Answer:

To calculate the standard free-energy change (ΔG°) for a reaction at 25°C (298 K), you can use the Gibbs-Helmholtz equation, which is:

ΔG° = ΔH° - TΔS°

Where:

- ΔG° is the standard free-energy change.

- ΔH° is the standard enthalpy change (given in kJ/mol).

- T is the temperature in Kelvin (298 K for 25°C).

- ΔS° is the standard entropy change (given in J/(mol·K)).

You'll need the standard enthalpy change (ΔH°) and standard entropy change (ΔS°) for each reaction. Let's calculate these values and then find ΔG°:

a. CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

ΔH° (ΔH for the reaction) = ΣΔH(products) - ΣΔH(reactants)

ΔH° = [ΔH(CO2) + 2ΔH(H2O)] - [ΔH(CH4) + 2ΔH(O2)]

You'll need to look up the standard enthalpies of formation for CH4, CO2, H2O, and O2. After calculating ΔH°, you'll also need the standard entropy values to calculate ΔS°.

b. 2MgO(s) → 2Mg(s) + O2(g)

ΔH° (ΔH for the reaction) = ΣΔH(products) - ΣΔH(reactants)

ΔH° = [2ΔH(Mg) + ΔH(O2)] - [2ΔH(MgO)]

You'll need the standard enthalpy of formation values for Mg, O2, and MgO. After calculating ΔH°, you'll also need the standard entropy values to calculate ΔS°.

Once you have both ΔH° and ΔS° for each reaction, you can use the Gibbs-Helmholtz equation to find ΔG° for each reaction at 25°C (298 K). The negative sign indicates spontaneity:

ΔG° = ΔH° - TΔS°

Please provide the values of ΔH° and ΔS° for each reaction if available, or specify if you need assistance with those calculations.