Use conservation of energy to explain an inverse relationship between enthalpy and entropy

Entropy is the measure of degree of disorder in a system. Greater the disorder, more is the entropy. For example, if a gas reactant molecule is decomposed into 2 smaller molecule, its entropy increases. 

On other hand, enthalpy deals with heat exchange between system and surrounding.Negative enthalpy value indicates that reaction is exothermic, while positive enthalpy value suggest that reaction is endothermic in nature.

Both entropy and enthalpy deal with the formation of products. However,  entropy deals with the degree of disorder in system and enthalpy deals with the energy of reactants vs products. 

Now, according to Law of conservation of energy, total energy of universe remains conserved. Thus, consider the following decomposition reaction:

H2O     →        H2     +    (1/2)O2

Here, the energy has to be supplied for occurrence of reaction. Hence, enthalpy is  positive. However, entropy of system increases because of increase in disorder in system. Thus, entropy is favoring the formation of product, while enthalpy is against the formation of product, due to its positive value.  

law of conservation of matter