Enthalpy is a thermodynamic quantity equal to the internal energy of a system plus the product of its volume and pressure.

Enthalpy of a system is defined by the relation,

H= U + pV…………………………..1

U: is the internal energy

p: is the pressure of the systems

V: is the volume of the systems.

U, p and V are state variables, as such H which depend on them is also a state function. That is, the enthalpy of a system in a particular state is completely independent of the manner in which that state has been achieved, If H1, and H2 are the enthalpies of the initial and the final states of a system, then the enthalpy change accompanying the process is given by,

ΔH=H2 + H1………………………………2

As such our equation can be rearrange in the following ways

= (U2+p2V2) – (Ul + plVl)

By collecting likes items we have another equation bellow

= ΔU + (p2V2 – plVl) ………………..3

But in a situation in which we have a constant pressure process(pl = p2=p), the equation 3 can be written as shown below

ΔH =ΔU + p(V2 – V1)

By multiplying p in the bracket of (V2 – V1), then our equation become

ΔH =ΔU+ pΔV ………………………………4

But in a case of finite change, then the equation 4 can be Rewriting finite in the following

qp = ΔU+ pΔV ……………………………5

this means, the heat capacity at constant pressure is equal to the partial

differential of H with respect to temperature at constant pressure. Interestingly

for an ideal gas. H depends on 7″ only and not on p;

Using this equation in Equation 5, then we have

qp= ΔH ………………6

The subscript p in qp stands for the constant pressure condition.

In other words, the enthalpy change is equal to the heat absorbed by the system at constant pressure.

For a small change in enthalpy, we can write

dqp = dH ………………………………….7

In a situation that there is no phase change or chemical reaction, then we have.

dH = CpdT = nCpdT …………………8

In order to obtain ΔH value when an ideal gas is hated from temperature T1 to T2,

at constant pressure, the integrated form of Eq. 1.36 is to be used.

ΔH = ${\int}_{T1}^{T2}CpdT={\int}_{T1}^{T2}\overline{)C}pdT$…………………………9

Since many laboratory processes are carried out at constant pressure (atmospheric pressure), the enthalpy change of a system is of great significance. It may be noted that since the absolute value of the internal energy of a system is not known, it is also impossible to know the absolute enthalpy of the system. Fortunately, for most processes we are only concerned with the changes in enthalpy which may be measured by taking any suitable reference states of elements.

In reference to specific heat capacity with constant pressure, our Cp can be defined as Cp =$\left(\frac{\partial H}{\partial T}\right)$ this tells us that, the heat capacity at constant pressure is equal to the partial differential of H with respect to temperature at constant pressure. Interesting for an ideal gas, H depends on T only and not on P;

i.e = $\left(\frac{\partial U}{\partial T}\right)$v =0 for an ideal gas.

Those processes in which heat is supplied to the system are called endothermic and, in those system ΔH is given a positive sign, while those ssytem which loss heat are called exothermic processes (in which heat is evolved), ΔH is given a negative sign. Enthalpy changes connected with certain typical processes are given special Names base on the process they are connected to. For example,

enthalpy of vaporization or evaporation is the enthalpy change accompanying the conversion of one mole of a liquid to its vapour.

Similarly, enthalpy of fusion and sublimation are the enthalpy changes accompanying fusion or sublimation of one mole of a substance.

For a chemical reaction, the ‘enthalpy of reaction is the difference in the enthalpies of the products and the reactants as per the stoichiometry given in the chemical equation. Hope you understand these tutorial, if not you are free to ask question base on what you need clarification on, via comment. You question will be attended to. Thank you. Hope to see you visit our next tutorial post which will be on relationship between Cp and Cv values of an ideal gas.

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