# Enthalpy

Enthalpy is the measurement of heat or energy in the thermodynamic system, and it is the most fundamental concept in the branch of thermodynamics. Enthalpy is important in many branches of science and engineering, including chemistry, physics, and the material sciences. There are some real-life applications of enthalpy, such as in power generation and chemical manufacturing.

In this article, we will learn about the Definition of Enthalpy, Enthalpy Formulas, and various relations between Enthalpy and others in detail.

## What is Enthalpy?

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 Formula

Mathematical definition of enthalpy can be represented as:

H = U + PV

where,

• H is Enthalpy
• U is Internal Energy
• P is Pressure
• V is Volume

## 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. Enthalpy of Fusion changes with increases with temperature and other parameter.

## 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 vapour state without an increase in temperature. The symbol of Enthalpy of Vaporization is âˆ†H vap. Enthalpy of Vaporization changes with increases with temperature and other parameter.

### Enthalpy of Freezing Water

Enthaly 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 electronsn 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.

## 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 (Î”H) will depend on the initial and the final states of the system

Thus, change in enthalpy is represented by Î”H and is given by the following formula:

Î”H = 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 Î”H will be,

Î”H = (U2 + P2V2) – (U1+ P1V1)

â‡’ Î”H = U2 + P2V2 – U1 -P1V1

â‡’ Î”H = (U2 – U1) + (P2V2 -P1V1)

Î”H = Î”U + Î”(PV)

where,

• Î”U is the Change in Internal Energy
• Î”(PV) is the Change in Product of Pressure and Volume

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

Î”H = Î”U + PÎ”V

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 = Î”U +PÎ”V

Thus from the above two equations, we get,

Î”H = 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 change of a reaction

## Relationship between Î”H and Î”U

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

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

Î”H = Î”U + PÎ”V

â‡’ Î”H = Î”U + P(V2 – V1)

â‡’ Î”H = Î”U + 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

â‡’ Î”H = Î”U + n2RT – n1RT

â‡’ Î”H = Î”U + RT (n2 – n1)

â‡’ Î”H = Î”U + RT Î”n

### Requirements for Î”H to be equal to Î”U

There are two cases when Î”H and Î”U 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 (Î”V = 0). Then change in enthalpy will change as Î”H = Î”U.
• When there are only solids or liquids involved in the reactions then we can neglect Î”V as the change in them due to the pressure is significant. So, Î”H = Î”U.

There reaction in which the moles of gaseous products and reactants are the same (i.e. n2 = n1). So, Î”H =Î”U

## Entropy Vs Enthalpy

The differences between Enthalpy and Entropy are discussed 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

Now let’s learn about them in detail.

### 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 Ã— Î”V

Assume Pex = P, then the equation becomes

W = -P( V2 – V1)

â‡’ W = PV1 – PV2

Using the Ideal gas equation,

â‡’ W = n1RT – n2RT

â‡’ W = -RT (n2 – n1)

â‡’ W= – RT Î”n

## 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,

Î”U = 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)

Î”U = 10 kJ – 3 kJ

âˆ´ Î”U = +7 kJ

and, Qp = Î”H

âˆ´ Qp = +10kJ

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

Problem 2: For a reaction, 5 kJ of heat is released from the system and 10 kJ of work was done on the system. What are the changes in the Internal energy and Enthalpy of the system?

Solution:

According to first law of thermodynamics,

Î”U = Q + W

Q = -5 kJ, W = +10 kJ

Î”U = -5 kJ +10 kJ = +5 kJ

and Qp = Î”H

âˆ´Qp = -5 kJ

Thus, the Internal energy increases by 5 kJ and Enthalpy decreases by -5 kJ.

Problem 3: 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 Î”H if Î”U is 400 J.

Solution:

Î”H = Î”U + PÎ”V

Î”H = Î”U + P(V2 – V1)

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

Î”U = 400 J

V1 = 5 dm3 = 5 Ã— 10-3 m3

and V2 = 10 dm3 = 10 Ã— 10-3 m3

Substituting the values in the equation

Î”H = 400 J + 3.036 Ã— 105 Nm-2 * (10 Ã— 10-3 m3 – 5 Ã— 10-3 m3)

â‡’ Î”H = 400 J + 3.036 Ã—105 Nm-2 * (15 – 5) Ã— 10-3 m3

â‡’ Î”H = 400 J + 3.036 Ã— 103 J

â‡’ Î”H = 3436 J.

Problem 4: 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) â†’ 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 = – Î”n RT

â‡’ 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 Ã— 420 K Ã— (2 – 2.5) mol

â‡’ W = -8.314 Ã— 420 Ã— (-0.5) J

â‡’ W = 1745.94 J

Problem 5: Calculate the change in enthalpy (Î”H) 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) â†’ 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 Î”H for the combustion of methane, we need to use the standard enthalpies of formation of the reactants and products. The Î”H can be calculated using the formula:

Î”H = Î£nÎ”Hf(products) – Î£nÎ”Hf(reactants)

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

Î”H = [1Ã—(-393.5 kJ/mol) + 2Ã—(-285.8 kJ/mol)] – [1Ã—(-74.8 kJ/mol) + 2Ã—(0 kJ/mol)]

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

â‡’ Î”H = -802.2 kJ/mol – (-74.8 kJ/mol)

â‡’ Î”H = -727.4 kJ/mol

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

## Enthalpy-FAQs

### 1. What is a State Function?

Any property of a system whose value depends on the current state of the system and is independent of the path followed to reach that state is called the state function.

Example of state function is Temperature.

### 2. 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.

### 3. How to Calculate Change in Enthalpy?

The change in enthalpy ( Î”H) can be obtained by

Î”H = Î”U + RT Î”n

### 4. What are 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

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

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

Î”H = Î”U + Î”(PV)

where,

• Î”U is the Change in Internal Energy
• Î”(PV) is the Change in Product of Pressure and Volume

### 6. What is the 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,

Î”U = Q + W

### 7. What is the Enthalpy Unit?

The Enthalpy of any reaction is measured in Joule per Mole.

### 8. What is Enthalpy Vs 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.

### 9.How to Find Enthalpy of a Reaction?

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

### 10. 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.

### 11. 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.

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