Hess's law

As enthalpy is a state function for a chemical reaction it is independent of the path by which the products are obtained.

Hess's law of heat summation states that for a chemical equation that can be written as the sum of two or more steps,the enthalpy change for the overall equation equals the sum of the enthalpy change for the individual steps.

In other words, no matter how you go from the reactants to products,the enthalpy change for the overall chemical change is the same.

To understand Hess's law fully and to see how you can use it,consider an example:

Suppose you want to find the enthalpy change for the combustion of graphite to carbon monoxide

2C(graphite ) + O2(g) ---------->  CO2 (g)

Direct determination of this enthalpy change is very difficult but applying Hess's law ,it is possible:

Imagine that the combustion of carbon monoxide takes place in two steps:

C(graphite) +  O2(g)---------------> CO2

2CO2(g) ------------->  2CO(g) + O2(g)

Step 1 :  C(graphite) + O2(g)---------------> CO2

In this step you burn 1 mol of graphite in 1 mol of oxygen to produce 1 mol of carbon dioxide. 

Step 2 ; 2CO2(g) ------------->  2CO(g) + O2(g)

In this step you decompose this carbon dioxide to give 2 mol of carbon monoxide and 1 mol of oxygen.

Step 3 : The net result is the combustion of graphite in 1mol of oxygen to give 2 mol of carbon monoxide .You can obtain this result  by adding the two steps cancelling out the 2 mol of CO2 and 1 mol of O2 on the both sides of the equation.

   2 X ( C(graphite) + O2(g)--------> CO2 ) (We are mutiplying this equation by 2 to obtain desired result

             2C(graphite) + 2O2(g)---------------> 2CO2 

             2CO2(g) ------------->  2CO(g) + O2(g) 

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  2C(graphite ) + O2(g) ---------->  CO2 (g)

 According the the Hess's law the enthalpy change for the overall equation(which is the equation you want) equals the sum of the enthalpy changes for the individual steps.Now you determine the enthalpy change of the desired equation.

Step 4 :the enthalpy change of this reaction is C(graphite) + O2(g)---------------> CO2 ΔH=-393.5 kj but as you multiplied this equation by 2 to obtain desired equation you should multiply the enthalpy change of this reaction by 2 as well so,  ΔH = 2 x -393.5 kj 

2C(graphite) + 2O2(g)---------------> 2CO2   ΔH = 787 kj

The enthalpy of change  2CO(g) + O2(g) --------------> 2CO2(g) is known which is ΔH = -566.0 kj but we need ot find ΔH of this reaction 2CO2(g) ------------->  2CO(g) + O2(g)  which is the reverse of the above mentioned reaction , so if you reverse the equation you simply reverse the sign of ΔH of the reaction

 2CO2(g) ------------->  2CO(g) + O2(g)   ΔH = 566.0 kj

you can see enthalpy change value is same but the sign is oppsite .

Step 4: so the final step is simply to find the enthalpy change of the desired reaction

   2C(graphite) + 2O2(g)---------------> 2CO2   ΔH = 787 kj

             2CO2(g) ------------->  2CO(g) + O2(g)  ΔH = 566.0 kj

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  2C(graphite ) + O2(g) ---------->  CO2 (g)   ΔH = -221.0 kj

So, this way you can see how we can find the enthalpy change of a reaction that is diffcult to determine experimentally using Hess's Law.