Chemistry Enthalpy Change, `Δ_r H` of a Reaction – Reaction Enthalpy

Topics Covered :

● Enthalpy Change, `Δ_r H` of a Reaction – Reaction Enthalpy
● Standard Enthalpy of Reactions
● Enthalphy Changes during Phase Transformations
● Standard Enthalpy of Formation

Enthalpy Change, `Δ_r H` of a Reaction – Reaction Enthalpy :

`=>` In a chemical reaction, reactants are converted into products and is represented by,

Reactants → Products

`=>` The enthalpy change accompanying a reaction is called the `color{red}("reaction enthalpy")`.

● The enthalpy change of a chemical reaction, is given by the symbol `color{purple}(Δ_r H)`

`color{purple}(Δ_r H = ("sum of enthalpies of products") – ("sum of enthalpies of reactants"))`

`color{purple}( = underset(i)Sigma a_i H_text(products) -underset(i)Sigma b_i H_text(reactants))` ...........(6.14)

● Here symbol `color{purple}(Sigma)` (sigma) is used for summation and `color{purple}(a_i)` and `color{purple}(b_i)` are the stoichiometric coefficients of the products and reactants respectively in the balanced chemical equation. For example, for the reaction

`color{purple}(CH_4 (g) + 2O_2 (g) → CO_2 (g) +2H_2O (l))`

`color{purple}(Delta_r H = underset(i)Sigma a_i H_text(products) -underset(i)Sigma b_i H_text(reactants))`

` color{purple}(= [ H_m (CO_2 , g) +2H_m (H_2O , l) ] - [ H_m (CH_4 , g +2H_m (O_2 , g) ])`

where `color{purple}(H_m)` is the molar enthalpy.

`color{green}("Usefulness of Enthalpy Change" )` Enthalpy change is a very useful quantity.

(i) Knowledge of this quantity is required when one needs to plan the heating or cooling required to maintain an industrial chemical reaction at constant temperature.

(ii) It is also required to calculate temperature dependence of equilibrium constant.

Standard enthalpy of reactions :

`=>` Enthalpy of a reaction depends on the conditions under which a reaction is carried out. It is, therefore, necessary that we must specify some standard conditions.

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
`color{green}("Definition ")` The standard enthalpy of reaction is the enthalpy change for a reaction when all the participating substances are in their standard states.

`color{green}("Standard State" )` The standard state of a substance at a specified temperature is its pure form at `1` bar.

`color{red}("Example ")` The standard state of liquid ethanol at `298` `K` is pure liquid ethanol at `1` bar; standard state of solid iron at `500` `K` is pure iron at `1` bar. Usually data are taken at `298` `K`.

● Standard conditions are denoted by adding the superscript `color{purple}(⊖)` to the symbol `color{purple}(ΔH)`, e.g., `color{purple}(ΔH^⊖)`

Enthalpy changes during phase transformations :

`=>` Phase transformations also involve energy changes.

`color{red}("Example ")` Ice requires heat for melting. Normally this melting takes place at constant pressure (atmospheric pressure) and during phase change, temperature remains constant (at `273` `K`).

`color{purple}(H_2O(s) → H_2O(l))`; `color{purple}(Delta_text(fus)H^(⊖) = 6.00kJ mol^(-1))`

● Here `color{purple}(Δ_text(fus) H^(⊖))` is enthalpy of fusion in standard state.

● If water freezes, then process is reversed and equal amount of heat is given off to the surroundings.

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
`color{green}("Standard Enthalpy of Fusion" )` The enthalpy change that accompanies melting of one mole of a solid substance in standard state is called standard enthalpy of fusion or molar enthalpy of fusion, `color{purple}(Δ_text(fus) H^(⊖))`.

● Melting of a solid is endothermic, so all enthalpies of fusion are positive.

`=>` Water requires heat for evaporation. At constant temperature of its boiling point `T_b` and at constant pressure :

`color{purple}(H_2O (l) → H_2O(g) ; Delta_text(vap) H^(⊖) = +40.79 kJ mol^(-1))`

`color{purple}(Δ_text(vap)H^(⊖))` is the standard enthalpy of vaporization.

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
`color{green}("Standard Enthalpy of Vaporization ")` Amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure (1bar) is called its standard enthalpy of vaporization or molar enthalpy of vaporization, `Δ_text(vap)H^(⊖)`

`=>` Sublimation is direct conversion of a solid into its vapour.

● Solid `color{purple}(CO_2)` or ‘dry ice’ sublimes at `195` `K` with `color{purple}(Δ_text(sub)H^⊖=25.2 kJ mol^(–1))`; naphthalene sublimes slowly and for this `color{purple}(Delta_text(sub) H^⊖ = 73.0kJmol^(-1))`

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
`color{green}("Standard Enthalpy of Sublimation ")` Standard enthalpy of sublimation, `color{purple}(Δ_text(sub)H^⊖)` is the change in enthalpy when one mole of a solid substance sublimes at a constant temperature and under standard pressure (`1` bar).

`color{red}("Note ")` The magnitude of the enthalpy change depends on the strength of the intermolecular interactions in the substance undergoing the phase transfomations.

`color{red}("Example ")` The strong hydrogen bonds between water molecules hold them tightly in liquid phase. For an organic liquid, such as acetone, the intermolecular dipole-dipole interactions are significantly weaker. Thus, it requires less heat to vaporise `1` mol of acetone than it does to vaporize `1` mol of water.

`=>` Table 6.1 gives values of standard enthalpy changes of fusion and vaporisation for some substances.
Q 3017823780

A swimmer coming out from a pool is covered with a film of water weighing about `18g`. How much heat must be supplied to evaporate this water at `298 K` ? Calculate the internal energy of vaporisation at `100°C`.

`Delta_text(vap)H^(⊖) ` for water at `373K = 40.66 kJ mol^(–1)`


We can r epresent the process of evaporation as

`18 g H_2O (l) oversettext(vaporisation)→ 18 g H_2O (g)`

No. of moles in `18 g H_2O(l)` is `= (18 g)/(18 g mol^(-1)) = 1 mol`

`Delta_text(vap)U = Delta_text(vap)H^(⊖) -PDeltaV = Delta_text(vap)H^(⊖) - Deltan_g RT`

(assuming steam behaving as an ideal gas).

`Delta_text(vap)H^(⊖) - Deltan_gRT = 40.66 kJ mol^(-1)`

`-(1)(8.314 J K^(-1) mol^(-1) ) (373 K) (10^(-8)kJ J^(-1))`

`Delta_text(vap)U^(⊖) = 40.66kJ mol^(-1) -3.10 kJ mol^(-1) `

` = 37.56 kJ mol^(-1)`

Standard enthalpy of formation :

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
`color{green}("Definition" )` The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation (also known as reference states) is called Standard Molar Enthalpy of Formation.

● Its symbol is `color{purple}(Δ_fH^⊖)`, where the subscript `‘ f ’` indicates that one mole of the compound in question has been formed in its standard state from its elements in their most stable states of aggregation.

● The reference state of an element is its most stable state of aggregation at `25°C` and `1` bar pressure.

`color{red}("Example ")` The reference state of dihydrogen is `H_2` gas and those of dioxygen, carbon and sulphur are `O_2` gas, `color{purple}(C_text(graphite))` and `color{purple}(S_text(rhombic))` respectively.

● Some reactions with standard molar enthalpies of formation are given below.

`color{purple}(H_2(g) +1/2 O_2 (g) → H_2O(l)) ; `

`color{purple}(Delta_f H^⊖ = -285 kJ mol^(-1))`

`color{purple}(C_text(graphite, s) +2H_2 (g)→ CH_4(g)); `

`color{purple}(Δ_f H^⊖ = −74.8kJmol^(-1))`

`color{purple}(2C_text{(graphite,s)} +3H_2(g) +1/2 O_2(g) → C_2H_5OH (l)) ; `

`color{purple}(Delta_f H^⊖ = -277.7 kJ mol^(-1))`

`color{red}("Note ")` (i) Standard molar enthalpy of formation, `color{purple}(Δ_fH^⊖)`, is just a special case of `Δ_rH^⊖`, where one mole of a compound is formed from its constituent elements, as in the above three equations, where `1` mol of each, water, methane and ethanol is formed.

(ii) In contrast, the enthalpy change for an exothermic reaction :

`color{purple}(CaO(s) + CO_2 (g) → CaCO_3(s)) ; `

`color{purple}(Delta_fH^⊖ = - 178 kJ mol^(-1))`

is not an enthalpy of formation of calcium carbonate, since calcium carbonate has been formed from other compounds, and not from its constituent elements.

(iii) Also, for the reaction given below, enthalpy change is not standard enthalpy of formation, `color{purple}(Δ_fH^⊖)` for `color{purple}(HBr(g))`.

`color{purple}(H_2 (g) +Br_2 (l) →2HBr (g)) ; `

`color{purple}(Delta_f H^⊖ = -72.8 kJ mol^(-1))`

Here two moles, instead of one mole of the product is formed from the elements, i.e.,

`color{purple}(Delta_r H^⊖ = 2 Delta_f H^⊖)`

● Therefore, by dividing all coefficients in the balanced equation by 2, expression for enthalpy of formation of `HBr (g)` is written as

`color{purple}(1/2 H_2 (g) +1/2 Br_2(l) → HBr (g)) ; `

`color{purple}(Delta_fH^⊖ = -36.4 kJ mol^(-1))`

`=>` Standard enthalpies of formation of some common substances are given in Table 6.2.

`=>` By convention, standard enthalpy for formation, `color{purple}(Δ_fH^⊖),` of an element in reference state, i.e., its most stable state of aggregation is taken as zero.

`=>` Suppose, you are a chemical engineer and want to know how much heat is required to decompose calcium carbonate to lime and carbon dioxide, with all the substances in their standard state.

`color{purple}(CaCO_3 (s)→CaO(s) +CO_2 (g) ; Delta_r H^⊖ = ?)`

● Here, we can make use of standard enthalpy of formation and calculate the enthalpy change for the reaction. The following general equation can be used for the enthalpy change calculation.

`color{purple}(Delta_r H^⊖ = underset(i)Sigma a_i Delta_f H^⊖ ("products") - underset(i)Sigma b_i Delta_f H^⊖) ("reactants"))` .........(6.15)

where `color{purple}(a)` and `color{purple}(b)` represent the coefficients of the products and reactants in the balanced equation.

● Let us apply the above equation for decomposition of calcium carbonate. Here, coefficients ‘a’ and ‘b’ are `1` each. Therefore,

`color{purple}(Delta_r H^⊖ = Delta_f H^⊖ [CaO(s) ]+Delta_gH^⊖ [CO_2(g)] - Delta_f H^⊖ [CaCO_3(s)])`

` color{purple}(=1(-635.1 kJ mol^(-1) ) +1(-393.5kJ mol^(-1) )-1 (-1206.9 kJ mol^(-1) ))`

`color{purple}(= 178.3 kJ mol^(-1))`

● Thus, the decomposition of `color{purple}(CaCO_3)` (s) is an endothermic process and you have to heat it for getting the desired products.