# What is Enthalpy? Definition, Formula, Equation, Unit, Endothermic & Exothermic Reaction

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Posted by Osman Gezer, 2/15/24

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Enthalpy is a fundamental concept in thermodynamics, which is the branch of science that deals with the study of energy and its transformation in physical and chemical systems. It is a property of a system that describes the total energy of the system, including both its internal energy and the energy associated with its surrounding environment. Enthalpy helps us understand and quantify the heat flow in various processes and reactions.

## What is Enthalpy?

Enthalpy (H) is defined as the sum of the internal energy (U) of a system and the product of its pressure (P) and volume (V), as given by the equation H = U + PV. It is a state function, meaning it depends only on the initial and final states of a system and is independent of the path taken to reach those states. Enthalpy is usually expressed as the change in enthalpy (ΔH) for a process between initial and final states.

## What is Internal Energy?

Internal energy (U) is the energy associated with the microscopic particles (atoms, molecules, or ions) within a system. It includes the kinetic energy of these particles due to their motion and the potential energy due to their interactions. The internal energy of a system can change due to heat transfer (q) or work done (w) on or by the system, as given by the first law of thermodynamics: ΔU = q – w.

## What is Thermodynamics?

Thermodynamics is the branch of science that deals with the study of energy and its transformations in physical and chemical systems. It is based on a set of fundamental principles known as the laws of thermodynamics. These laws govern the behavior of energy in various processes and provide a framework for understanding and predicting the behavior of systems at the macroscopic level.

## Enthalpy Formula

The formula for calculating the change in enthalpy (ΔH) is ΔH = ΔU + PΔV, where ΔU is the change in internal energy, P is the pressure, and ΔV is the change in volume. This formula relates the change in enthalpy to changes in internal energy and work done by or on the system. It is important to note that if the pressure is constant, the change in enthalpy is equal to the heat transferred at constant pressure (qP).

## Enthalpy Equation

The equation for calculating the enthalpy change (ΔH) for a process at constant pressure is ΔH = qP, where qP is the heat transferred at constant pressure. This equation is based on the fact that at constant pressure, the heat flow (qP) is equal to the change in enthalpy. If the process is exothermic (heat is released), the ΔH will be negative, indicating a decrease in enthalpy. If the process is endothermic (heat is absorbed), the ΔH will be positive, indicating an increase in enthalpy.

## How To Calculate Enthalpy

Calculating the enthalpy change for a process involves several steps. Here is a step-by-step guide on how to calculate enthalpy:

Step 1: Determine the initial and final states of the system.

Step 2: Calculate the change in internal energy (ΔU) using the formula ΔU = q – w, where q is the heat transferred and w is the work done.

Step 3: Calculate the change in volume (ΔV) if the process involves a change in volume.

Step 4: Calculate the change in enthalpy (ΔH) using the formula ΔH = ΔU + PΔV, where P is the pressure.

Step 5: Determine the sign of ΔH. If ΔH is negative, the process is exothermic. If ΔH is positive, the process is endothermic.

## Enthalpy Symbol

The symbol used to represent enthalpy is H. It is derived from the Greek letter “eta” (Η), which is the first letter of the word “enthalpy” in Greek (ἐνθάλπω).

## Enthalpy Diagram

An enthalpy diagram, also known as a reaction profile or energy profile diagram, is a graphical representation of the change in enthalpy during a chemical reaction. It shows the energy of the reactants, the energy of the products, and the energy changes that occur during the reaction. Enthalpy diagrams are useful for understanding the energy changes associated with different steps of a reaction and for predicting the overall energy change of the reaction.

## Enthalpy Units

The SI unit for enthalpy is the joule (J). However, in practice, enthalpy is often expressed in kilojoules (kJ) or calories (cal). One calorie is equivalent to 4.184 joules. The choice of units depends on the scale and context of the problem being studied.

## Enthalpy Change

Enthalpy change (ΔH) refers to the change in enthalpy that occurs during a physical or chemical process. It can be positive or negative, depending on whether the process is endothermic (absorbs heat) or exothermic (releases heat). The enthalpy change for a reaction is determined by the difference in enthalpy between the products and the reactants.

## Enthalpy of Fusion

The enthalpy of fusion is the amount of heat required to change a substance from a solid to a liquid phase at its melting point. It is also known as the heat of fusion. The enthalpy of fusion is typically expressed in joules per mole (J/mol) or calories per gram (cal/g). It represents the energy needed to overcome the intermolecular forces holding the solid together and convert it into a liquid.

## Enthalpy of Vaporization

The enthalpy of vaporization is the amount of heat required to change a substance from a liquid to a gaseous phase at its boiling point. It is also known as the heat of vaporization. The enthalpy of vaporization is typically expressed in joules per mole (J/mol) or calories per gram (cal/g). It represents the energy needed to overcome the intermolecular forces holding the liquid together and convert it into a gas.

## Enthalpy of Freezing Water

The enthalpy of freezing water is the amount of heat released when water changes from a liquid to a solid phase at its freezing point. It is also known as the heat of fusion in the context of water. The enthalpy of freezing water is typically expressed in joules per mole (J/mol) or calories per gram (cal/g). It represents the energy released as the water molecules come together to form a solid crystal lattice.

## Ionization Enthalpy

Ionization enthalpy, also known as ionization energy, is the amount of energy required to remove an electron from an atom or a positive ion. It is typically expressed in electron volts (eV) or kilojoules per mole (kJ/mol). Ionization enthalpy is an important property of elements and is related to the stability and reactivity of atoms and ions.

## Activation Enthalpy

Activation enthalpy, also known as activation energy, is the minimum amount of energy required for a reaction to occur. It represents the energy barrier that must be overcome for the reactants to form products. Activation enthalpy is an important concept in chemical kinetics and is related to the rate at which reactions proceed.

## Specific Enthalpy

Specific enthalpy, also known as heat content or heat capacity, is the enthalpy per unit mass of a substance. It is typically expressed in joules per kilogram (J/kg) or calories per gram (cal/g). Specific enthalpy is useful for determining the amount of heat required to raise the temperature of a given mass of a substance.

## Standard Enthalpy of Formation

The standard enthalpy of formation is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states. It is typically expressed in kilojoules per mole (kJ/mol). The standard enthalpy of formation is useful for determining the energy content of a compound and is often used in thermochemical calculations.

## Enthalpy of Reaction

The enthalpy of reaction, also known as the heat of reaction, is the enthalpy change that occurs during a chemical reaction. It represents the difference in enthalpy between the products and the reactants. The enthalpy of reaction is typically expressed in kilojoules per mole (kJ/mol) and is used to quantify the energy changes associated with a chemical reaction.

## Enthalpy of Phase Transition

The enthalpy of phase transition is the enthalpy change that occurs when a substance undergoes a change in phase, such as melting, boiling, or sublimation. It represents the energy required to break or form intermolecular forces and is related to the stability and physical properties of the substance. The enthalpy of phase transition is typically expressed in kilojoules per mole (kJ/mol).

## Relationship between ΔH and ΔU

The change in enthalpy (ΔH) for a process at constant pressure is equal to the change in internal energy (ΔU) plus the product of pressure and volume (PΔV). This relationship is based on the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat transferred to the system minus the work done by the system. If the pressure is constant, the work done by the system is given by PΔV.

## Effect of Temperature on Enthalpy

The change in temperature can have a significant effect on the enthalpy of a system. As the temperature increases, the kinetic energy of the particles in the system also increases, leading to an increase in the internal energy and hence the enthalpy of the system. Conversely, as the temperature decreases, the internal energy and enthalpy of the system decrease.

## Endothermic and Exothermic Reactions

Endothermic reactions are those in which heat is absorbed from the surroundings, resulting in an increase in the enthalpy of the system. These reactions typically feel cold to the touch and require an input of energy to proceed. On the other hand, exothermic reactions are those in which heat is released to the surroundings, resulting in a decrease in the enthalpy of the system. These reactions typically feel warm to the touch and release energy as they proceed.

## Difference Between Enthalpy and Entropy

Enthalpy and entropy are both thermodynamic properties that describe the state of a system. However, they represent different aspects of the system’s energy and behavior. Enthalpy is a measure of the total energy of a system, including both its internal energy and the energy associated with its surrounding environment. Entropy, on the other hand, is a measure of the disorder or randomness of a system. While enthalpy relates to energy transfer, entropy relates to the distribution of energy within a system.

## Solved Examples on Enthalpy

Let’s solve a few examples to better understand how to calculate enthalpy:

Example 1: Calculate the enthalpy change for the combustion of methane (CH4) according to the following reaction: CH4(g) + 2O2(g) → CO2(g) + 2H2O(g). The enthalpy of formation values are as follows: ΔHf(CH4) = -74.8 kJ/mol, ΔHf(CO2) = -393.5 kJ/mol, and ΔHf(H2O) = -285.8 kJ/mol.

Solution:

The enthalpy change for the reaction can be calculated using the enthalpy of formation values of the reactants and products.

ΔH = ΣΔHf(products) – ΣΔHf(reactants)

ΔH = [ΔHf(CO2) + 2ΔHf(H2O)] – [ΔHf(CH4) + 2ΔHf(O2)]

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

ΔH = -393.5 kJ/mol – 571.6 kJ/mol + 74.8 kJ/mol

ΔH = -890.3 kJ/mol

Example 2: Calculate the enthalpy change for the reaction NH3(g) + HCl(g) → NH4Cl(s) using the enthalpy of formation values: ΔHf(NH3) = -45.9 kJ/mol, ΔHf(HCl) = -92.3 kJ/mol, and ΔHf(NH4Cl) = -314.4 kJ/mol.

Solution:

The enthalpy change for the reaction can be calculated using the enthalpy of formation values of the reactants and product.

ΔH = ΣΔHf(products) – ΣΔHf(reactants)

ΔH = ΔHf(NH4Cl) – [ΔHf(NH3) + ΔHf(HCl)]

ΔH = -314.4 kJ/mol – [-45.9 kJ/mol – 92.3 kJ/mol]

ΔH = -314.4 kJ/mol + 138.2 kJ/mol

ΔH = -176.2 kJ/mol