Calculate the standard free-energy change for the following reaction at 25 °C. Standard reduction potentials can be found here.
2Au^3+(aq) + 3Cr(s) <-----> 2Au(s) + 3Cr^2-(aq)
To calculate the standard free-energy change (ΔG°) for a reaction using standard reduction potentials, you need to use the equation:
ΔG° = -nFΔE°
Where:
- ΔG° is the standard free-energy change
- n is the number of moles of electrons transferred in the balanced equation
- F is the Faraday constant (96,485 C/mol)
- ΔE° is the standard cell potential, which is calculated by subtracting the reduction potential of the anode from the reduction potential of the cathode.
Step 1: Find the standard reduction potentials for the half-reactions involved in the reaction.
The half-reactions involved in this reaction are:
1. Au^3+(aq) + 3e^- → Au(s)
2. Cr(s) → Cr^2-(aq) + 2e^-
You can find the standard reduction potentials for these reactions in a table of standard reduction potentials. Look up the values for Au^3+/Au and Cr/Cr^2-.
Step 2: Calculate the standard cell potential (ΔE°).
Since the overall reaction is a combination of the two half-reactions, you need to subtract the reduction potential of the anode (Cr) from the reduction potential of the cathode (Au^3+).
ΔE° = E°(cathode) - E°(anode)
Step 3: Determine the number of moles of electrons transferred (n).
Looking at the balanced chemical equation, you can see that 3 moles of electrons are transferred for every 2 moles of Au^3+ and 3 moles of Cr.
Step 4: Plug the values into the ΔG° equation and solve for ΔG°.
ΔG° = -nFΔE°
Once you have calculated the value of ΔG°, you will have the standard free-energy change for the reaction at 25 °C.