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Hess Law of Constant Summation

Since the molar enthalpies of reactants and products involved in a chemical reaction have definite values, it is obvious that the enthalpy change of the reaction would also have a definite value, irrespective of the way the reaction is carried out. Thus, if we transform a specified set of reactants to a specified set of products by more than one sequence of reactions, the total enthalpy must be same for every sequence. This rule, which is a consequence of the law of conservation of energy, is known as Hess's law of constant heat summation. 

Hess's law can be stated as follows:
"The heat involved in a given chemical reaction is the same whether the process occurs in one step or several steps".

In support of Hess's law, we site below two methods of preparing carbon dioxide gas from carbon and oxygen.
Method I: C(s) + O2(g) → CO2(g) Δ H1=-393.5 kJ mol-1
Method II: C(s) + ½ O2(g) 
 CO(g)Δ H2 =-110.3 kJ mol-1
CO(g) + ½ O2(g) 
 CO2(g) Δ H3 =-283.2 kJ mol-1
Obviously Δ H1 = Δ H2 +ΔH3.

The chemical reactions can be the treated as ordinary algebraic expression and can be added or subtracted to yield the required reaction. The corresponding enthalpy changes are also manipulated in the same way to give the enthalpy change for the desired reaction.

Since ΔH stands for the change of enthalpy when reactants (substances on the left-hand side of the arrow) are converted into products (substances on the right-hand side of the arrow) at the same temperature and pressure, it follows that if the reaction is reversed (i.e. products are written on the left-hand side and reactants on the right-hand side), then the numerical value of ΔHremains the same but its sign changes. This statement is known as Lavoisier and Laplace law.

One of the important applications of Hess's law is that the change of enthalpy of a chemical reaction, which is difficult to determine experimentally, can be obtained by using this law. For example, ΔH2 cited above is difficult to determine experimentally. Obviously, according to Hess's law, it is equal to ΔH1 - ΔH3.

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