πΎ) = 241750 π½
βπΆπ = πΆπ(π»2) +1
2πΆπ(π2) β πΆπ(π»2π)
= (28.83 +1
2β 29.12 β 33.56) π½ πΎβ1πππβ1
= 9.83 π½ πΎβ1πππβ1
Therefore,
βπΆπ β βπ = (9.83π½ πΎβ1πππβ1 ) β (50 πΎ)
= 491.5 π½ πππβ1
βπ»Β°(341 πΎ) = βπ»Β°(291 πΎ) + βπΆπ β βπ
= 241750 + 491.5 = 242241.5 π½ πππβ1
CHEMISTRY
Paper No. 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Surface chemistry, Fast kinetics)
Module No. 6: Thermochemistry and Hessβs law
12. Summary
The branch of chemistry which deals with the energy changes involved in
chemical reaction is called thermochemistry
The relation between enthalpy at constant volume (qv) and enthalpy at constant
pressure (qp) is given by:
p v gq q n RT
Enthalpies of reactions at 25ΒΊC can be determined if ΞHΒΊf values of the
reactants and products involved in the reactions are known as
ΞHΒΊ = Ξ£ΞHΒΊf (products) - Ξ£ΞHΒΊf (reactants)
Kirchhoff equation is given by
P, C P, D P, A P, B PP
( H)cC dC aC bC C
T
Maximum flame temperature is defined as the maximum temperature
attained by the flame zone (containing the resultant gases) due to the heat evolved
by the combustion of the fuel under adiabatic conditions at constant pressure
If the combustion is carried out under adiabatic conditions at constant volume,
the maximum temperature attained is called maximum explosion temperature
Hessβs law was established by the Russian chemist German H. Hess in 1840
Hessβs law states that the amount of heat evolved and absorbed in a process,
including a chemical change, is the same whether the process takes place in one or
several steps, i.e., total change in enthalpy do not change during the course of the
reaction
Hessβs law states that changes in enthalpy are additive. Thus for a single
reaction change in enthalpy ΞH is given by:
π₯π»πππππ‘πππΒΊ = β π₯π»π(πππππ’ππ‘π )
ΒΊ β β π₯π»π(πππππ‘πππ‘π )ΒΊ