# Enthalpy: Definition, Formula and Reactions

Last Updated : 03 Apr, 2024

Enthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let’s know more about Enthalpy in detail below.

## Enthalpy Definition

Enthalpy is total energy of heat in the system which is equivalent to the sum of total internal energy and resulting energy due to its pressure and volume. The system has internal energy because of the molecule in motion and the state of molecules as well. The molecules in motion generate kinetic energy and due to vibrations and electric energy of atoms, the system can have energy in the potential form as well.

Other than this, internal energy also includes energy stored in the form of chemical bonds as we know the breaking of bonds releases energy in an exothermic reaction.

### Enthalpy Symbol

In thermodynamics, Enthalpy is denoted by H. The enthalpy change (ΔH) plays a crucial role in quantifying the heat exchange between a system and its surroundings.

### Enthalpy Units

Enthalpy is typically measured in units of energy per mole, such as joules per mole (J/mol) in the International System of Units (SI) or calories per mole (cal/mol) in the calorie-based system.

## Enthalpy Formula

Enthalpy can be represented as:

H = U + PV

where,

### Enthalpy Change

Enthalpy is a state function (those functions which are only dependent on the initial and final state of the process, not the path taken by the process) as its constituents U, P, and V are state functions. As enthalpy is a state function, change in enthalpy (ΔH) will depend on the initial and the final states of the system.

Thus, change in enthalpy is represented by ΔH and is given by the following formula:

ΔH = H2 – H1

Where,

• H1 is the Initial State Enthalpy of System
• H2 is the Final State Enthalpy of System

As we know, the formula for Enthalpy is H = U + PV, and then

H1 = U1 + P1V1

H2 = U2 + P2V2

Using, the values of H1 and H2, value of ΔH will be,

ΔH = (U2 + P2V2) – (U1+ P1V1)

⇒ ΔH = U2 + P2V2 – U1 -P1V1

⇒ ΔH = (U2 – U1) + (P2V2 -P1V1)

ΔH = ΔU + Δ(PV)

where,

• ΔU is the Change in Internal Energy
• Δ(PV) is the Change in Product of Pressure and Volume

Now, at a constant pressure P1 = P2 = P (Isobaric Process)

ΔH = ΔU + PΔV

Consider pressure inside and outside are the same for this isobaric process (i.e. Pex = P) then the formula for the isobaric process will become,

Qp = ΔU +PΔV

Thus from the above two equations, we get,

ΔH = Qp

Thus from this derived formula, we understand that the increase in enthalpy of a system is equal to the heat absorbed by it at a constant pressure.

### Enthalpy of Fusion

Enthalpy of Fusion is the amount of heat energy required to convert a unit mass of a solid at its melting point into a liquid without an increase in temperature. It changes with the increase in temperature and other parameters.

### Enthalpy of Vaporization

Enthalpy of Vaporization is the amount of heat energy required to convert a unit mass of a liquid at its boiling point into a vapor state without an increase in temperature. Its symbol is ∆H vap. Enthalpy of Vaporization changes with increases with temperature and other parameter.

### Enthalpy of Freezing Water

Enthalpy of freezing water is the heat change required to change liquid ice to water and the its is equal to -6.00 kJ/mole.

### Ionization Enthalpy

Ionization Enthalpy of an element is defined as the amount of energy required to remove an electron from the isolated gaseous in its gaseous state. Ionization energy depends on the force of attraction of electrons and the nucleus.

• Ionization Enthalpy decreases from top to down in a Group.
• Ionization Enthalpy increases from left to right in a Group.

### Activation Enthalpy

Activation Enthalpy of the reaction is defined as the energy required to proceed a reaction. It is the minimum amount of energy that is necessary for the reactants in a chemical reaction to proceed and form the product.

## Relationship between ΔH and ΔU

As we already established that ΔH and ΔU are related by the equation ΔH = ΔU + PΔV, at constant pressure. For reactions between solids and liquids, ΔV is very small because as pressure varies, solids or liquids won`t get affected significantly. So, for these reactions remove PΔV from the equation and write ΔH = ΔU

However, for the reactions involving gases, which are easily affected by the change in pressure, ΔV should strictly be considered.

ΔH = ΔU + PΔV

⇒ ΔH = ΔU + P(V2 – V1)

⇒ ΔH = ΔU + PV2 – PV1

where,

• V1 is the Volume of Gas Reactants in Initial State
• V2 is the Volume of Gas Products in Final State

Here we consider the reactants and the product to be ideal, so we can use the ideal gas equation (PV = nRT). Let’s consider there are n1 moles of gaseous reactants that produce n2 moles of gaseous products. The ideal gas equation becomes

PV1 = n1RT and PV2 = n2RT

⇒ ΔH = ΔU + n2RT – n1RT

⇒ ΔH = ΔU + RT (n2 – n1)

⇒ ΔH = ΔU + RT Δn

### Requirements for ΔH to be equal to ΔU

There are two cases when ΔH and ΔU become equal, which are as follows:

• When the reaction is conducted inside a closed container it prevents the alteration of the volume of the system (ΔV = 0). Then change in enthalpy will change as ΔH = ΔU.
• When there are only solids or liquids involved in the reactions then we can neglect ΔV as the change in them due to the pressure is significant. So, ΔH = ΔU.

There reaction in which the moles of gaseous products and reactants are the same (i.e. n2 = n1). So, ΔH =ΔU

## Difference between Entropy and Enthalpy

Let’s understand the differences between Enthalpy and Entropy in the table below:

Enthalpy

Entropy

The total heat associated with a system is called the enthalpy of the system. The measure of degree of randomness of the molecule is defined as the entropy of the molecule.
Enthalpy is measured in regular conditions. Entropy is measured under controlled conditions.
Enthalpy of any reaction is measured in Joule per Mole. Entropy of any reaction is measured in Joule per Kelvin.
Enthalpy change of any reaction must be minimum in any process. Entropy change of the system must be maximum in any process.

## Endothermic and Exothermic Reactions

A reaction is a process in which two or more two reactants react to form some products we can have a reaction in which we are required to give some energy on the other hand some redactions can give energy to the products. So on this basis, we can have two types of reactions that include

• Endothermic Reactions
• Exothermic Reactions

### Endothermic Reactions

If in any chemical reaction heat is given to the reaction for it to proceed this reaction is called the endothermic reaction. Thus, an endothermic reaction takes heat from the surrounding and makes the surroundings cooler.

### Exothermic Reactions

If in any chemical reaction heat is produced as the result of the reaction then it is called the exothermic reaction. Thus, an exothermic reaction gives heat to the surrounding and makes the surroundings warmer.

## Work done in Chemical Reactions

The work done at constant pressure and temperature by a system is given by

W = – Pex × ΔV

Assume Pex = P, then the equation becomes

W = -P( V2 – V1)

⇒ W = PV1 – PV2

Using the Ideal gas equation,

⇒ W = n1RT – n2RT

⇒ W = -RT (n2 – n1)

⇒ W= – RT Δn

Related :

## Sample Problems on Enthalpy Formula

Problem 1: For a reaction, the system absorbs 10 kJ of heat and does 3 kJ of work on its surroundings. What are the changes in the Internal energy and Enthalpy of the system?

Solution:

According to the First law of thermodynamics,

ΔU = Q + W

Q = +10 kJ and W = -3 kJ

(W = -3 kJ because the work is done on the surrounding by the system so the system has lose that energy)

ΔU = 10 kJ – 3 kJ

∴ ΔU = +7 kJ

and, Qp = ΔH

∴ Qp = +10kJ

Thus, the Internal energy increases by 7 kJ and Enthalpy by 10 kJ.

Problem 2: An Ideal gas expands from a volume of 5 dm3 to 15 dm3 against a constant external pressure of 3.036 x 105Nm-2. Find ΔH if ΔU is 400 J.

Solution:

ΔH = ΔU + PΔV

ΔH = ΔU + P(V2 – V1)

Assume that Pex = P,   P =3.036 *105 N m-2

ΔU = 400 J

V1 = 5 dm3 = 5 × 10-3 m3

and V2 = 10 dm3 = 10 × 10-3 m3

Substituting the values in the equation

ΔH = 400 J + 3.036 × 105 Nm-2 * (10 × 10-3 m3 – 5 × 10-3 m3)

⇒ ΔH = 400 J + 3.036 ×105 Nm-2 * (15 – 5) × 10-3 m3

⇒ ΔH = 400 J + 3.036 × 103 J

⇒ ΔH = 3436 J.

Problem 3: Calculate the work done in the following reaction when 2 moles of HCl are used at Constant pressure at 420 K.

4HCl (g) + O2 (g) → 2Cl2 (g) + 2H2O (g)

State, whether the work done, is by the system or on the system.

Solution:

According to the Formula to calculate the work done in chemical reactions,.

W = – Δn RT

⇒ W = – RT ( n2 – n1 )

2 moles of HCl react with 0.5 mole of O2 to give 1 mole of  Cl2 and 1 mole of H2O

Hence, n1 = 2.5,  n2 = 2, R = 8.314 JK-1  mol-1  , T = 420 K

Substituting the values in the equation,

W = – 8.314 J K-1 mol-1 × 420 K × (2 – 2.5) mol

⇒ W = -8.314 × 420 × (-0.5) J

⇒ W = 1745.94 J

Problem 4: Calculate the change in enthalpy (ΔH) for the combustion of methane (CH4) if the standard enthalpy of formation of methane is -74.8 kJ/mol.

The combustion reaction of methane is:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

The standard enthalpy of the formation of CO2(g) is -393.5 kJ/mol and the standard enthalpy of the formation of H2O(l) is -285.8 kJ/mol.

Solution:

To calculate the ΔH for the combustion of methane, we need to use the standard enthalpies of formation of the reactants and products. The ΔH can be calculated using the formula:

ΔH = ΣnΔHf(products) – ΣnΔHf(reactants)

where n is the stoichiometric coefficient of each species in the balanced chemical equation.

ΔH = [1×(-393.5 kJ/mol) + 2×(-285.8 kJ/mol)] – [1×(-74.8 kJ/mol) + 2×(0 kJ/mol)]

[Standard enthalpy of formation of O2(g) is 0]

⇒ ΔH = -802.2 kJ/mol – (-74.8 kJ/mol)

⇒ ΔH = -727.4 kJ/mol

Therefore, the change in enthalpy for the combustion of methane is -727.4 kJ/mol.

## Enthalpy – FAQs

### What does Enthalpy mean?

Enthalpy is a thermodynamic property representing the total heat content of a system.

### What is Internal Energy?

Every substance is associated with a definite amount of energy. This energy is stored in a substance (System) is called its internal energy and is denoted by U. The internal energy is the sum of kinetic energies of all the molecules, ions and atoms of the system, the potential energies associated with the forces between the particles, the kinetic and potential energies of nuclei and electrons in the particles and the energy associated with existence of mass of the system.

### How to Calculate Change in Enthalpy?

The change in enthalpy ( ΔH) can be obtained by

ΔH = ΔU + RT Δn

### What is Isobaric Process?

Most chemical reactions are run in open containers under constant pressure. In such reactions the volume of the system is allowed to change, such kind of processes are called as Isobaric processes.

Examples:

• Boiling of Water and its Conversion into Steam
• Freezing of Water into Ice

### What is Relation between Enthalpy Change and Internal Energy Change?

Relation between enthalpy change and internal energy change is as follows:

ΔH = ΔU + Δ(PV)

where,

• ΔU is the Change in Internal Energy
• Δ(PV) is the Change in Product of Pressure and Volume

### What is First Law of Thermodynamics?

First Law of Thermodynamics is simply the law of conversation of energy. According to this law the total energy of a system and its surroundings remain constant when the system changes from initial state to final state. The law is stated in different ways but the meaning is the same that the energy  is conserved in all the changes.

Mathematical expression for the First Law of Thermodynamics,

ΔU = Q + W

### What is SI Unit of Enthalpy?

The SI unit of enthalpy is the joule (J). Enthalpy is measured in joules per mole (J/mol) or simply joules (J), depending on the context.

### What is the difference between Enthalpy and Entropy?

Enthalpy is the measure of the overall amount of energy in the system whereas Entropy is the measure of the randomness in the system.

### How to Find Enthalpy of a Reaction?

Enthalpy of a reaction is calculated using the formula, ∆H = m x s x ∆T.

### What is Enthalpy of Fusion?

Enthalpy of Fusion is also called Latent Heat of Fusion, is the amount of Energy supplied to a solid substance to convert its state to the liquid state.

### What is Enthalpy of Vaporization?

Enthalpy of Vaporization is also called Latent Heat of Vaporization, is the amount of Energy supplied to a liquid substance to convert its state to the vapor state.

### What is Enthalpy of Atomization?

Enthalpy of atomization, often denoted as ΔHᵥ, is the amount of energy required to break apart one mole of a compound’s molecules into individual atoms in their gaseous state.

### What is Enthalpy of Formation?

Enthalpy of formation, often denoted as ΔHᵒf, is the change in enthalpy that occurs when one mole of a compound is formed from its constituent elements in their standard states.

### What is Enthalpy of Solution?

Enthalpy of solution, often denoted as ΔHsol ,is a thermodynamic quantity that represents the heat change associated with the dissolution of a substance in a solvent.

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