# Hess’s law of constant heat summation

It states that, “The amount of heat evolved or absorbed in a chemical change is the same whether the process takes place in one step or in several steps”. (i.e. it follows 1st Law of Thermodynamics)

For example, carbon can be oxidised to $CO_2$ either directly or in two different steps as given below:

I st method $C(s) + O_2 (g) \to CO_2 (g) \Delta H = -94.3 kcal$

$II method \hspace{2mm}C(s) + \dfrac{1}{2} O_2(g) \to CO(g) \Delta H_1 = -26.0 kcal$

$CO(g) + \dfrac{1}{2} O_2(g) \Delta H_2 = -68.3 kcal$

According to Hess’s law $\Delta H$ must be equal to $\Delta H_1 + H_2$ which is true.

Applications of Hess’s law:

(i)     Determination of  transition

It helps in the determination of enthalpy of transition during allotropic modification.

E.g.

$P(yellow) \to H_3PO_4(l) \Delta -2.386 kcal \\[3mm] P(red) \to H_3PO_4 (l) \Delta H = -2.113 kcal$

According to Hess’s law this difference in the enthalpy of reaction represents the change.

I.e.

$p(yellow) \to p(red) \Delta - (2.386 - 2.223)$

$= -0.273 kcal$

Hence the enthalpy of transition in this case = -0.273 kcal.

(ii)    Determination of enthalpy of formation

It helps in the determination of enthalpy of formation which cannot be determined experimentally e.g. it is not possible to calculate enthalpy of formation of CO experimentally, but can be calculated by Hess’s law.

Since,

$C(s) +O_2(g) \to CO_2(g) \Delta H = -94.3 kcal$

$C(s) + \dfrac{1}{2}O_2(g) \to CO(g) \Delta H_1 = x kcal$

$CO(g) + \dfrac{1}{2}O_2 (g) \to CO_2 (g) \Delta H_2 = -68.3 kcal$

$\because \Delta H = \Delta H_1 + H_2 \\[3mm] or -94.3 = x + (-68.3)$

$or \hspace{3mm} x = -26.0 kcal$

(iii)  Bond Energy

It may be defined as, “The quantity of heat evolved when a bond is formed between two free atoms in a gaseous state to form a molecular product in a gaseous state”. It is also known as enthalpy of formation of the bond.

It may also be defined as, “The average quantity of heat required to break (dissociate) bonds of that type present in one mole of the compound”.

E.g.

$C (g) + 4H (g) \to C H_4 (g) \Delta H - 398 kcal$

According to definition, the average bond energy per mole of C — H bond is -398 / 4 kcal = -99.5 Kcal.

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