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# What is enthalpy?

The enthalpy is a thermodynamic property whose change under conditions of constant temperature and pressure determines the heat energy of a substance or system associated with a chemical reaction or physical process. Being a state function, it is represented by the capital letter H, where ΔH is its variation.

It is one of the most fundamental extensive properties for studying the thermochemistry of many reactions; that is to say, we speak of the detachment or absorption of heat between the reaction medium and its surroundings. Thus, we say that a reaction is exothermic if its ΔH is negative (ΔH <0), or endothermic if it is positive (ΔH> 0).

Ice, for example, has an enthalpy, H ice , while water also has its own enthalpy, H water . When ice melts, an enthalpy variation occurs, called ΔH fus or heat of fusion (H water -H ice ). The enthalpy of water is higher than that of ice, causing the ΔH fus for ice to be positive and have a value of +6.01 kJ / mol.

Enthalpy and its variation are usually expressed in units of joule or calories. The enthalpy change +6.01 kJ / mol indicates that a mole of ice must absorb 6.01 kJ of heat energy or heat to melt.

### Enthalpy and its variation

Enthalpy itself is incalculable, because it depends on variables that are difficult to measure accurately. A good comparison would be to want to measure the total volume of the oceans: there will always be portions of it below the earth or scattered between the continents. For this reason, and in practice, H cannot be determined; but yes ΔH.

To arrive at a mathematical expression that allows the calculation of ΔH, we must first start from the fundamental definition of enthalpy:

H = U + PV

Being U the internal energy of the system or substance in question, and PV the pressure-volume work that this system exerts on the surroundings in order to exist. Since we are interested in calculating ΔH and not H, we have:

ΔH = ΔU + Δ (PV)

If the pressure is constant, the equation will be:

ΔH = ΔU + PΔV

We know on the other hand that:

ΔU = q + w

Being q the heat and w the work. Substituting we have:

ΔH = q + w + PΔV

But also, we know that:

w = – PΔV

And therefore:

ΔH = q   – PΔV + PΔV

ΔH = q

That is, the ΔH for a reaction or process, carried out under constant pressure, will be equal to the heat q generated or absorbed.

### Enthalpy changes of reactions

The assumption that the pressure remains constant is possible if the reaction occurs under the earth’s atmosphere . For example, the ice in winter landscapes melts without experiencing any pressure other than that of our atmosphere. On the other hand, it also applies to reactions in liquid media, or those that do not produce large amounts of gases.

These reactions absorb or release heat q equal to ΔH, which in turn, is the difference in enthalpies between products and reactants:

ΔH = H Products – H Reactants

## Enthalpy types

It is common practice to speak of ΔH and H as if they were the same: the two are called enthalpies. However, when it comes to types, H is unique for each substance or system; while ΔH, on the other hand, is subject to the nature of the reaction or process itself.

In this sense, we first have positive (ΔH> 0) or negative (ΔH <0) enthalpy variations; Some correspond to endothermic processes or reactions (the surroundings are cooled), while the latter have to do with exothermic processes or reactions (the surroundings are heated).

The sign ‘+’ or ‘-‘ that accompanies ΔH therefore tells us if there is release or absorption of heat in a certain reaction or process; which have their characteristic ΔH, as part of their thermochemical properties.

So we have infinities of types of enthalpies, which can be classified according to physical processes or chemical reactions.

### Physical processes

#### Phase change enthalpy

Substances need to absorb or release heat to pass from one material state or phase (solid, liquid or gas) to another. For example, ice absorbs heat to melt, so the enthalpy for this phase change corresponds to that of fusion, ΔH fus , also called latent heat of fusion.

#### Enthalpy of solution or mixture

Substances when dissolved or mixed in a solvent medium can absorb or release heat, therefore having an enthalpy ΔH dis or ΔH Mixture .

### Chemical reactions

#### Formation enthalpy

It is the heat associated, ΔHº f , to the formation of a compound, specifically one mole of it, from its constituent elements under standard conditions of pressure and temperature (T = 298.15 K and P = 1 atm).

#### Decay enthalpy

It is the associated heat, ΔH des , to the degradation of a compound into smaller and simpler substances. It is generally positive, since heat is needed to break the bonds of the molecules.

#### Enthalpy of hydrogenation

It is the associated heat, ΔH h , to the addition of a hydrogen molecule to a compound, usually a hydrocarbon.

#### Enthalpy of combustion

It is the heat released, ΔH comb , when a substance burns reacting with oxygen. It is negative, since heat and light (fire) are released.

## Examples of enthalpies

Finally, mention will be made of some specific examples of enthalpies:

### Methane combustion

CH 4 + 2O 2 → CO 2 + 2H 2 O

ΔH = -890.3 kJ / mol

That is to say, that one mole of CH 4 upon combustion releases 890.3 kJ of heat energy.

### Ethylene hydrogenation

CH 2 = CH 2 + H 2 → CH 3 CH 3

ΔH = -136 kJ / mol

One mole of ethylene releases 136 kJ of heat when hydrogenated to ethane.

### Dissolution of salt in water

Table salt, NaCl, dissolves in water to separate the Na + and Cl  ions from the crystal lattices and surround itself (hydrate) with water molecules:

NaCl (s) → Na + (aq) + Cl  (aq)

ΔH = +3.87 kJ / mol

That is, dissolving the salt in water should consequently cool the glass or container. However, the amount of heat absorbed is very small, so that our hands will hardly even feel a slight change in temperature.

### Dissolution of potassium chlorate in water

On the other hand, potassium chlorate, KClO 3 , does have a very positive ΔH dis :

KClO 3 (s) → K + (aq) + ClO  (aq)

ΔH = +41.38 kJ / mol

Which means that to dissolve in water it absorbs a lot of heat. And therefore, the container will cool down noticeably, and we will see that the vapor from the surrounding water will moisten its outer surface.

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