The equilibrium temperature (Teq) is estimated as around 2310 K for the transformation from I2(s) to I2(g).
To estimate the temperature at which the free energy change (ΔG) for the transformation from solid iodine (I2(s)) to gaseous iodine (I2(g)) is zero, we can use the relationship between ΔG, temperature (T), enthalpy change (ΔH), and entropy change (ΔS). The equation is given by ΔG = ΔH - TΔS.
For this specific transformation, the enthalpy change (ΔH) can be calculated as the difference in enthalpies between I2(g) and I2(s), and the entropy change (ΔS) is the difference in entropies for the same states.
ΔH = H_I2(g) - H_I2(s) = 260.57 kJ/mol - 116.73 kJ/mol = 143.84 kJ/mol
ΔS = S_I2(g) - S_I2(s) = 62.25 J/(mol⋅K) - 0 J/(mol⋅K) = 62.25 J/(mol⋅K)
Now, rearranging the equation ΔG = ΔH - TΔS to solve for temperature (T) when ΔG is zero:
0 = ΔH - TeqΔS
Teq = ΔH/ΔS = 143.84 kJ/mol / 62.25 J/(mol⋅K)
Teq ≈ 2310 K
So, the estimated temperature at which the free energy change for the transformation from I2(s) to I2(g) is zero is approximately 2310 K.