To calculate the standard Gibbs energy changes for the following reactions, we need the standard Gibbs energy of formation (∆Gf°) values for each compound involved in the reactions. Unfortunately, you have not provided the values for any of the compounds. However, I can guide you on how to calculate the standard Gibbs energy change once you have the necessary values. The standard Gibbs energy change for a reaction (∆Gr°) can be calculated using the following equation: ∆Gr° = ∑(n × ∆Gf° (products)) - ∑(n × ∆Gf° (reactants)) where: - ∆Gr° is the standard Gibbs energy change for the reaction - n is the stoichiometric coefficient of each compound in the reaction - ∆Gf° is the standard Gibbs energy of formation for each compound For reaction (a) CH4 + 2O2 → CO2 + 2H2O, the equation would be: ∆Gr° = (1 × ∆Gf°(CO2)) + (2 × ∆Gf°(H2O)) - (1 × ∆Gf°(CH4)) - (2 × ∆Gf°(O2)) For reaction (b) 2MgO → 2Mg + O2, the equation would be: ∆Gr° = (2 × ∆Gf°(Mg)) + (1 × ∆Gf°(O2)) - (2 × ∆Gf°(MgO)) Once you have the standard Gibbs energy of formation values, plug them into the respective equations and calculate ∆Gr° for both reactions.