Calculate the standard free energy of the following reactions
at 25C, using standard free energies of formation.
a. C2H4(g) � 3O2(g) ±£ 2CO2(g) � 2H2O(l)
b. CaCO3(s) � 2H�(aq) ±£ Ca2�(aq) � H2O(l) � CO2(g)
dHrxn = (n*dHf products) - (n*dHf reactants)
To calculate the standard free energy of a reaction, you need to know the standard free energies of formation for all the reactants and products involved in the reaction. The standard free energy of formation (ΔG°f) is the change in free energy that occurs when one mole of a compound is formed from its constituent elements, under standard conditions (25°C and 1 atm pressure).
a. Let's calculate the standard free energy of reaction for the given equation: C2H4(g) + 3O2(g) → 2CO2(g) + 2H2O(l)
1. Firstly, we need to find the standard free energies of formation for each compound involved in the reaction. The values can be found in reference tables or databases. Let's assume the values are:
ΔG°f(C2H4) = +65 kJ/mol
ΔG°f(O2) = 0 kJ/mol
ΔG°f(CO2) = -394 kJ/mol
ΔG°f(H2O) = -285 kJ/mol
2. Now, we can calculate the standard free energy change (ΔG°) for the reaction using the following equation:
ΔG°reaction = ∑[νΔG°f(products)] - ∑[νΔG°f(reactants)]
where ν is the stoichiometric coefficient of each compound.
ΔG°reaction = [2 × ΔG°f(CO2) + 2 × ΔG°f(H2O)] - [ΔG°f(C2H4) + 3 × ΔG°f(O2)]
ΔG°reaction = [2 × (-394 kJ/mol) + 2 × (-285 kJ/mol)] - [65 kJ/mol + 3 × 0 kJ/mol]
ΔG°reaction = -788 kJ/mol - 65 kJ/mol
ΔG°reaction = -853 kJ/mol
Therefore, the standard free energy change (ΔG°) for the given reaction is -853 kJ/mol.
b. Let's calculate the standard free energy of reaction for the given equation: CaCO3(s) + 2H+(aq) → Ca2+(aq) + H2O(l) + CO2(g)
1. Find the standard free energies of formation for each compound involved in the reaction. Assume the values are:
ΔG°f(CaCO3) = -1207 kJ/mol
ΔG°f(H+) = 0 kJ/mol
ΔG°f(Ca2+) = -546 kJ/mol
ΔG°f(H2O) = -285 kJ/mol
ΔG°f(CO2) = -394 kJ/mol
2. Calculate the standard free energy change (ΔG°) for the reaction:
ΔG°reaction = [ΔG°f(Ca2+) + ΔG°f(H2O) + ΔG°f(CO2)] - [ΔG°f(CaCO3) + 2 × ΔG°f(H+)]
ΔG°reaction = [-546 kJ/mol + (-285 kJ/mol) + (-394 kJ/mol)] - [-1207 kJ/mol + 2 × 0 kJ/mol]
ΔG°reaction = -1225 kJ/mol + 1207 kJ/mol
ΔG°reaction = -18 kJ/mol
Therefore, the standard free energy change (ΔG°) for the given reaction is -18 kJ/mol.