Explanation
$$\Delta H_{f^0} = \Delta H_{sub} + IE+\Delta H_{diss} + EA + U$$
$$\Delta H_{f^0} = 108+496+122-349-788 = 411\, kJ/mol$$
The enthalpy change in the formation of an ionic lattice from the gaseous isolated sodium and chloride ions is $$-788$$ $${ kJ }/{ mole }$$. That enthalpy change, which corresponds to the reaction $${ Na }_{ (g) }+{ Cl }_{ (g) }\rightarrow { NaCl }_{ (s) }$$, is called the lattice energy of the ionic crystal. Although the lattice energy is not directly measurable, there are various ways to estimate it from theoretical considerations and some experimental values. For all known ionic crystals, the lattice energy has a large negative value. It is ultimately the lattice energy of an ionic crystal which is responsible for the formation and stability of ionic crystal structures.
For sodium chloride, the Born - Haber cycle is as shown in the image.
It is sometimes convenient to provide the value for $$\Delta { H }_{ rxn }$$ along with the balanced chemical equation for a reaction (also known as a thermochemical equation):
$$2{ H }_{ 2(g) }+{ O }_{ 2(g) }\longrightarrow 2{ H }_{ 2 }{ O }_{ (g) },\Delta { H }_{ rxn }=-483.6kJ$$
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum or reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric).
$$\Delta G=\Delta H-T\Delta S$$
A reaction is non-feasible if $$\Delta G$$ is positive. So, if $$\Delta H $$ is positive and $$\Delta S$$ is negative then $$\Delta G$$ is always positive irrespective of their magnitude.
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