Calculate ΔG∘rxn and E∘cell for a redox reaction with n = 1 that has an equilibrium constant of K = 28?
What would the answer be to this? Could someone work this out for me please?
ΔG∘rxn = ......kj
E∘cell = ......V
To calculate ΔG∘rxn (standard Gibbs free energy change) and E∘cell (standard cell potential), you can use the relationship between the equilibrium constant (K) and Gibbs free energy change (ΔG∘rxn), as well as the relationship between ΔG∘rxn and E∘cell.
1. Relationship between K and ΔG∘rxn:
The equation relating K and ΔG∘rxn is as follows:
ΔG∘rxn = -RT ln(K)
In this equation:
- ΔG∘rxn is the standard Gibbs free energy change (in joules or kilojoules).
- R is the ideal gas constant (8.314 J/(mol K) or 0.008314 kJ/(mol K)).
- T is the temperature in Kelvin.
- ln denotes the natural logarithm function.
- K is the equilibrium constant for the reaction.
2. Relationship between ΔG∘rxn and E∘cell:
The equation relating ΔG∘rxn and E∘cell is as follows:
ΔG∘rxn = -nF E∘cell
In this equation:
- ΔG∘rxn is the standard Gibbs free energy change.
- n represents the number of electrons transferred in the reaction.
- F is the Faraday constant (96,485 C/mol or 96.485 kC/mol).
- E∘cell is the standard cell potential (in volts).
Now, let's solve for ΔG∘rxn and E∘cell using the given information.
Given data:
- For a redox reaction with n = 1, K = 28.
- You haven't provided the temperature (T), so we'll assume room temperature of 298 K.
1. Calculate ΔG∘rxn:
ΔG∘rxn = -RT ln(K)
= -(8.314 kJ/(mol K))(298 K) ln(28)
≈ -19.8 kJ
Therefore, ΔG∘rxn = -19.8 kJ.
2. Calculate E∘cell:
ΔG∘rxn = -nF E∘cell
-19.8 kJ = -(1 mol)(96.485 kC/mol) E∘cell
E∘cell = -19.8 kJ / (96.485 kC/mol)
≈ -0.205 V
Therefore, E∘cell = -0.205 V.
Please note that the negative signs indicate that the reaction is spontaneous in the forward direction (as given by the equilibrium constant).