# Thermodynamics

### Thermodynamics

The word “thermodynamics” is derived from Greek words therme (heat) and dinamics (flow or motion) .

Thermodynamics mainly deals with the transformation of heat into mechanical energy and vice versa .

#### LIMITATIONS OF THERMODYNAMICS

(i) It does not give any direct information about the nature or structure of matter.

(ii) It does not give any indication of how fast the reaction will proceed. Or we can say that , time is not included as a variable. However , thermodynamics can predicts the feasibility of a process under given condition.

(iii) In dealing with the thermodynamic , matter finds no consideration except as a carrier of energy.

(iv) The law of thermodynamics apply on the matters in bulk i.e, on macroscopic system and not on individual atoms or molecules of the microscopic system.

#### SOME BASIC TERMS AND CONCEPTS

(i) Thermodynamic System : or simply system is an assembly of a very large number of particles having a certain value of pressure ,temperature and volume is called thermodynamic system.

Surrounding : Everything outside the system which can directly effect the system is called surrounding.

Boundary : Boundary is present between surrounding and system it separate both the things and it can be imaginary or real.

Different types of boundaries are as follows :

(a) Rigid wall : It is a wall whose shape and position is fixed . If it is impermiable , it does not allow the passage of matter.

(b) Adiabatic boundary : It is that type of wall which when held rigid will not allow passage of matter or energy.

(c) Diathermic wall : It is that type of wall which when held rigid will not allow passage of matter but allow passage of energy.

(ii) Types of system : There are three types of systems :

(a) Open system :  In this type of system ,energy as well as matter can be exchanged with the surrounding and boundary is not sealed and not insulated.

Example :

Sodium reacts with water in an open beaker in which hydrogen(matter) is evolved and heat energy is transfered to the surrounding.

(b) Closed system : This type of system can exchange energy in the form of heat , work and or radiations but not the matter with its surrounding . In this system diathermic boundary is present which is sealed but not insulated.

(c) Isolated system : This type of system , there is no exchange of matter and energy takes place between system and surrounding. In this system boundary is sealed and insulated , adiabatic and rigid boundary is present.

#### ON THE BASIS OF COMPOSITION , THERE ARE TWO TYPES OF SYSTEM

(a) Homogeneous system : When the particles of system is uniformly distributed through out the system then the system is called homogeneous system. Homogeneous system is made up of one phase only but components may be one or more.

Example : A pure single solid , liquid or gas , mixture of gases and a true solution.

(b) Heterogeneous system :  A system is said to be heterogeneous when it is not uniform throughout the system. Heterogeneous system is made up of two or more phases but components may be same or different.

Example : Ice in water, liquid and vapour , sand and water .

(iii) Macroscopic properties : Macroscopic means bulk quantity of matter. And macroscopic properties are the properties associated with bulk quantity of matter some examples are pressure , viscosity , density , volume, melting point etc.

Subdivided into two types :

(a) Intensive properties : are the properties whose magnitude does not depend upon the quantity of matter present in a system or size of the system. Example : pressure , viscosity, temperature , density , surface tension , refractive index ,  molality , molarity , specific heat , dielectric constant etc.

(b) Extensive properties : are the properties whose magnitude depend upon the quantity of matter present in a system or size of the system. Example : Total mass, volume , enthalpy , internal energy, entropy , gibbs free energy , heat capacity, number of moles , internal energy etc

NOTE : If extensive properties are expressed in per mole or per gram it become intensive property . for example : mass and volume are extensive properties but density(mass per unit volume) is intensive property.

(iv) Thermodynamic variables : properties like pressure , volume , temperate which help us to study the behaviour of thermodynamic system are called thermodynamic variables. The fundamental properties which determine the state of a system are called state variables or state functions . State variable are depend only upon initial and final state of the system not upon the path followed.

The properties which used to describe the state of the thermodynamic system are :

1. Pressure (P)
2. Temperature (T)
3. Volume (V)
4. Internal energy (E or U)
5. Enthalpy (H)
6. Entropy (S)
7. Free energy (G)
8. Number of moles (n)

NOTE : Heat and Energy are not state function actually they are modes of transfer of energy

Functions which depend upon path followed are called path dependent functions. Example : Heat and work etc

(v) Thermodynamic processes : When thermodynamic system changes from one state to another state , the operation is called process.

Different types of processes are :

(a) Isothermal process : The process is termed as isothermal process if temperature remains constant (fixed) i.e, ​$$dt=0$$​. In isothermal process heat is exchanged with the surrounding and the system is not thermally isolated. Also, internal energy of the system is constant ​$$\Delta{U}=0$$​ . Evaporation and Condensation is a isothermal process.

(b) Adiabatic process : The process is termed as adiabatic process if no exchange of heat takes place between system and the surrounding i.e, ​$$q=0$$​ . System is thermally isolated. This can be done by placing the system in an insulated container i.e, thermos flask.

(c) Isobaric process : The process is termed as isobaric process if pressure remain fixed throughout the change i.e., ​$$dp=0$$​ .

(d) Isochoric process : The process is termed as isochoric process if volume remain fixed throughout the change i.e., ​$$dv=0$$​ .

(e) Cyclic process : When a system undergoes a number of different processes and finally comes to the initial state is called cyclic process. In this ​$$dU=0$$​ and ​$$dH=0$$​.

(f) Reversible process (g) Irreversible process
It is an ideal process and take infinite time. It is a spontaneous process and takes finite time.
The driving force is infinitesimally greater than the opposing force. The driving force is much greater than the opposing force.
It is in equilibrium at all stages. Equilibrium exist only in its initial and final stages only.
Work obtained is maximum. Work obtained is not maximum.
It is difficult to realise in practice. It can be performed in practice.
A reversible process can be brought back to initial state without producing any permanent effect in the adjacent surrounding. An irreversible process cannot be brought back to the initial state without avoiding a permanent change in the surrounding.

(vi) Internal energy :  of a system is the sum of internal molecular kinetic and internal potential energy at rest . Internal energy = internal kinetic energy + internal potential energy . Internal potential energy is due to the intermolecular force between the constituent particle of the system. Internal kinetic energy is due to molecular motion i.e., translational motion , vibrational and rotational motion .

NOTE : Internal energy of an ideal gas is purely kinetic as there is no intermolecular force in ideal gas.

Internal energy is a state functions i.e., ​$$\Delta{U}=(U_{final}-U_{initial})$$​ .

The internal energy of a gas can be increased in two ways :

i . By doing work on the system.

ii . By heating the system.

Characteristics of the internal energy :

i . Internal energy is an extensive energy.

ii . Internal energy is a state property.

iii . Internal energy does not depend upon the path followed to reach final position.

iv . There is no change in internal energy in a cyclic process.

(vii) Heat and work :  When ever a system changes from one state to another , change in energy happens. And this change in energy can be commonly seen in the form of heat and work.

(a) HEAT : Heat is defined as quantity of energy . It is denoted by q and it is a path dependent quantity. Energy transfer in the form of heat takes place if two object with different temperature brought in contact .

Exothermic process – In this process heat is evolved from the system . q is negative for exothermic process.

Endothermic process – In this process heat is absorbed by the system . q is positive for endothermic process.

(b) Work : James joule, in 1850 showed that there is a dynamic relationship between the mechanical work “w” and heat produced “H” .

$$w\propto{H}$$

$$w=JH$$

Here , J = joule mechanical equivalent of heat

Let us consider a system with an adiabatic wall . In this system, the internal energy of the system increases if the work is done on the system and the internal energy of the system decreases if the work is done by the  system . In adiabatic process ,

$\Delta{U}=U_{2}-U_{1}=w_{ad}$

w=-ve , if the work is done on the system.

w=+ve if the work is done by the system.

#### THERMODYNAMICS EQUILIBRIUM AND ZEROTH LAW OF THERMODYNAMICS

Two bodies are said to be in thermal equilibrium if no transfer of heat takes place when they are in contact.

According to ,zeroth law of thermodynamics if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

OR

If three or more systems are in thermal contact with each other by means of diathermal walls and are all in thermal equilibrium together, then any two systems taken separately are in thermal equilibrium with each other.

#### FIRST LAW OF THERMODYNAMICS

It is merely the law of conservation of energy. It is given by Robert Mayer and Helmholtz.

STATEMENT 1 : Energy can neither be created, nor be destroyed but can be converted from one form to another.

STATEMENT 2 : The total energy of the universe is constant.

STATEMENT 3 : Whenever a quantity of one kind of energy disappears, an exactly equivalent quantity of energy in some other form must appears.

STATEMENT 4 : It is impossible to construct a perpetual motion machine which could produce work without consuming energy.

STATEMENT 5 : The total energy of an isolated system remains constant though it may change from one form to another.

STATEMENT 6 : There is an exact equivalence between work and heat i.e., when work is transformed into heat or heat into work, the quantity of work is mechanically equivalent to heat.

Mathematical formulation of First law

When a system is changed from initial state to final state , it undergoes a change in the internal energy from ​$$U_{in}$$​ to ​$$U_{fi}$$​.

Thus , ​$$\Delta{U}=U_{final}-U_{initial}$$

The change in internal energy can be brought by two ways :

(i) Either by allowing the heat flow into the system {absorption} or out of the system (evolution).

(ii) By doing work on the other system or the work done by the system.

Consider a system whose internal energy is ​$$U_{1}$$​ . If the system is supplied q amount of heat , the internal energy of system will become ​$$U_{1}+q$$​ . Now, if work is also done on the system , the final internal energy is ​$$U_{2}$$​.

$U_{2}=U_{1}+q+w\\U_{2}-U_{1}=q+w\\\Delta{U}=q+w$

where, “q” is the heat absorbed and “w” is the work done on the system.

If work done by the system then it become

$\Delta{U}=q+(-w)=q-w$

WORK : If a object is displaced through a distance ​$$dx$$​ against a force F, then the amount of work done is defined as :

$$w=F\times{dx}$$

or

Work = Intensity factor ​$$\times$$​ Capacity factor

Where intensity factor is a measure of force against which work is done and capacity factor is a measure for the extent for which work is done.

(a) Gravitational work : If a body is moved to a certain height against gravity , the work is done which is numerically equal to ​$$mgh$$​ where m= mass , g=acceleration due to gravity , h=height and also mg is intensity factor and h is capacity factor.

(b) Electrical work : If a charged particle is moved from one potential region to another , then work is done which is numerically equal to QV. Where Q is charge (capacity factor) and V is potential difference (intensity factor).

(c) Work of expansion or pressure-volume work :

Let us take a cylinder filled with gas whose volume is “V”with a weightless piston whose area of cross-section is “A” let the pressure be “p” on piston which is slightly less than internal pressure ,as the gas expands piston moves upward with a displacement of ​$$dl$$​ So, work done is :

$dw=force\times{displacement}\\dw=pressure\times{area}\times{displacement}\\dw=P\times{A}\times{dl}\\dw=p\times{dV}~[A\times{dl}=changes~to~volume]$

​If the change in volume be ​$$V_{initial}$$​ to ​$$V_{final}$$​ then the total work done be

$w=\int_{V_1}^{V_2} P~dV$

$=P(V_2-V_1)=P\times{\Delta{V}}\\or\\=P_{ext}\times{\Delta{V}}$

But if external pressure is slightly more than the internal pressure then contraction takes place in volume of gas i.e, as its energy is decreasing that’s why the work is given in minus.

### Work done in reversible isothermal expansion :

Let us take a ideal gas filled in cylinder having massless piston and cylinder is not insulated. The external pressure is equal to internal pressure ​$$P_{ext}=P_{gas}=P$$​ and if internal pressure is decreased by an infinitesimal amount ​$$dp$$​ , the gas will expand by infinitesimal amount of volume ​$$dV$$​ as a result of expansion the pressure in cylinder falls to ​$$P_{gas}-dP$$​ i.e., it become again equal to external pressure adn thus piston comes to rest this process is repeated many time and each time volume expand by ​$$dV$$​ .

Since, the system is in thermal equilibrium with the surrounding , the infinitesimally small cooling produced due to expansion is balanced by the absorption of heat from that surroundings and the temperature remains constant throughout the expansion.

The work done in each expansion is given as :

$d_{w}=-(P_{ext}-dP)dV\\d_{w}=-P_{ext}.dV\\d_{w}=-P.dV$

Minus sign indicate that the work is done by gas (there is expansion)

$$dV.dP$$​is neglected as they are infinitesimal quantities, is neglected.

The total amount of work done when volume changes from ​$$V_{1}$$​ to ​$$V_{2}$$​:

$w=-\int_{V_1}^{V_2}P~dV$

For an ideal gas ,

$P=\dfrac{nRT}{V}$

So,

$w=-nRT\int_{V_1}^{V_2}~\dfrac{dV}{V}\\w=-nRT~log_e~\dfrac{V_2}{V_1}\\w=-2.303nRT~log_{10}\dfrac{V_2}{V_1}$

At constant temperature , according to Boyle’s law

$P_1V_1=P_2V_2\\\dfrac{V_2}{V_1}=\dfrac{P_1}{P_2}$

So,

$w=-2.303nRT~log_{10}\dfrac{P_1}{P_2}$

Isothermal compression work of an ideal gas can be derived by same method and it has exactly same value with a positive sign

$w_{compression}=2.303nRT~log_{10}\dfrac{V_1}{V_2}$

OR

$w_{compression}=2.303nRT~log_{10}\dfrac{P_2}{P_1}$

Free Expansion : Expansion of a gas against zero pressure or expansion in vaccum is called free expansion.

$w_{compression}=-P_{external}\times{\Delta{V}}\\w_{compression}=-0\times{\Delta{V}}\\w_{compression}=0$

No work is done in free expansion.

$\Delta{U}=q+w\\\Delta{U}=q-P_{ext.}\Delta{V}\\\Delta{U}=q-0\times\Delta{V}\\\Delta{U}=q$

Thus , in free expansion change in heat of a system is equal to internal energy. Same result will come at constant volume.

Irreversible isothermal change :  Work done in irreversible isothermal change may be calculated as :

$q=-w=P_{ext}.(V_{final}-V_{initial})$

Adiabatic process : In this process heat is neither absorbed nor evolved from the system i.e., q=0

$\Delta{U}=w_{adiabatic}$

### ENTHALPY AND ENTHALPY CHANGE

If we talk about atmospheric pressure ,most of the places are having same amount of pressure as most of the places is plane and also many chemical reaction we do in open which is at constant pressure as the surrounding have. So ,we can say that conversion of one state of system into another takes place under constant pressure.And at constant pressure in a chemical reaction there can be increase or decrease in volume.If expansion occurs then some heat is utilised in doing work against constant pressure then the resultant heat would be less than the heat evolved in constant volume.

On the other hand , if the reaction proceed with contraction in volume, the work is done on the system and heat evolved will be more than the heat evolved at constant volume .

Thus , it is clear from above that the heat change of a system in constant pressure do not merely depend upon the internal energy alone but also on the contraction and expansion of volume of the system against the atmospheric pressure.

Enthalpy is denoted by H and it is defined as the sum of internal energy and the product of pressure-volume energy of the system under a particular set of conditions.It is also sometimes called Heat content

$H=E+P.V$

Differential form

$\Delta{H}=\Delta{E}+P\Delta{V}$

also written as

$\Delta{H}=\Delta{U}+w$

Each substance has a definite value of enthalpy in a particular state. Enthalpy is also an extensive property and a state property.

Change in enthalpy

$\Delta{H}=H_{final}-H_{initial}$

​In a chemical reaction

$\Delta{H}=H_{products}-H_{reactants}$

According to first law of thermodynamics

$q=\Delta{U}+w$

$$\Delta{H}=q$$​ as pressure is constant

Thus , enthalpy change is a measure of heat change (evolve or absorbed) taking place during a process at constant pressure.

According to first law of thermodynamics,

$\Delta{U}=q+P.\Delta{V}$

At constant volume,

$\Delta{V}=0\\\Delta{U}=0\\\Delta{U}=q_{v}$

Thus, ​$$\Delta{U}$$​ expresses thermal change at constant volume.

### Relationship between ​$$\Delta{U}$$​ and ​$$\Delta{H}$$​

Let us considered a chemical reaction takes place at constant pressure and constant temperature and gas is evolved. Lets write ideal gas equation of reactant and product.

Where ​$$V_{A}$$​ is the volume of reactants and ​$$V_{B}$$​is the volume of products ,​$$n_{r}$$​ is the number of moles of reactants and ​$$n_{p}$$​ is the number of moles of products

$PV_{A}=n_{r}RT\\PV_{B}=n_{p}RT\\P(V_{B}-V_{A})=(n_{p}-n{r})RT\\P\Delta{V}=\Delta{n}RT$

Putting the value of ​$$P.\Delta{V}$$​in ​$$\Delta{H}=\Delta{E}+P.\Delta{V}$$

$\Delta{H}=\Delta{U}+\Delta{nRT}$

OR

$q_{p}=q_{v}+\Delta{nRT}$

$\begin{bmatrix}Energy~change\\at~constant\\pressure,~P\end{bmatrix}=\begin{bmatrix}Energy~change\\at~constant\\volume,~V\end{bmatrix}+\begin{bmatrix}change~in~the\\number~of~\\gaseous~moles\end{bmatrix}\times{RT}$

### Conditions under which ​$$\Delta{H}=\Delta{U}$$​ or ​$$q_{p}=q_{v}$$​

(i) When the reaction is carried out in a closed vessel i.e.,​$$\Delta{V}=0$$

(ii) When reaction involves only solids or liquids or solutions, i.e., no gaseous species is involved then the volume change in solids and liquids is usually negligible.

(iii) When in a chemical reaction, the total number of gaseous molecules of reactants and total number of gaseous molecules of products are equal, i.e., ​$$n_{p}=n_{r}$$

Examples :

$H_{2}(g)+Cl_{2}(g)\rightarrow{2HCL}(g);~n_{r}=2,n_{p}=2\\N_{2}(g)+O_{2}(g)\rightarrow{2NO(g)};~n_{r}=2,n_{p}=2$

### Conditions under which ​$$\Delta{H}\not=\Delta{U}$$​

(i) When in a reaction the number of moles of gaseous products is greater than the number of moles of gaseous reactants, ​$$\Delta{H}$$​will be having higher value than ​$$\Delta{U}(n=+ve)$$​.Example :

$PCl_{5}(g)\rightleftharpoons{PCl_{3}(g)}+Cl_{2}(g);~\Delta{n}=2-1=1\\2NH_{3}(g)\rightleftharpoons{N_{2}(g)}+3H_{2}(g);~\Delta{n}=4-2=2$

(ii) A reaction in which number of moles of gaseous products is less than number of moles of gaseous reactants, ​$$\Delta{H}$$​ will be having lesser value than ​$$\Delta{U}(\Delta{n=-ve})$$.Example :

$2SO_{2}(g)+O_{2}(g)\rightleftharpoons2SO_{3}(g);~\Delta{n}=2-3=-1\\CO(g)+\dfrac{1}{2}O_{2}(g)\rightleftharpoons{CO_{2}}(g);~\Delta{n}=1-\dfrac{3}{2}=-\dfrac{1}{2}$

Conclusion : When

$\Delta{n}=0;~\Delta{H}=\Delta{U}\\\Delta{n}>0;~\Delta{H}>\Delta{U}\\\Delta{n}<0;~\Delta{H}<\Delta{U}$

### Characteristics of Enthalpy:

(i) Enthalpy is a state function.

(ii) Enthalpy is a extensive property.

(iii) Enthalpy independent of path followed.

Standard Enthalpy Change : A temperature of 25° C or 298 k and a pressure of one atmosphere form a standard state. The enthalpy change of a reaction when all the reactants and products are in their standard states is known as the standard enthalpy change. Which is represented by H° or ​$$\Delta{H_{298~k}}$$​.

### HEAT CAPACITY

Heat capacity of the system is defined as the quantity of heat required to raise the temperature of a system by 1°. It is also called thermal capacity.

Let a very small amount of heat ​$$dq$$​ be given to the system and the temperature of the system be rises by ​$$dT$$

$Heat~capacity=\dfrac{dq}{dT}$

Specific Heat Capacity :  of a system is the amount of heat required to raise the temperature of unit mass of a substance through one degree. It is denoted by ​$$s$$​.

Amount of ​$$\Delta{Q}$$​ of heat is given to a mass ​$$m$$​ of the substance and its temperature rises by ​$$\Delta{T}$$​ then the specific heat is

$s=\dfrac{\Delta{Q}}{m\Delta{T}}$

Specific heat of a gas

at constant pressure

$s_{p}=\dfrac{\Delta{Q}}{m\Delta{T}}$

at constant volume

$s_{v}=\dfrac{\Delta{Q}}{m\Delta{T}}$

also

$thermal~capacity=m\times{s}$

Molar Heat Capacity : is defined as the heat given per mole to the system per unit rise in the temperature. Denoted by ​$$C$$

$C=\dfrac{\Delta{Q}}{n\Delta{T}}$

For 1 mole substance (n=1)

$C=\dfrac{\Delta{Q}}{\Delta{T}}$

At constant volume , heat change of the system is equal to internal energy i.e.,​$$\Delta{Q}=\Delta{E}$$

$C_{v}=\dfrac{\Delta{E}}{\Delta{T}}$

At constant pressure,​

$$\Delta{Q}=\Delta{E}+P.\Delta{V}=\Delta{H}$$

$C_{p}=\dfrac{\Delta{H}}{\Delta{T}}$

Mayer’s Relation

The difference between ​$$C_{p}$$​ and ​$$C_{v}$$​ is equal to the work done by 1 mole of gas in expansion when heated through 1° C.

Work done by the gas at constant pressure = ​$$P.\Delta{V}$$​

For 1 mole of gas PV=RT.

When temperature is raised by 1° C , the volume changes from ​$$\Delta{V}$$​ to ​$$\Delta{V}+V$$​, thus

$PV=RT\\P(V+\Delta{V})=R(T+1)\\P\Delta{V}=R$

Hence,

$C_{p}-C_{v}=w\\C_{p}-C_{v}=P.\Delta{V}\\C_{p}-C_{v}=R$

The ratio of molar heat is denoted by ​$$\gamma$$

$\gamma=\dfrac{C_{p}}{{C_{V}}}$

Value of ​$$\gamma$$​ is used to determine atomicity of a gas.

### Origin of Enthalpy Change in a reaction

Why in some reaction energy is evolved while in other energy is evolved. To answer this we believe that every matter is having some internal energy or intrinsic energy or chemical energy. And when reactants combine to form product , there is readjustment of energies takes place and if ​$$E_{1}$$​ and ​$$E_{2}$$​ are the total energies of reactants and product respectively. Then three cases exist.

(i) When ​$$E_{1}=E_{2}$$​ no change in energies i.e., no energy is evolved and no energy is absorbed.

(ii) When ​$$E_{1}>E_{2}$$​ the difference of ​$$(E_{1}-E_{2})$$​ energy is evolved i.e., heat is evolved.

(iii) When ​$$E_{1}<E_{2}$$​ the difference of ​$$(E_{2}-E_{1})$$​ energy is absorbed i.e., heat is absorbed.

OR

In a chemical reaction, the chemical bonds in reactant broke down and new bonds are formed in products. And to break bonds energy is required (absorption takes place) and in formation of bonds ,energy is released.

Since, the bond energy varies from one bond to another, it is bound to be an energy change called the enthalpy of the reaction.

Simplest case is in gaseous reaction , we have

$\begin{bmatrix}Enthalpy~change\\of ~a~reaction\end{bmatrix}=\begin{bmatrix}Energy~required~\\to~break~the~bonds\\of~the~reactants\end{bmatrix}-\begin{bmatrix}Energy~released~\\in~the~formation~of\\bonds~in~the~products\end{bmatrix}$

### Exothermic and Endothermic Reactions

The reaction in which heat is evolved is called exothermic reaction.

The amount of heat energy released during the reaction is shown on the side of products with a plus sign

$A+B\rightarrow{C+D+q(Heat~energy)} \\C(s)+O_{2}(g)\rightarrow{CO_{2}(g)+393.5~kj}\\NaOH(aq)+HCl(aq)\rightarrow{NaCl(aq)+H_{2}O(aq)+57.1~kj\\H_{2}(g)+\dfrac{1}{2}O_{2}(g)\rightarrow{H_{2}O(l)+85.8~kj}}$

In all these reaction the total enthalpy of product is less than the total enthalpy of reactants,

$H_{P}<H_{R}$

Hence, enthalpy change ​$$\Delta{H}$$​ at constant pressure and constant volume is given by

$\Delta{H}=H_{P}-H_{R}$

$=-ve$

Thus, for exothermic reactions , enthalpy change is negative

$2SO_{2}(g)+O_{2}(g)\rightarrow{2SO_{3}(g)};~\Delta{H}=-694.6~kj\\2C_{4}H_{10}(g)+13O_{2}(g)\rightarrow{8CO_{2}}(g)+10H_{2}O(g);~\Delta{H}=-5316~kj\\H_{2}(g)+Cl_{2}(g)\rightarrow2HCl(g);~\Delta{H}=185~kj$

The reactions in which heat is absorbed is called endothermic reactions.

Amount of heat absorbed during the reaction is show by writing ​$$+q$$​ with reactant or by writing ​$$-q$$​ with the product.

$A+B+q\rightarrow{C+D}$

or

$A+B\rightarrow{C+D}-q$

$N_{2}(g)+O_{2}(g)+180.5~kj\rightarrow{2NO}(g)\\N_{2}(g)+O_{2}(g)\rightarrow{2NO{g}-180.5~kj}$

In endothernic reactions, the total enthalpy of products is more than total enthalpy of reactants,

$H_{P}>H_{R}$

Thus, the enthalpy change ​$$\Delta{H}$$​ at constant pressure and constant volume can be given as :

$\Delta{H}=H_{p}-H_{R}$

$=+ve$

Thus, for endothermic reactions , the enthalpy change is positive.

$2HgO(s)\rightarrow{2Hg(l)}+O_{2}(g);~\Delta{H}=+180~kj\\2SO_{3}(g)\rightarrow{2SO_{2}(g)+O_{2}(g)};~\Delta{H}=+694.6~kj$

### Thermochemical Equation

A chemical equation  which show the heat change during a chemical reaction is called thermochemical equation.

(i) Equation should be balanced equation.

(ii) The physical state of the chemical is represented with the chemical elements like (aq), (s) , (g) ,(l) .

(iii) In case if any allotrophic element the name of alotrophic form must be mentioned.

(iv) Heat change during chemical change is show by two ways in older convection we use +ve (exothermic) or -ve (endothermic) heat evolved is added to the right side of the product but in modern convection we use change in enthalpy ​$$\Delta{H}$$​+ve for endothermic and -ve for exothermic reaction.

(v) Generally , value of change in enthalpy ​$$\Delta{H}$$​ is taken at standard values at 25° C and at 1 atmospheric pressure.

(vi) If the coefficient of substances are multiplied or divided by some number , the value of ​$$\Delta{H}$$​ is also multiplied or divided by same number.

$H_{2}(g)+\dfrac{1}{2}O_{2}(g)\rightarrow{H_{2}O(g};~\Delta{H}=-2418~kj\\2H_{2}(g)+O_{2}(g)\rightarrow{2H_{2}O};(g)~\Delta{H}=-483.6~kj$

### Heat of reaction or Enthalpy of reaction

Heat of reaction is defined as the amount of heat evolved or absorbed when quantities of the substance indicated by the chemical equation have completely reacted.

$\Delta{H}=\sum{H_{P}}-\sum{H_{R}}$

Factor which influence the heat of reaction

There are numerous factors which affect the magnitude of heat of reaction :

(i) Physical state of reactants and products :