Chemical reactions are generally carried out at constant pressure (atmospheric pressure) so it has been found useful to define a new state function Enthalpy (`H`) (earlier defined in thermodynamics):

`H = U + PV`

and hence, `Delta H = DeltaU + Delta(PV)`

At constant pressure

`Delta H = Delta U + P Delta V`

Combining with first law,

`Delta H = q_P`

Hence, transfer of heat at constant pressure brings about a change in the enthalpy of the system.

`text(Enthalpy change)`, `Delta_rH` `text(of a reaction-Reaction enthalpy-Heat of reaction)`

The enthalpy change accompanying a reaction is called the reaction enthalpy. It may also be defined as the amount of heat lost or gained in the chemical reaction, when all the reactants and products are maintained at the same temperature and pressure. The enthalpy change of a chemical reaction may be given as

`Delta_r H =` (sum of enthalpies of products )-(sum of enthalpy of reactants)

`= sum(nu_P H)_text(products) - sum(nu_P H)_text(reactants)`

where `nu` is the stoichiometric coefficients of reactants and products, respectively.

`text(Types of Reactions)` :

(i) `text(Exothermic Reactions)` : `text(Heat is evolved during the reaction. For such reactions)` `Delta_r H` is negative, which implies that

`sum nu_p H (text(products)) < sum nu_R H (text(reactants))`

(ii) `text(Endothermic Reactions)` : `text(Heat is absorbed during the reaction. For such reactions)` `Delta_r H` is positive, which implies that

`sum nu_p H (text(products)) > sum nu_R H (text(reactants))`

`text(Note)` :

(i) For a reaction whose `Delta H = + ve` and `Delta E = - ve`, what will be the classification as exothermic and endothermic.

(ii) In general, reactions have `Delta H` and `Delta E` of same sign unless the values of `Delta H` and `Delta E` are exceptionally small.

Factors affecting `Delta H` reactants & products

(i) Physical states of reactants & products

(ii) Allotropic forms of elements

(iii) Reaction conditions (constant pressure or constant volume)

(i) Condition of constant `P` or `V` : Heat changes at constant volume are expressed as `Delta E`.

Heat changes at constant pressure are expressed as `Delta H`

Also for a change `Delta H= Delta E+P Delta V ..... (1)`

where `P` is the pressure and `Delta V` is change in volume.

Also `Delta H` and `Delta E` are related together as

`Delta H = Delta E + Delta n_g RT.........................(2)`

Where `DeltaH` and `Delta E` are change in enthalpy and change in internal energy for a given change respectively.

`Delta n_g =` Moles of gaseous products -Moles of gaseous reactants.

`R` = Molar gas constant

`T` = Temperature in Kelvin

`text(NOTE)` : While using eq. (2) for numerical one should keep in mind that for

`a.` For calculation of `Delta n_g` only gaseous moles of reactants and products are considered.

`b.` lf `Delta n_g = 0; Delta H = Delta E`

`c.` `Delta n_g` may be `+ve` or `-ve` integer or fraction.

`d.` Put `R` in the same units in which `delta H` and `Delta E` are given.

`e.` Normally reactions are carried out at constant pressure and therefore, heat changes are to be taken as `Delta H` unless stated otherwise.

(ii) Physical nature of reactants and products :

For reactants: `C_text(Diamond) + O_2(g) + CO_2(g)` `[Delta H = -94.3 kcal]`

`C_text(Amorphous) + O_2(g) + CO_2(g)` `[Delta H = -97.6 kcal]`

For products : `H_2(g) +1/2 O_2(g) -> H_2O_(l)` `[Delta H = -68.3 kcal]`

`H_2(g) +1/2 O_2(g) -> H_2O_(l)` `[Delta H = -57.0 kcal]`

Therefore, it is necessary to write physical state of reactants and products while writing thermochemical equation.

(iii) Temperature :The variation of `Delta H` or `Delta E` with temperature is expressed in terms of Kirchhoff's equation as

`Delta H_2 -DeltaH_1 = DeltaC_p(T_2-T_1)` or `Delta E_2 -Delta E_1 =Delta C_v(T_2-T_1)`

Where `DeltaH_1` and `DeltaE_1` are heats of reaction at temperature `T_1`

`DeltaH_2` and `DeltaE_2` are heats of reaction at temperature `T_2`

`Delta C_p = sum nu_p C_(p(text(product))) - sum nu_pC_(p(text(Reactant)))`

`Delta C_v = sum nu_p C_(v(text(product))) - sumnu_pC_(v(text(Reactant)))`

`C_p` and `C_v` are molar specific heats at constant `P` and `V` respectively.

`text(Note)` :
(i) The above expression should be used only when all the gases involved are ideal and reaction occurs at constant temperature.

(ii) lt is advisable to start with `DeltaH = DeltaE + Delta(PV)` which is a general expression and then depending upon data appropriate expressions should be used.

The enthalpy of chemical reactions and phase transition do vary with temperature. Although the variation in `DeltaH` with temperature is
usually small compared to the value of `DeltaH` itself.

consider a reaction `A -> B` at temperature `T_1` and pressure `P`

`text(Since H is state function :-)` Change in enthalpy in cyclic process is equal to zero. To calculate enthalpy change `(DeltaH_2)` at temperature `T_2` at constant pressure consider cyclic process shown in figure. It is clear `Delta H_3 =` change in enthalpy of `A` when temperature is raised from `T_1` to `T_2` at constant pressure.

`Delta H = int_(T_1)^(T_2)C_(p,B) dT`

`Delta H =` change in enthalpy taking `1` mole of `B` at constant pressure from `T_1` to `T_2`

`Delta H_4 = int_(T_1)^(T_2)C_(p,A) dT` now :

`Delta H_3 + Delta H_1 + Delta H_4 = Delta H_2`

`=> Delta H_2 - Delta H_1 = Delta H_3 + DeltaH_4 => DeltaH_2 -DeltaH_1 = int_(T_1)^(T_2)(C_(p,B) - C_(p,A)) dT`

`=> DeltaH_2 -deltaH_1 = Delta_r C_p(T_2-T_1)`

If `Delta_r C_p` is independent of temperature

`text(Standard enthalpy of Reaction)` `Delta_rH^o`
As enthalpy of a reaction depends on the conditions under which a reaction is carried out, it is necessary to specify some standard conditions. The standard enthalpy of reaction is the enthalpy change for a reaction, when all the participating substance (reactants and products) are in their standard condition.

`text(Note)` :

(i) `text(The standard condition are)` :
`ast` Solid/liquid/gas should be at `1` bar.

`ast` For substance dissolved in solution concentration should be `1``M`.

(ii) Standard conditions in Thermodynamics does not specify any temperature. However in Electrochemistry it is taken as `298` `K`.

(i) `text(Enthalpy of Formation)`, `Delta_fH` : It is the enthalpy change when one mole of a substance is formed from its elements in their most abundant naturally occurring form (also called reference states).

`H_2(g) + 1/2 O_2(g) -> H_2O(l) ; Delta_f H_(H_2O(l)) = -285.8 kJ` `mol^-1`

`text(Note)` :

(a) By convention, enthalpy of formation `Delta_fH` of an element in reference state is taken as zero.

(b) The enthalpy of formation can be used to determine the enthalpy change of any reaction as

`Delta_r H = underset(i)suma_iDelta_fH_text(products) -underset(i)sum b_iDelta_fH_text(reactamts) `

where `a_i` and `b_i` represent the coefficients of the products and reactants in the balanced chemical equation.

(c) `DeltaH_f` data can be used to compare stability of isomer and allotropes.

(d) The reference state of commonly used elements are : See Table 1.

(ii) `text(Enthalpy of Combustion)`, `Delta_CH` : lt is the enthalpy change when one mole of the substance undergo complete combustion to give combustion products.

`CH_4(g) + 2O_2(g) -> CO_2(g) + 2H_2O(l)`; `Delta_cH = - 890.8 kJ mol^(-1)` at `298 K`.

The combustion products of the substances are See Table 2.


(iii) `text(Enthalpy of Transition)` : It is the enthalpy change when one mole of one allotropic form changes to another under conditions of constant temperature and pressure. For example

`C(text(graphite)) -> C(text(diamond))`, `Delta_(trs) H = 1.90 kJ mol^(-1)`

(iv) `text(Bond Enthalpies (Bond energies))`, `Delta_text(bond)H` : The bond enthalpy of diatomic molecules like `H_2`, `Cl_2`, `O_2` etc. may be defined as the enthalpy change when one mole of covalent bonds of a gaseous covalent substance is broken to form products in the gas phase, under conditions of constant pressure and temperature. For example

`Cl_2(g) -> 2Cl(g) ; Delta_(Cl-Cl)H = + 242 kJ mol^(-1)`

`O_2(g) -> 2O(g) ; Delta_(O-O)H = + 428 kJ mol^(-1)`

In case of polyatomic molecules, bond dissociation enthalpy is different for different bonds within the same molecule. In such cases, mean bond enthalpy is used. Mean bond enthalpy may be defined as the average enthalpy change to dissociate a particular type of bond in the compounds.

In gas phase reactions, the standard enthalpy of reaction, `Delta_r H^o`, is related with the bond enthalpies of reactants and products as

`Delta_rH^o = sum` bond enthalpies (reactants) `- sum` bond enthalpies (products)

`=sum in` of reactants `- sum in` of products

(v) `text(Ionisation Enthalpy)` `(Delta_I H)` : It is the enthalpy change when an electron is removed from an isolated gaseous atom or in its ground state under conditions of constant temperature and pressure.

`X(g) -> X^+ (g) + e^(-)`

(vi) `text(Electron Gain Enthalpy)` `(Delta_(eg)H)` : It is the enthalpy change when an electron is added to a neutral gaseous atom to convert it into a negative ion under conditions of constant temperature and pressure.

`X(g) + e^(-) -> X^(-) (g)`

(vii) `text(Lattice Enthalpy)` `(Delta_(text(lattic))H)` : (The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state under conditions of constant temperature and pressure.

`Na^(+) Cl^(-) -> Na^(+)(g) + Cl^(-)(g)`;

`Delta_(text(Lattice))H = + 788 kJ mol^(-1)`

Lattice enthalpy can also be defined for the reverse process. In that case the value of `DeltaH_(LE)` will be negative.

`text(Born- Haber Cycle For NaCl)` : This cycle is based on thermochemical changes taking place in the formation of a lattice. This cycle
can be used to determine lattice energy which cannot be directly measured. It is defined as that energy released when one mole of the ionic compound (lattice) is formed its isolated ions in the gaseous state under standard condition.

`nA^(m+)(g) + mB^(n-)(g) -> A_nB_m(s)`

`Delta H = -U ` (lattice energy)

Formation of `NaCl(s)` lattice involves thus.

`S + I + (epsilon_(Cl-Cl))/2 -E -U =q`

hence, `U` can be calculated.

here, `S = ` enthalpy of sublimation of `Na(s) = Delta H_(text(sublimation))`

`I =` ionisation energy of `Na(g) = DeltaH_(text(ionization))`

`epsilon =` bond energy of `Cl_2`

`U =` lattice energy

`q =` enthalpy of formation of `NaCl(s) = Delta H_(text(formation))`

If lattice is `MgX_2(s)` then

`S + (I_1 + I_2) + epsilon - 2E - U = q`

where, `(I_1 + I_2) =` total ionisation energy to form `Mg^(2+)(g)`.

(viii) `text(Enthalpy of Atomisation)`, `Delta_aH` : It is the enthalpy change when one mole of a substance is completely dissociated into atoms in the gaseous state, under constant pressure and temperature condition.

For example

`H_2(g) -> 2H(g)`; `Delta_a H = 435.0 kJ mol^(- 1)`

`CH_4(g) -> C(g) + 4H(g)`; `Delta_aH = 1665 kJ mol(- 1)`

(ix) `text(Enthalpy of Hydration)`, `Delta_(hyd)H` : It is the enthalpy change when one mole of an anhydrous (or partly hydrated) compound combines with the required number of moles of water to form a specific hydrate at the specified temperature and
pressure. For example :

`CuSO_4(s) + 5H_2O(l) -> CuSO_4*5H_2O(s)`; `Delta_(hyd)H = - 78.20 kJ mol^(- 1)`

(x) `text(Enthalpy of Solution)`, `Delta_(sol)H` : It is the enthalpy change when one mole of a substance is dissolved in a specified amount of solvent under conditions of constant temperature and pressure. When large volume of solvent is taken, the enthalpy change is called enthalpy of solution at infinite dilution. For example :

`NaCl(s) -> NaCl(aq)`; `Delta_(sol)H = + 4 kJ mol^(-1)`

or, `NaCl(s) -> Na^(+) (aq) + Cl^(-)(aq)`; `Delta_(sol)H = + 4kJ mol^(- 1)`

(xi) `text(Enthalpy of Neutralisation)`, `Delta_(n e t)H` : It is the enthalpy change when one g-equivalent of an acid and one g-equivalent of a base undergo complete neutralisation in aqueous solution and all the reactants & products are at the same specified temperature and pressure.

`HCl(aq) + NaOH(aq) -> NaCl(aq) + H_2O(l) ; Delta_(n e t)H = - 57.7 kJ eq^(- 1)`

The enthalpy of neutralisation of strong acid and strong base is always constant (`-57.7 kJ eq^(- 1)`), independent from the acid and base taken. However, the magnitude of enthalpy change of neutralisation decreases when any one of the acid or base taken is weak.

The value (`- 57.7 kJ eq^(- 1)`) is the value when acids and bases are taken in their infinitely diluted state. If acids and basis are having some other concentration, then value will differ.

When two or more double bond are in conjugation, there is possibility of delocalization of electron through conjugation. The Phenomenon is called resonance. Due to resonance, the molecule gain stability. The actual structure of molecule is average of many possible canonical structure possible for molecule. Whenever there is possibility of Resonance energy is difference in energy of most
stable canonical structure and energy of actual molecule.

Whenever there is possibility of resonance in molecule, the molecule become more stable and bond breaking become difficult.

`text(Calculation of resonance energy using bond energy)` : Resonance energy can be calculated using the formula

`Delta H` (Actual) - `DeltaH` (theoretical) = resonance energy of products - Resonance energy of reactants

The proof of above formula is given by following diagram.
Consider a reaction
`A(g) + B^(ast)(g) -> C(g) + D^(ast)(g)`

where`(ast)` showing that molecules exhibit phenomena of resonance. Remember where ever resonance take place, bond breaking become difficult.

Actual energy required to break a bond is equal to `in_(text(actual)) = in_(text(theoretical)) - ` resonance energy

`DeltaH_(text(actual)) = in_A +in_B - R.E_B - {in_C +in_D -R.E_D}`

`DeltaH_(text(actual)) = (in_A +in_B -in_C -in_D) + R.E_B -RE_D `

`[Delta H_(text(actual)) - DeltaH_(text(Theoretical)) = R.E_(text(products))-R.E_(text(reactants))]`

`text(Note)` : The value of resonance energy may be positive or negative, but assign it's sign on the basis that resonance always increases the stability and decreases the energy of molecule. Due to resonance in a molecule, bond breaking become difficult hence actual energy required to break a bond = theoretical bond energy - resonance energy.