# Enthalpy

According to first law of thermodynamics,

q= ΔU + PΔV

If the process is carried out at constant volume , ΔV=0

qv = ΔU

where v indicates constant volume.

Internal energy change is the heat absorbed or evolved at constant volume.

ΔU is a state function, therefore qv ,is also a state function.

If the process is carried out at constant pressure, the work of expansion is given by

w = –P ΔV

where ΔV is the increase in volume and P is the constant pressure.

q=ΔU – w

where q is the heat absorbed by the system, ΔU is the increase in internal energy of the system and w is the work done by the system.

Under conditions of constant pressure, putting w= –P ΔV and representing the heat absorbed by qp we get,

qp = ΔU +  PΔV

When the system absorbs qp joules of heat, its internal energy increases from U1 to U2 and the volume increases from V1 to V2.Then, we have,

ΔU = U2 – U1

ΔV = V2 -V1

qp = ( U2 – U1 ) + P ( V2 -V1)

qp= ( U2 + PV2 ) – ( U1 + PV1)

The thermodynamic quantity U + PV is called heat content or enthalpy of the system and is represented by symbol H.

H= U + PV

If H2 is the enthalpy of the system in the final state and H1 is the value in the initial state, then

H2 = U2 + PV2

H1 = U1 + PV1

qp =H2 -H1

qp =ΔH

Enthalpy change of a system is equal to the heat absorbed or evolved by the system at constant pressure.

As most of the reactions are carried out at constant pressure ,the measured value of the heat evolved or absorbed is the enthalpy change enthalpy.

ΔH= ΔU + PΔV

Enthalpy change accompanying a process may be defined as the sum of the increase in internal energy of the system and the pressure- volume work done i.e. the work of expansion.

The energy stored within the substance or the system that is available for conversion into heat is called the heat content or enthalpy of the system or substance.

The absolute value of heat content or enthalpy of a substance or a system cannot be measured.

U and V are extensive properties therefore the enthalpy is also an extensive property.

Relation between heat of reaction at constant pressure and at constant volume

qp =ΔH and qv = ΔU

ΔH= ΔU + PΔV

ΔH= ΔU + P(V2 – V1)

ΔH= ΔU + (PV2 – PV1)

where V1 is the initial volume and V2 is the final volume of the system.

For ideal gas,

PV = nRT

PV1 =n1 RT

PV2 =n2 RT

where n1 is the number of moles of gaseous reactants and n2 is the number of moles of gaseous products.

ΔH= ΔU + (n2RT -n1RT)

ΔH= ΔU + (n2 – n1 )RT

ΔH= ΔU + Δng RT

where Δn= n2 -n1 is the difference between the number of moles of the gaseous products and those of the gaseous reactants.

qp = qv – ΔngRT

Conditions under which qp =qv or ΔH = ΔU

1) When the reaction is carried out in closed vessel so that volume remains constant, i.e. ΔV= 0.

2)When reaction involves only solids or liquids or solution but no gaseous reactant and product. This is because the volume changes of the solids and liquids during a chemical reaction and negligible .

3)When reaction involves gaseous reactants and products but their number of moles are equal in the reactions.