State and explain the Hess's law of constant heat summation.

Explanation

Hess's law: Energy changes remains constant whether the reactions take place in single step or in several steps.
I. Formation of `CO_(2)`: `CO_(2)` can be formed ether in one step or in two steps.
a) `C_(("graphite))"+O_(2)(g)toCO_(2)(g),DeltaH=-393.5kJ`
b) `C_(("graphite"))+(1)/(2)O_(2)(g)toCO(g),DeltaH=-110.5kJ`
`CO(g)+(1)/(2)O_(2)(g)toCO_(2),DeltaH=-283.5kJ`
Total `DeltaH=-393.52kJ`
Reaction 'a' is completed in single step and reaction 'b' is completed in two steps. But in both the cases energy changes remain constant, which proves Hess's law.
II. Formation of `NH_(4)Cl(aq):`
a) `NH_(3)(g)+H_(2)O(l)toNH_(3)(ad),DeltaH=-35.1kJ`f
`HCl(g)+H_(2)O(l)toHCl(aq),DeltaH=-72.9kJ`
`NH_(3)(aq)+HCl(aq)toNH_(4)Cl(aq),DeltaH=-51.5kJ`
Total `DeltaH=-159.5kJ`
b) `H=NH_(3)(g)+HCl(g)toNH_(4)Cl(g),DeltaH=-176.1kJ`
`NH_(4)Cl(s)+H_(2)O(l)toNH_(4)(aq),(DeltaH=+16.3kJ`
Total `DeltaH=-159.8kJ`
In both reactions (a) and (b), the heat of formation of `NH_(4)Cl(aq).` is the same. which proves Hess's law.
Uses of Hess's law: It is used to determine
1) Heat of formation.
2) Heat of reaction.
3) Crystal lattice energy.
4) Transition temperature of allotropic forms.