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# Thermodynamic System

02nd Jan 2021 @ 15 min read

Physical Chemistry

The enthalpy (H) of a thermodynamic system is the sum of the internal energy (U) and pressure-volume energy (PV).

H = U + PV

The internal energy is the total energy contained in the system, and pressure-volume energy is the energy spent against the external pressure “P” to create volume “V” of the system. We can interpret the enthalpy as the internal energy when the system was zero volume.

In chemistry, our concern is not with the absolute value of enthalpy but rather the change in the enthalpy.

The absolute enthalpy cannot be estimated directly since the value of the absolute internal energy cannot be reckoned for real systems. Further, in chemistry and thermodynamics, we are interested in measuring the change in enthalpy, not its absolute value.

The change in enthalpy (ΔH) is given as:

ΔH = ΔU + Δ(PV) = ΔU + VΔP + PΔV = ΔU + VΔP + PΔV

From the first law of thermodynamics, we know ΔU = Q − PΔV.

Substituting, ΔH = Q − PΔV + VΔP + PΔV = Q + VΔP

We can conclude from the previous equation, the change in enthalpy for a constant-pressure system is equal to the heat exchange, ΔH = Q.

Further, for a reversible process, Q = TΔS.

ΔH = TΔS + VΔP

Enthalpy has many purposes, especially in chemistry. We measure the change in energy using the enthalpy change. For the rest of the article, we will discuss various types of enthalpy change.

### Enthalpy of vaporization

The enthalpy of vaporization or the latent heat of vaporization is the energy supplied to convert a unit quantity of liquid to vapor. It is dependent on the temperature and pressure. Its value increases with an increase in the pressure, while with temperature, the latent heat decreases and becomes zero after the critical temperature of the fluid.

Since vaporization is a physical change and there is no breaking of chemical bonds, the enthalpy of vaporization of a liquid is decided by the intermolecular forces.

The liquids with stronger intermolecular forces will have a higher latent heat than the liquids with weaker intermolecular forces. Usually, the enthalpy of vaporization is reported at the normal boiling point (Tb) of a liquid. For example, the enthalpy of vaporization of water is 40.65 kJ/mol at 100°C.

ΔH(vap) = H(vap) − H(liq) = Tb ΔS(vap) + VΔP

### Enthalpy of condensation

The enthalpy of condensation is the opposite of the enthalpy of vaporization. In condensation, the vapor condenses to form a liquid.

ΔH(cond) = H(liq) − H(vap)

Thus, we can says: ΔH(cond) = − ΔH(vap)

For water, ΔH(cond) = − ΔH(vap) = −40.65 kJ/mol at 100°C.

The enthalpy of condensation of water is negative obviously because water vapor has more energy than liquid water.

### Enthalpy of sublimation

Sublimation is the process in which solid directly transforms into vapor. For example, ice transforms straight to vapor without converting into liquid. The enthalpy of sublimation for H2O is 51.1 kJ/mol at 273.15 K. ΔH(sub) = H(vap) − H(solid) Under the same state condition (T, P), the enthalpy of vapor is higher than the liquid, which in turn is higher than solid. So, the enthalpy of sublimation is always higher than the enthalpy of vaporization. ΔH(sub) > ΔH(vap) Enthalpy of fusion The enthalpy of fusion is the amount of energy required to convert a unit quantity of solid into a liquid. It can be expressed in the energy unit per mole or energy unit per kg. For example, the heat of fusion for converting 1 kg of ice to liquid-state water is 333.55 kJ at 0 °C.

ΔH(fus) = H(liq) − H(solid)

Solidification is the reverse of fusion, so ΔH(fus) = − ΔH(sol)

Also, the enthalpy of fusion is always less than the enthalpy of sublimation. ΔH(sub) > ΔH(fus) for the same pressure and temperature.

Sublimation is the addition of fusion and vaporization if the temperature and pressure are kept the same through the change.

Thus, ΔH(fus) + ΔH(vap) = ΔH(sub) @ T, P

### Enthalpy of mixing

When two or more different substances are mixed, the result is a mixture.A mixture may behave differently from its individual components. The properties, like boiling point, melting point, may not concur with the weighted sum of the individual components’ properties.

This is due to the fact that there is a change in the intermolecular structure after mixing. In individual components, if pure, every particle is surrounded by particles of the same species. For example, in pure water, every water molecule is surrounded by other water molecules. But this changes if any external component, says ethanol is added.

In the above illustration, A and B are mixed. This mixing alters the intermolecular forces. And because of this change, there is a change in enthalpy due to mixing.

We calculate the enthalpy of mixing as the difference of the enthalpy of the mixture (H(mix)) and the sum of the enthalpy of the individual components (ΣH(i)).

ΔH(mix) = H(mix) − ΣH(i)

If mixing is endothermic, then the enthalpy change is positive, while it is negative in exothermic.

In an ideal mixture, the enthalpy change due to mixing is zero since every particle is identical to every other particle in the mixture.

Note: Mixing does not involve reacting species. There are no chemical reactions, so the enthalpy change due to mixing comes only from the breaking and formation of intermolecular forces.

### Enthalpy of dilution and solution

Enthalpy of dilution and solution are two subsets of enthalpy of mixing. In dilution, we are diluting a single component of a solution, and in solution, the enthalpy change is from the mixing of pure solutes and a solvent to form a solution.

### Enthalpy of hydration

When one mole of gaseous ions dissolves in a sufficient amount of water, the change in enthalpy is called the enthalpy of hydration. In hydration, cations and anions interact with the polarity of water molecules. Cations, positively charged species, are influenced by electronegative oxygen, while anions attract hydrogen atoms of water.

### Enthalpy of Formation

The change in the enthalpy when a mole of a substance is formed from its constituent elements such that all elements are in their standard states is called the enthalpy of formation. The enthalpy of formation is normally quoted for Standard Temperature and Pressure unless otherwise mentioned.

The standard states of elements are defined as the most stable states under 1 bar pressure. For example, diatomic hydrogen gas is the most stable state of hydrogen under 1 bar pressure.

Consider the following the reaction:

2H2(g) + C(graphite) --> CH4(g)

In the above reaction, 1 mol of methane is formed from 2 mol of hydrogen and 1 mol of graphite. Since all the elements are in standard stable states, the enthalpy change is called the enthalpy of formation.

### Enthalpy of reaction

A chemical reaction involves the breaking of chemical bonds and the formation of new bonds. The energy change before and after the reaction is called the enthalpy of reaction.

The difference in the enthalpy is the total enthalpy of the products minus the total enthalpy of the reactants.

ΔH(rxn) = ΣH(reactant) − ΣH(product)

If ΔH(rxn) is negative, the reaction is exothermic, while the positive value indicates the endothermicity.

### Enthalpy of combustion

The enthalpy of combustion is the energy released when one mole of a substance is completely burned/combusted with oxygen. Combustion is an exothermic reaction, so the enthalpy change is negative ΔH(com) < 0.

When we talk about combustion, the reactants are presumably organic compounds and fuels. The heat of combustion is commonly known as the calorific value of a fuel. And it is expressed in the energy unit per mole, the energy unit per kg, or the energy unit per L.

The prime products are carbon dioxide and water vapor.

In the above reaction, 1 mol of cyclopentane is combusted completely to give carbon dioxide and water vapor. The heat of combustion is −3129 kJ/mol.

### Enthalpy of Atomization

Atomization is the process in which all constituent atoms of a compound are completely separated. The products are gaseous, individual atoms. The change in enthalpy in the atomization is called the enthalpy of atomization.

In atomization, there is only the breaking of bonds; no new bonds are formed. So, it is obvious that energy is always supplied, and the change in enthalpy is always positive. ΔH(at) > 0.

Consider the following example.

CH4(g) --> C(g) + 4H(g)

When one molecule of methane is atomized, we get an atom of gaseous carbon and four atoms of monatomic hydrogen.

### Enthalpy of Neutralization

The enthalpy of neutralization is a special case of the enthalpy of reaction. In neutralization, acid and a base react to form salt and water. The heat released in the process is the enthalpy of neutralization. Since the neutralization is an exothermic reaction, the enthalpy of neutralization is negative. ΔH(neu) < 0.

HCl(aq) + NaOH(aq) --> NaCl(aq) + H2O(l)

When one mole of aqueous HCl reacts with one mole of aqueous NaOH, we get ΔH(neu) = −57.9 kJ.

Note: the enthalpy of neutralization varies according to the strength of acid and base.

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