The standard enthalpy change (ΔH°) for a chemical reaction is the amount of heat absorbed or released when one mole of the reactants in their standard states react to form one mole of the products in their standard states, at a specified temperature and pressure. It can be determined from the equilibrium constant (K) of the reaction at different temperatures using the Van't Hoff equation.



The Van't Hoff equation relates the equilibrium constant (K) of a reaction at two different temperatures (T1 and T2) to the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) of the reaction.

ln(K2/K1) = -ΔH°/R [(1/T2) - (1/T1)]

where R is the gas constant (8.314 J/mol∙K).



Given: K1 = 2.0 at T1 = 400 K and K2 = 3.0 at T2 = 500 K.

We can use the Van't Hoff equation to calculate ΔH° for the gas phase reaction.

ln(3.0/2.0) = -ΔH°/R [(1/500) - (1/400)]

Simplifying, we get:

ΔH° = -R ln(3.0/2.0) [(1/500) - (1/400)]

ΔH° = -8.314 J/mol∙K ln(1.5) [(1/500) - (1/400)]

ΔH° = -8.314 J/mol∙K x 0.04314

ΔH° = -359.6 J/mol

Therefore, the standard enthalpy change (ΔH°) for the gas phase reaction is approximately -360 J/mol.



The standard enthalpy change (ΔH°) for a gas phase reaction can be calculated from the equilibrium constant (K) of the reaction at different temperatures using the Van't Hoff equation. In this case, the calculated ΔH° was -360 J/mol.