Energy is defined, operationally as the attitude of a body to do a job. The units of energy and work are the same: the joule in the SI and the calorie as an empirical unit of measurement, 1 cal. = 4.18 J.
Energy can come in different forms, the main ones being: mechanical, electromagnetic, thermal, chemical, nuclear and radiant.
Energy can neither be created nor destroyed, but it can be transformed from one form to another, it can be transported and stored.
Principle of conservation of energy
The total energy of the universe remains constant. Matter and energy are closely linked: matter can be considered as an energy store. When a transformation of matter takes place, the energy content of this warehouse changes accordingly.
The energy of material bodies is of two types: potential and kinetic . Potential energy is the energy possessed by a body, in a force field, by virtue of its position. Even though the body is immobile it is always present and manifests itself when it transforms into another form of energy.
Two electrically charged particles, kept still and close together, possess potential energy:
The energy “hidden” in the system tends to generate a movement: the particles move away spontaneously in the first case and approach in the second, a part of the potential energy is transformed into kinetic energy.
Other examples are gravitational energy and the energy present in a compressed spring. Kinetic energy is a form of energy that bodies possess when they are in motion, and it is greater the higher the speed and mass of the body.
Ec = 1 \ 2m v2
The particles that make up substances (molecules, atoms and ions) possess “in their small way” these two forms of energy: kinetic and potential. The molecules of gases (liquids and solids) are in continuous motion and therefore each of them has a certain amount of kinetic energy.
Obviously, the movement of the particles does not correspond to a movement of the body constituted by them, but that form of energy called thermal energy. The thermal energy possessed by a body is an extensive quantity precisely because it is due to the sum of the kinetic energy of all the particles that constitute it.
A set of particles (atoms, molecules or ions) can be considered a “store” of potential energy. This form of energy is the result of the multiple electromagnetic interactions that are established between particles (bonds between atoms, between ions, between molecules, etc.), for this reason it is called chemical energy.
In any case, it is a question of potential energy, or position, because it is determined by the reciprocal arrangement of the particles with the relative interactions of an attractive and repulsive type. In fact, atoms are made up of electrons and protons with electric charge, and each particle generates, even if of infinitesimal intensity, a field of forces that acts on the surrounding particles.
While thermal energy increases or decreases when matter heats or cools, chemical energy is more “hidden” and becomes manifest only when matter transforms, that is when chemical reactions or changes in the state of aggregation occur since these phenomena modify the reciprocal arrangements and forces between particles.
During the passage from the solid to the liquid state and then to the gaseous state, the breaking of the intermolecular bonds that hold the particles together occurs. To carry out this operation it is necessary to spend energy and it is for this reason that, in order to pass from the solid to the gaseous state, it is necessary to supply energy to the system: these state changes are therefore endothermic processes.
When you pass from the gaseous state to the liquid state and then to the solid state, the reverse process takes place, and the bonds between the particles are recomposed: these processes are therefore exothermic and to make them happen, the system must be cooled, i.e. heat is removed. The amount of heat, released or acquired, by a certain amount of substance, during a change of state is called latent heat.
During the changes of state the temperature remains constant, in fact there is the breaking or the formation of new bonds, that is a variation of the quantity of chemical energy possessed by the body. For example, during fusion the heat supplied (latent heat of fusion) is transformed into chemical energy, and does not change the overall amount of thermal energy, so the body melts at a constant temperature.
During solidification, however, a part of the chemical energy is transformed into heat (latent heat of solidification) so that the substance, while subtracting heat from it during the transition of state, maintains a constant temperature.
The overall energy content of the substances has been defined internal energy, it consists of: kinetic energy + potential energy of the particles.
E kinetics = translational energy + vibrational energy + rotational energy
E potential = binding energy
In monatomic gases there is potential energy and translational energy. The energy of substances is very complex and it is impossible to determine their absolute value. In physics and chemistry primarily affect the changes in internal energy: D E .
Chemical reactions are always accompanied by energy exchanges with the external environment. If the reaction produces heat it is called exothermic, if to proceed it needs heat from the environment it is called endothermic.
It is the energy needed to break a bond, or: energy released by the formation of a bond. It is expressed in Kcal / mole; for example, the energy of the HH bond is equal to 104 Kcal / mole.
When one mole of H2 is formed from two moles of single H atoms, 6.02 · 1023 HH bonds, 104 Kcal are released from the system to the environment.
The exothermicity or the endothermicity of a chemical reaction is to be found in the processes that occur at the molecular level during the reaction, and exactly:
- Breaking of chemical bonds in the molecules of the reactants;
- Formation of new chemical bonds between atoms in the reaction products.
To break the bonds between the atoms of the reactants it is necessary to supply energy (endothermic process), while when the new bonds are formed between the atoms that make up the reaction products, energy is released (exothermic process).
If the energy to break the bonds between the atoms of the reactants is greater than the energy released by the formation of the bonds in the products, the reaction is endothermic; while if the energy released by the formation of bonds in the products is greater than the energy to break the bonds in the reactants, the reaction is exothermic.
First law of thermodynamics
The change in internal energy, D E , of a system following a transformation is equal to the heat absorbed by the system, Q , minus the work done by the system, W
DE = Q – W
A ” Q ” is given a positive sign if the heat flows towards the system, and a negative sign if the system releases heat to the environment. Work ” W ” is given a positive sign if the system does work, and a negative sign is given if the environment is doing work on the system.
If the work exchanged by the system is only mechanical, that is of the P · DV type , from the previous relation we obtain: D E = Q – P · DV .
If the reaction is carried out in a closed vessel, D V = 0 (constant volume), from the previous it results: D E = Q (v) .
The heat carried out by a chemical transformation, at constant volume, is identified with the variation of a state function: the internal energy: D E = E products – E reactants .
If a system during a chemical reaction absorbs energy from the environment, its final energy is greater than the initial one and D E is positive.
If it releases energy to the environment D E is negative.
The variation of a state function from an initial state (1) to a final state (2) does not depend on the intermediate values assumed by the variable, i.e. it does not depend on the path traveled by the system, but depends exclusively on the values assumed by the variable in the final state and in the initial state.
Since most of the chemical reactions take place at constant pressure, atmospheric pressure, a quantity called enthalpy has been introduced in thermodynamics, defined as:
H = E + P · V .
If we only consider transformations at constant pressure, in which the volume, passing from the reactants to the products, changes, the enthalpy variation will become: D H = DE + P · DV .
Knowing that DE is given by: D E = Q – W and that for a transformation at constant pressure, in which a change in volume occurs, the system performs a ” P – V ” job corresponding to P · DV , we obtain: D E = Q – P · DV if we substitute the expression of DE in the formula relating to D H we obtain: D H = Q – P · DV + P · DV which, simplified, gives us: D H = Qp .
This equation simply says that the heat of reaction measured at constant pressure, Qp , is equal to D H of the reaction.
In a reaction conducted at constant pressure, the enthalpy variation is given by:
DH = SH (products) – SH (reactants) = Q (p)
Enthalpy is also a state function and therefore the amount of heat exchanged (carried out or absorbed) by a reaction conducted at constant pressure is independent of any reactions or intermediate steps, but depends only on the initial state (enthalpy of the reactants) and on the final state (enthalpy of the products).
Since the determination of the heat carried out by a reaction is generally carried out by means of the “calorimetric bomb ” calorimeter, that is in a closed container (constant volume) the heat put into play by a reaction is identified in this case with the D E:
DE = Q (v) .
Known D E for reactions in which substances in the gaseous phase are present, the D H can easily be calculated :
DH = DE + P DV .
Applying to each gas the equation of ideal gases PV = nRT results in D (PV) = Dn (RT) .
Substituting: D H = DE + Dn (RT) .
The term D n is obtained by subtracting from the sum of the total moles of the reaction products, the sum of the total moles of the reactants, taking into account only the moles of the substances in the gaseous state.
Exothermic reaction at constant pressure
By conducting the reaction in a cylinder equipped with a movable piston, when a gaseous substance is formed, or the number of moles of gaseous substances in the reaction products increases, the piston will be pushed against the atmospheric pressure and inside the system the pressure will remain constant.
But the gas, moving the piston, does work, and the necessary energy comes from the total energy released by the reaction.
Therefore the quantity of energy released as reaction heat at constant pressure ( D H ), is less than the energy released by the reaction ( D E ), since a part of this is used to carry out the expansion work: P DV = Dn (RT) .
|-DH = -DE + P · DV||E: negative because sold by the system|
|DH: negative because sold by the system|
|P · DV: positive because made by the system|
If during an exothermic chemical reaction a system expands against the constant pressure of the atmosphere the D H of the reaction is, in absolute value, slightly less than D E .
If during the reaction the system is contracted, against the constant pressure of the atmosphere, (decrease in the number of moles in the gaseous state) the D H the reaction is, in absolute value, slightly higher than the D E . (see numerical examples).
If a reaction takes place without any change in the number of moles of the gaseous substances, or between substances in solution and in the solid state D H = DE , enthalpy and internal energy can be identified for chemical species in the liquid and solid state, it follows Q (p) = Q (v) .
Calculate at 25 ° C the D H ° of the formation reaction of one mole of sulfuric anhydride (P = 1 atm) starting from its elements in their respective standard states, it being known that at the same temperature the reaction:
S (s) + 3/2 O2 (g) —–> SO3 (g)
it, conducted in a calorimetric bomb (constant volume), develops 94.15 Kcal for each mole of SO3 that is formed.
|DE ° = – 94.15 Kcal / mole||Dn = 1 – 3/2 = -1/2||T = 298 K|
By applying the equation D H ° = DE ° + Dn (RT) and replacing the data, we obtain:
DH ° = – 94.15 – (1/2 × 1.98 × 298 × 10-3) = – 94.45 Kcal / mole
(R = 0.0821 liters × atm × mole-1 × grade-1, R = 1.987 calories × moles-1 × grade-1)
For example the reaction:
CO (g) + ½ O2 (g) —–> CO2 (g)
DH = – 67344 cal / mole Dn (RT) = (1- 1.5) RT = 0.5
RT = 0.5 × 1.987 × 298 = – 296 cal / mole
DH = DE + DnRT
therefore we have:
– 67640 = DE + (- 296) DE = – 67344 cal / mole.
In both examples the energy carried out at constant pressure is greater than that carried out at constant volume, because the processes take place with a reduction in the number of moles of the gaseous components.
While the internal energy of a system is a function of state, the same cannot be said in general for the heat ( Q ) and the work ( W ) exchanged by the system when they are considered separately.
In fact, it can be shown that their numerical value is generally different depending on the “path traveled” by the system during the transformation. The heat exchanged, developed or absorbed, at constant pressure Q (p) is identified with the variation of a state function, the enthalpy, and therefore its value is independent of any intermediate reactions, but depends only on the initial state (enthalpy of the reactants) and the final state (enthalpy of the products). The same considerations apply to Q (v) .
Notes on thermochemistry: Hess’s law
The heat exchanged in a reaction that takes place at constant pressure Q (p) , or at constant volume Q (v) , is independent of any intermediate reactions, but depends only on the initial and final state of the chemical system, i.e. on the enthalpy or from the internal energy of the reactants and the products of the reaction.
In thermochemistry it is customary to take the outside as the protagonist, so that the heat developed in the reaction is preceded by the positive sign and the absorbed one by the negative sign.
For example the reaction
|Cs + O2 (g) —-> CO2 (g)||DH = 94 Kcal / mole|
On the other hand, in thermochemistry, the heat developed in the reaction will be indicated as Qp = + 94 Kcal / mole.
The above carbon combustion reaction can be broken down into two distinct phases with the intermediate formation of carbon monoxide:
|Cs + ½O2 (g) —-> CO (g)||DH = -27 Kcal / mole|
|COg + ½O2 (g) —-> CO2 (g)||DH = -67 Kcal / mole|
By adding member by member the stoichiometric equations of the two reactions, the equation of the complete carbon combustion reaction is obtained.
The sum of the enthalpies of the individual reactions also corresponds to the enthalpy of the complete CO2 combustion reaction.
|Cs + O2 (g) —-> CO2 (g)||DH = 94 Kcal / mole|
This agrees with the fact that enthalpy is a state function of the system, and when, in two different paths, the initial and final states coincide, the enthalpy variation will also be the same.