Hess Law

Hess Law is another way of manipulating the enthalpy change of the reaction.  It states that if a reaction is carried out in a series of steps, ∆H for the reaction will equal the sum of the enthalpy changes for the individual steps.  The overall enthalpy change  for the process is independent on the number of steps or the particular nature of the path.  Therefore we can calculate ∆H for any process provided we know the route of the step.

Let us try sample problems in order to understand Hess Law.

Sample Problem 1.

The enthalpy of combustion of C to CO₂ is -393.5 kJ/mol C, and the enthalpy of combustion of CO to CO₂ is -283.0 kJ/mol CO:

                             C(s)   +    O₂(g)   →   CO₂(g)                 ∆H = - 393.5 kJ/mol
                         CO(g)    +    1/2O₂(g)  →  CO₂(g)               ∆H =  -283.0 kJ/mol

Using these data, calculate the enthalpy of C to CO:

                          C(s)  +   1/2 O2(g)  →    CO(g) 

Solution:
 
 In the problem above, we have to analyze how the equation is being manipulated to arrive the net equation. Since the net equation show that C is in the reactant side, meaning the first equation is as is.  We also notice that CO is in the product side and therefore the second reaction is reversed.

                     C(s)   +    O₂(g)   →   CO₂(g)                          ∆H = -393.5 kJ/mol
                                   CO₂(g)  →    CO(s)  +   1/2O₂(g)       ∆H =   283.0 kJ/mol
                     C(s)  +   1/2O₂(g)  →  CO(s)                             ∆H = -110.5 kJ/mol             

CO₂ is cancelled out and one-half of O₂.

Sample Problem 2:

Carbon occurs in two forms, graphite and diamond.  The enthalpy of combustion of graphite is -393.5 kJ/mol and that of diamond is -395.4 kJ/mol. 

                   C(graphite)   +  O₂(g)  →   CO₂(g)                  ∆H =  -393.5 kJ/mol
                   C(diamond)  +  O₂(g)  →   CO₂(g)                  ∆H =  -395.4 kJ/mol

Calculate the ∆H for the conversion of graphite to diamond.

Solution:

Since the reactant is graphite the first equation is as is, and since diamond is in the product side, therefore the second equation is reversed and so the ∆H value will be the opposite.
            
                       C(graphite)   +  O₂(g)  →   CO₂(g)                              ∆H =  -393.5 kJ/mol
                                             CO₂(g) →   C(diamond)  +  O₂(g)        ∆H =  +395.4 kJ/mol 
                                  C(graphite)       →   C(diamond)                       ∆H =    +  1.9 kJ/mol

O₂ and CO₂ are cancelled out because both can be found in the reactant and product side.
                  

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