Calculate the standard free-energy change for the following reaction at 25 °C. Standard reduction potentials can be found here.

2Au(3+) + 3Cr-->2Au+3Cr(2+)

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Look up the potentials, add the oxidation half to the reduction half to obtain Eocell. Then dG = -nFE

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To calculate the standard free-energy change (ΔG°) for a reaction, you need to use the standard reduction potentials (E°) of the species involved.

The reaction given is:
2Au(3+) + 3Cr --> 2Au + 3Cr(2+)

To calculate ΔG°, follow these steps:

1. Determine the reduction half-reactions:
Au(3+) + 3e^- --> Au (reduction)
Cr --> Cr(2+) + 2e^- (oxidation)

2. Look up the standard reduction potentials (E°) for the half-reactions:
From the table of standard reduction potentials, we find:
E°(Au^3+/Au) = 1.498 V
E°(Cr/Cr^2+) = -0.74 V

3. Write the balanced equation for the overall reaction by adding the two half-reactions together (make sure the electrons cancel out):
Multiply the reduction half-reaction by 2 and the oxidation half-reaction by 3 to get the same number of electrons on both sides:
2Au(3+) + 6e^- --> 2Au
3Cr --> 3Cr(2+) + 6e^-
Combine the two half-reactions to obtain the balanced equation:
2Au(3+) + 3Cr --> 2Au + 3Cr(2+)

4. Calculate the ΔG° for the reaction using the Nernst equation:
ΔG° = -nFΔE°
where n is the number of moles of electrons transferred (in this case, n = 6), F is the Faraday constant (F = 96485 C/mol), and ΔE° is the difference in reduction potentials.

ΔE° = E°(reduction) - E°(oxidation)
ΔE° = (1.498 V) - (-0.74 V) = 2.238 V

Plug the values into the equation:
ΔG° = - (6)(96485 C/mol)(2.238 V) = - 1367779.88 J/mol

5. Convert the ΔG° from joules to kilojoules:
ΔG° = -1367779.88 J/mol = -1367.77988 kJ/mol

Therefore, the standard free-energy change for the given reaction at 25 °C is approximately -1367.8 kJ/mol.