The reaction below represents the decomposition of a generic diatomic molecule in its standard state.1/2 A2(g) → A(g)Assuming that the standard molar Gibbs energy of formation of A(g) is 8.12 kJ•mol–1 at 2500 Kand –72.20 kJ•mol–1 at 3500 K, determine the value of ΔH°rxn for these data assuming that ΔH°rxn is independent of temperature. Express your answer in kJ, in one decimal place.

To solve this problem, we need to use the Gibbs-Helmholtz equation, which relates the change in Gibbs free energy (ΔG) with the change in enthalpy (ΔH) and temperature (T). The equation is as follows:

ΔG = ΔH - TΔS

Where ΔS is the change in entropy. We can rearrange this equation to solve for ΔH:

ΔH = ΔG + TΔS

We know that ΔG is the standard molar Gibbs energy of formation, which is given as 8.12 kJ/mol at 2500 K and -72.20 kJ/mol at 3500 K. We also know that ΔS can be calculated from the change in ΔG with respect to temperature:

ΔS = (ΔG2 - ΔG1) / (T2 - T1)

Substituting the given values:

ΔS = (-72.20 kJ/mol - 8.12 kJ/mol) / (3500 K - 2500 K) ΔS = -80.32 kJ/mol / 1000 K ΔS = -0.08032 kJ/(mol•K)

Now we can substitute ΔS and the given ΔG and T values into the equation for ΔH:

ΔH = ΔG + TΔS ΔH = 8.12 kJ/mol + 2500 K * -0.08032 kJ/(mol•K) ΔH = 8.12 kJ/mol - 200.8 kJ/mol ΔH = -192.68 kJ/mol

So, the value of ΔH°rxn is -192.7 kJ/mol to one decimal place.