(a) Calculate the standard free-energy change (ΔG°) for the following oxidation-reduction reaction.
Cu(s) + Br2(aq) → Cu2+(aq) + 2 Br−(aq)
(b) Calculate the equilibrium constant for this reaction at 298 K.
To calculate the standard free-energy change (ΔG°) for the oxidation-reduction reaction, we can use the standard free-energy change equation:
ΔG° = -nFE°
Where:
- ΔG° is the standard free-energy change.
- n is the number of electrons transferred in the reaction.
- F is Faraday's constant (96,485 C/mol).
- E° is the standard cell potential.
(a) To determine the standard free-energy change (ΔG°), we need to find the standard cell potential (E°) and the number of electrons transferred (n).
1. First, find the standard reduction potentials of the half-reactions involved. We can look up the standard reduction potentials in a reference table, such as the NIST Standard Reference Database.
Cu2+(aq) + 2 e− → Cu(s) (Reduction)
E°1 = 0.337 V
Br2(aq) + 2 e− → 2 Br−(aq) (Oxidation)
E°2 = +1.087 V
2. The standard cell potential (E°) is the difference between the reduction and oxidation potentials:
E° = E°(reduction) - E°(oxidation)
E° = 0.337 V - 1.087 V
E° = -0.750 V
3. The number of electrons transferred (n) is equal to the number of electrons involved in the balanced equation. In this case, it's 2 electrons.
4. Now, substitute the values into the standard free-energy change equation:
ΔG° = -nFE°
ΔG° = -(2)(96,485 C/mol)(-0.750 V)
Calculate the value to find the standard free-energy change (ΔG°).
(b) To calculate the equilibrium constant (K) for the reaction at 298 K, we can use the Nernst equation:
ΔG° = -RTln(K)
Where:
- ΔG° is the standard free-energy change.
- R is the gas constant (8.314 J/mol·K).
- T is the temperature in Kelvin.
- K is the equilibrium constant.
1. Rearrange the equation to solve for K:
K = e^(-ΔG° / (RT))
2. Plug in the values:
- ΔG° is the value calculated in part (a).
- R is the gas constant (8.314 J/mol·K).
- T is the temperature in Kelvin (298 K).
Calculate the value to find the equilibrium constant (K).
dGo rxn = (n*dGo products) - (n*dGo reactants)
Then dGo = -RTlnK