To calculate the Gibbs free energy change G at standard conditions for the given reaction, we need to know the standard Gibbs free energy of formation Gf for each of the compounds involved in the reaction. The standard Gibbs free energy of formation is the change in Gibbs free energy when 1 mole of a compound is formed from its constituent elements in their standard states.The reaction is: CO2 g + 2H2 g CH3OH g The standard Gibbs free energy of formation for the compounds involved are:Gf CO2 = -394.4 kJ/molGf H2 = 0 kJ/mol since H2 is an element in its standard state Gf CH3OH = -162.2 kJ/molNow, we can calculate the Gibbs free energy change for the reaction using the following equation:G = [Gf products ] - [Gf reactants ]G = [Gf CH3OH ] - [Gf CO2 + 2 * Gf H2 ]G = -162.2 kJ/mol - -394.4 kJ/mol + 2 * 0 kJ/mol G = -162.2 kJ/mol + 394.4 kJ/molG = 232.2 kJ/molThe Gibbs free energy change at standard conditions for the given synthesis reaction is 232.2 kJ/mol.