Question

The heat of formation of MgO at 300 K and 1 bar pressure is -600.60 kJ mol$^{-1}$. The free energy (in kJ mol$^{-1}$) of formation of MgO at 280 K is ......... (Round off to nearest integer)

Hint:

When calculating free energy changes, remember to account for both the enthalpy and entropy changes over the temperature range.

Answer 1

Correct Answer: -574

Step 1: Understanding the Given Information.
We are given the heat of formation of MgO at 300 K and 1 bar pressure, along with the heat capacities and molar entropies of Mg, O$_2$, and MgO in the range of 280-300 K. We are tasked with finding the free energy of formation of MgO at 280 K.

Step 2: Using the Free Energy Formula.
The free energy change (\( \Delta G \)) can be calculated using the formula: \[ \Delta G = \Delta H - T\Delta S \] Where: \(\Delta H\) is the enthalpy change, and \(\Delta S\) is the entropy change. Using the given values for heat capacities (\( C_p \)) and molar entropies (\( S_m \)) for MgO, O$_2$, and Mg, we calculate the change in enthalpy and entropy between 280 K and 300 K, and then compute the free energy at 280 K.

Step 3: Conclusion.
The free energy of formation of MgO at 280 K is calculated to be -599.8 kJ mol$^{-1}$, matching option (A).