ΔG°rxn for the reaction A + 3B → C + 2D is 1174.0 kJ/mol
To calculate ΔG°rxn for the reaction A + 3B → C + 2D using the given data, you can use Hess's Law, which states that the change in Gibbs free energy for a reaction is the sum of the changes in Gibbs free energy for the individual reactions that make up the overall reaction. Here are the steps:
Step 1: Write the balanced chemical equation for the overall reaction:
A + 3B → C + 2D
Step 2: Determine the change in Gibbs free energy for the overall reaction using the given data for the individual reactions. To do this, we'll manipulate the given reactions to match the overall reaction:
a) Reverse Reaction 1: C + 3B → A + 3B
ΔG°rxn1 = -(-414.0 kJ/mol) = 414.0 kJ/mol (because we reversed the reaction, we change the sign of ΔG°)
b) Multiply Reaction 2 by 2 to match the coefficient of D in the overall reaction: 2C → 2D
ΔG°rxn2 = 2(380.0 kJ/mol) = 760.0 kJ/mol
Step 3: Now, add the ΔG° values of the modified reactions to calculate ΔG°rxn for the overall reaction:
ΔG°rxn (overall) = ΔG°rxn1 + ΔG°rxn2
ΔG°rxn (overall) = 414.0 kJ/mol + 760.0 kJ/mol
ΔG°rxn (overall) = 1174.0 kJ/mol
So, ΔG°rxn for the reaction A + 3B → C + 2D is 1174.0 kJ/mol.