Review of enthalpy: What is it and how does it work?

Contents

-What is the enthalpy

-Difference between internal energy and thermal energy

-Internal energy silos

- Potential energy

-Kinetic energy

-?What moves the molecules

-?How does kinetic energy exist in a molecule

-?What is work energy

-?Sign convention of work

-?Relation of enthalpy with work

-?Work-energy relation

-Enthalpy change

-?Enthalpy changes in chemical reactions

-?Enthalpy change and activation energy

-?Enthalpy, entropy, and free energy relation

?

Enthalpy tells us how much heat [energy] is in a system. Enthalpy is the total energy of a substance.

Enthalpy is the sum of [1] Internal energy and [2] work energy.

H = E + W, are enthalpy, internal energy, and work energy, respectively.

Internal energy is the sum of PE + KE.

Internal energy refers to the microscopic energy inside atoms and molecules.?Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects.

Difference between internal energy and thermal energy

Internal energy is a measure of the amount of kinetic and potential energy possessed by particles in a body.?Internal energy is all contained energy. Internal energy is invisible energy.?Thermal or heat energy is visible energy. You can feel the hotness or coldness of an object. You can measure temperature.

Internal energy silos:

There are many ways molecules contain/store energy - one of them is of course the thermal energy or to be more specific the heat capacity.

Some of the energy storage space of molecules

-In different?phases?of matter - ice at?0 degc contains less internal energy than water at 0 degc because some energy has broken then bonds. Phase transition energy, also known as latent heat, refers to the amount of energy needed to melt or freeze.

-As kinetic energy when particles move within a system

-As potential energies how atoms and molecules are held together

Therefore, internal energy and thermal energy are not at all the same. Internal energy is everything and?it?includes?thermal energy.

To know what is enthalpy you must have some knowledge of what is the energy of a molecule? Where does the energy of the molecule stay in the molecule? What does the energy of the molecule get used for? I will explain it in the easiest manner that everyone can understand and remember,

What is PE?

PE provides electrons energy to do work that we cannot see nor can estimate.

Electrons are continuously changing their position in the atoms as you can see in the image below. The electrons are transiting from one to another energy level in the atom. Energy levels are a little like the steps of a staircase through which electrons continuously go up and down around a nucleus.

When an atom or a molecule collides with another it gains energy. It goes to an excited state at a higher energy level away from the nucleus. Every time an electron goes away from the positive nucleus or returns back to its original energy level, it does work against the positive nucleus. Correspondingly there is a gain or loss of energy. This is potential energy. Potential energy increases with increasing temperature. At?a higher temperature, more atoms/molecules are in excited electronic states. Higher electronic states correspond to greater potential energy

Kinetic energy

The kinetic molecular theory of matter states that:

-Matter is made up of particles that are constantly moving.

-All particles have energy, the energy varies depending on the temperature. This in turn determines whether the substance exists in the solid, liquid, or gaseous state. Molecules in the solid phase have the least amount of energy, while gas particles have the greatest amount of energy.

- The temperature of a substance is a measure of the average kinetic energy of the particles.

What moves the molecules?

Have you ever wondered why the particles like atoms or molecules within a substance are always in motion? What moves the molecules? The answer is heat is moving the molecules. Heat is the kinetic energy of the molecules in a substance. The higher the temperature, the faster the molecules move. Due to the conservation of energy, if one particle loses energy, another gains energy. There can be a loss of energy by, for example, thermal radiation, but the sun and radioactive decay keep things warm here on Earth. Yet even if a substance were cooled to absolute zero, its particles would still be moving. This is called zero-point energy and it is the lowest energy

How does kinetic energy exist in a molecule?

There are three forms of kinetic energy KE [1]?KE translation [2] KE rotation and [3] KE vibration.??KE rotation and KE vibration arise from the rotation of a molecule about its axis and vibration in stretching and bending of the bonds between the atoms of the molecule. Their movement is restricted. Only the random translational motion of molecules or the translational kinetic energy of molecules in which one molecule continuously hits another and transfers energy from a higher temperature region to a lower temperature region generates heat and temperature.

Therefore, the temperature is not directly proportional to internal energy. Temperature is only translational kinetic energy that is just a part of internal energy.

Since temperature measures, only the kinetic energy part of the internal energy, two objects with the same temperature do not, in general, have the same internal energy

What does it mean?

While enthalpy, H = E + W, only the translational part of the kinetic energy contributes to temperature.

The next is what is work energy?

What is work energy?

In most simple language, in thermodynamics, work is the transfer of energy between the system and surroundings.

Thermodynamic work is force x distance. Example: Compression of gas.

Work like shaft work, stirring, and rubbing where there is no change in the volume of the system against its resisting pressure is not thermodynamic work. Work without change of volume is known as isochoric work.

Sign convention of work?[There are different views]

When a system does work on the surrounding the work is considered to be negative. In contrast, when the surrounding does work on the system work is considered to be positive.

What is the relation of enthalpy with work?

Irreversible and reversible work

Transfer of energy by work to surroundings is nearly reversible.

A system transferring energy to do work in surroundings, like a compressor supplies compressed air to do work in surroundings is near reversible. The energy-work conversion is nearly 100%. Such processes are idealized as adiabatic and frictionless because the process happens very rapidly.??

In contrast, the conversion of heat into work in a heat engine can never exceed the Carnot efficiency, as a consequence of the second law of thermodynamics. Such energy conversion, through work done relatively rapidly, in a practical heat engine, by a thermodynamic system on its surroundings, cannot be idealized, not even nearly, as reversible.

Work-energy relation

Why does one equate enthalpy H with the sum of internal energy E and work W?

The Work-Energy Theorem

The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

The work?W?done by the net force on a particle equals the change in the particle’s kinetic energy KE:

W = ΔKE = 1/2mv^2f?1/2mv2i [ Difference of KE between final and initial]

This is a great equation.

What does it mean?

Let us go back to the enthalpy equation

?H = ?E + ?W

To summarize, every substance has some energy and even that exists at absolute zero temperature consisting of its internal energy and work energy. Internal?energy is the sum of potential energy and kinetic energy. Molecules are constantly in motion and doing work and that needs energy. Work can be of two types [1] the system does work on the surrounding, like system compresses the surrounding and [2] the surrounding does work on the system like surrounding compresses the surrounding. In either case, there is a change in kinetic energy and therefore there is a change in internal energy and the same happens to the enthalpy. This is how the enthalpy or the total energy keeps an account of both internal energy and work energy.

You might wonder if work energy also contributes to enthalpy, why enthalpy has to track both internal energy and work. The answer is it depends on the type of thermodynamic process. For example, in an isothermal expansion of an ideal gas, there is no increase in work as PV = constant, but still, there will be a change in the potential energy of molecules as the electrons go up and down their energy level. Every time an electron collides with another, they change their energy level. Every time an electron goes away or comes closer to the nucleus it does work at the expense of the internal energy. The same applies to the isovolumetric process where there is no change in volume so there is no work. But still, there is a change in the potential energy of molecules.

Enthalpy change

Enthalpy = H = E + PV

1st?law of thermodynamics E2 - E1 = Q – W

In a constant pressure process, the work is given by W = P [V2 - V1]

Substitute E2 – E1 = Q – P [ V2-V1]

[E1+PV1] - [E2+PV2] = Q

Heat transfer at constant pressure Q = Cp [T2-T1], Q = [H2-H1] above equation

Therefore, the definition of enthalpy is [H2 – H1] = Cp [T2- T1]

We can write??H = Cp x??T

How does the enthalpy change with changes in thermodynamic systems?

?H = ?E + P?V

Isothermal process

For all gases, ?E = 0 hence ?H = P?V [ strictly internal energy never becomes zero even at absolute zero temperature.

For ideal gases both ?E = 0 and P?V = 0 [ PV = constant] hence ?H = 0

Isobaric process

An isobaric process occurs at constant pressure. Since the pressure is constant, the force exerted is constant and the work done is given as PΔV.

An isobaric expansion of gas requires heat transfer to keep the pressure constant.

The enthalpy change ΔH = Heat absorbed at constant pressure

Isovolumetric process

An isovolumetric or isometric process takes place at constant volume.

Then P?V = 0 and ΔH = ΔE

Adiabatic process

An adiabatic process is a process during which no heat enters or leaves the system.

We then have since, ΔE = ΔQ + PΔV, with ΔQ being 0, ΔE = PΔV, the change in internal energy is a function of work. The work-energy comes from internal energy.

Enthalpy changes [ Heat of reaction] in chemical reactions

Important points

At constant volume, the heat of the reaction is equal to the change in the internal energy of the system.

At constant pressure, the heat of the reaction is equal to the enthalpy change of the system.

Most chemical reactions occur at constant pressure, so enthalpy is more often used to measure the heat of the reaction than internal energy.

Enthalpy [H]?is the heat content of a system at constant pressure. The heat that is absorbed or released by a reaction at constant pressure is the same as the enthalpy change and is given the symbol?ΔH. Unless otherwise specified, all reactions are assumed to take place at constant pressure.

The change in enthalpy of a reaction is a measure of the differences in enthalpy of the reactants and products. The change in enthalpy is also called the?heat of the reaction?and is given the symbol ΔH.?The heat of a reaction is?the difference between the energy of bond formation (in the products) and bond breaking (in the reactants). ΔH can be negative or positive depending on whether the reaction is exothermic (heat is released, negative sign, -ΔH) or endothermic (heat is absorbed, a positive sign, +ΔH).

ΔH = H?products?– H?reactants

The enthalpy of a system is determined by the energies needed to break chemical bonds and the energies needed to form chemical bonds. Energy needs to be put into the system in order to break chemical bonds – they do not come apart spontaneously in most cases.

To be more precise, the first step in a reaction is the endothermic step of breaking the reactant bonds and the second is the exothermic step of making the product bonds. The energy change of the reaction can be viewed as the sum of these two steps, and results in two possibilities:

The exothermic step (2) is greater than the endothermic step (1) and the reaction is exothermic.

The endothermic step (1) is greater than the?exothermic step (2) and the reaction is endothermic.

?

ΔH(reaction) only depends on the initial (reactant) and final (product) state, because enthalpy is a state function this difference is path independent. What we do know is that the first step required energy and the second released energy. Enthalpy change ΔH is the energy difference between the initial and final states?

Example

Endothermic Reactions:?In endothermic reactions the heat is added to the system as reactants convert to products, and so the sign of ΔH is positive.

Reactants + Heat ---- > Product, ΔH > 0

? H2 [g] + ? I2 [g] ------ > HI [l], ΔH = + 25.9 kJ/mole HI

Exothermic reaction

Reactants + Heat → Products + Heat, ΔH <0

A reaction that releases energy is an exothermic reaction; its enthalpy change is negative. The enthalpy of the products is less than that of the reactants.

CH4 [g] + 2O2 [g] ----- > CO2 [g] + 2 H2O [g], ΔH = - 887 KJ/mole CH4

Typical calculation

CH4 [g] + 2O2 [g] ----- > CO2 [g] + 2 H2O [g],

In order to calculate the standard enthalpy of reaction, we need to look up the standard enthalpies of formation for each of the reactants and products involved in the reaction. These are typically found in various tables online. For this reaction, the data we need is:

ΔHf CH4(g) =?75?kJ/mol

ΔHf O2(g) =0?kJ/mol

ΔHf CO2(g) =?394?kJ/mol

ΔHf H2O(g) =?284?kJ/mol

Note that because it exists in its standard state, the standard enthalpy of formation for oxygen gas is 0?kJ/mol. Next, we sum up our standard enthalpies of formation. Keep in mind that because the units are in kJ/mol, we need to multiply by the stoichiometric coefficients in the balanced reaction equation.

∑ΔHf products = (1) (?394) +(2) (?284) =?962?kJ/mol

∑ΔHf reactants = (1) (?75) +(2)(0) =?75?kJ/mol

Now, we can find the standard enthalpy of reaction:

ΔHrxn = ∑ΔHf {products}?∑ΔH f{reactants}= (?962) ?(?75) =?887?kJ/mol

Enthalpy change and activation energy

Whichever direction you take activation energy Ea will always be more than the Enthalpy change because enthalpy change is the difference in the enthalpy of the products and the reactants whereas the activation energy is the difference in the enthalpy of the activated complex and the reactants. The enthalpy of the activated complex is always more than the enthalpy of the products and the reactants so both these quantities cannot be equal. An activated complex is an unstable arrangement of atoms that exists momentarily at the peak [ topmost point of activation energy curve] of the activation energy barrier. Because of its high energy, the activated complex exists for an extremely short period of time (about 10?13s ).

For both exothermic as well as endothermic reactions it is not a necessary condition for the activation energy to be equal to the Enthalpy change as activation energy is always greater than the Enthalpy change.

Enthalpy change on the activation energy diagram

In both cases of endothermic [LHS image] and exothermic [RHS image] reactions you may see the following:

[1] Activation energy > Energy of reactants and energy of products

[2]?In exothermic reactions, the energy of product > energy of reactant,?- ?H

[3] In endothermic reactions, the energy of reactant > energy of the product, + ?H

Enthalpy, entropy, and free energy relation

Enthalpy is the amount of internal energy contained in a compound whereas entropy is the amount of intrinsic disorder within the compound. Entropy is a measure of how far the system is from equilibrium. The more near a system is to equilibrium, the more is the disorder. The free energy, we call Gibbs?free energy,??G= ?H-T?S?is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but no matter) at constant temperature and pressure. Since the free energy is a measure of the maximum work that can be extracted from a thermodynamic system it is only possible in a completely reversible process.

?G=??H-T?S?[ G is free energy, H is enthalpy, T is temperature and S is entropy]

When??G?= 0 the reaction is at equilibrium,?when ?G > 0 the reaction is not spontaneous,?when??G < 0?the reaction is spontaneous.

In other words, Gibbs free energy combines enthalpy and entropy into a single value. Gibbs free energy is the energy associated with a chemical reaction that can do useful work. It equals the enthalpy minus the product of the temperature and entropy of the system. ΔG predicts the direction of a chemical reaction. The combined effect of??H and T?S?makes a reaction spontaneous,??G < 0

The table below shows the combined effect of ?H and T?S to make ?G < 0

Credit? Google and LibreTexts

?