Notes On Thermodynamic Quantity: Enthalpy - CBSE Class 11 Chemistry
To study the heat changes in a chemical reaction at constant temperature and constant pressure, a new thermodynamic function called enthalpy was introduced.

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.
H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.
Change in enthalpy =  Enthalpy of products - Enthalpy of reactants
∆H = HP-HR
From the first law of thermodynamics
∆U =qp-P∆V
qp =heat absorbed by the system
-P∆V=work done by the system.
For finite changes at constant pressure,         
∆H= ∆U+∆(PV)
∆H=∆U+P∆V         (∵ P is constant )           
∆H=qp                       
∆H=-Ve for exothermic reactions
∆H=+Ve for endothermic reactions.
 
Relation between ∆H &∆U:
Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant
∆H=∆U+P∆V
∆H=∆U+P(0)
∆H=∆U
 
The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.
Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is VA and the number of moles in the reactants is nA. Similarly, the volume of the products is VB and the number of moles in the product is nB.
According to the ideal gas equation,
Pv=nRT
pvA=nART                               
pvB= nBRT
Thus
pvB- pvA = nBRT- nART
p(vB- vA) =RT(nB-nA)
p∆v =∆ngRT
∆H=∆U +p∆v
∆H=∆U+∆ngRT
 
Heat capacity:  The capacity to absorb heat energy and store it is known as the heat capacity of a system.
 q=C .∆T
 Where C is called the heat capacity of the system.
If q calories is the heat absorbed by the mass m and the temperature rises from T1 to T2, the heat capacity
C is given by the expression
C = q /T2-T1
Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.
The SI units of molar heat capacity are J0k-1mole-1.
 
Relation between molar heat capacity at constant volume, which is denoted by Cv and molar heat capacity at constant pressure, which is denoted by Cp:

q=C∆v
At constant volume
qv=Cv∆T =∆U
At constant pressure
qp = Cp∆T =∆H
The difference between Cp and CV for one mole of an ideal gas can be derived as follows: 
The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)
For 1 mole of gas pv =RT
∆H= ∆U+∆(RT)
R is aconstant
∆H= ∆U+R∆T
Cp∆T= Cv∆T+R∆T
Since  ∆T=1
Cp= C+R
R = Cp- Cv                

Summary

To study the heat changes in a chemical reaction at constant temperature and constant pressure, a new thermodynamic function called enthalpy was introduced.

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.
H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.
Change in enthalpy =  Enthalpy of products - Enthalpy of reactants
∆H = HP-HR
From the first law of thermodynamics
∆U =qp-P∆V
qp =heat absorbed by the system
-P∆V=work done by the system.
For finite changes at constant pressure,         
∆H= ∆U+∆(PV)
∆H=∆U+P∆V         (∵ P is constant )           
∆H=qp                       
∆H=-Ve for exothermic reactions
∆H=+Ve for endothermic reactions.
 
Relation between ∆H &∆U:
Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant
∆H=∆U+P∆V
∆H=∆U+P(0)
∆H=∆U
 
The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.
Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is VA and the number of moles in the reactants is nA. Similarly, the volume of the products is VB and the number of moles in the product is nB.
According to the ideal gas equation,
Pv=nRT
pvA=nART                               
pvB= nBRT
Thus
pvB- pvA = nBRT- nART
p(vB- vA) =RT(nB-nA)
p∆v =∆ngRT
∆H=∆U +p∆v
∆H=∆U+∆ngRT
 
Heat capacity:  The capacity to absorb heat energy and store it is known as the heat capacity of a system.
 q=C .∆T
 Where C is called the heat capacity of the system.
If q calories is the heat absorbed by the mass m and the temperature rises from T1 to T2, the heat capacity
C is given by the expression
C = q /T2-T1
Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.
The SI units of molar heat capacity are J0k-1mole-1.
 
Relation between molar heat capacity at constant volume, which is denoted by Cv and molar heat capacity at constant pressure, which is denoted by Cp:

q=C∆v
At constant volume
qv=Cv∆T =∆U
At constant pressure
qp = Cp∆T =∆H
The difference between Cp and CV for one mole of an ideal gas can be derived as follows: 
The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)
For 1 mole of gas pv =RT
∆H= ∆U+∆(RT)
R is aconstant
∆H= ∆U+R∆T
Cp∆T= Cv∆T+R∆T
Since  ∆T=1
Cp= C+R
R = Cp- Cv                

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