Calculate the standard reduction potential for the reaction of Cu(III) to Cu(II)
Use the following data:
1) Cu^+3 + 2e^- -> Cu^+, E°1 = 1.28 V
2) Cu^+2 + e^- -> Cu^+, E°2 = 0.15 V
3) Cu^+2 + 2e^- -> Cu(s), E°3 = 0.34 V
4) Cu^+ + e^- -> Cu(s), E°4 = 0.52 V
To calculate the standard reduction potential for the reaction of Cu(III) to Cu(II), we can use the Nernst equation, which relates the standard reduction potential of a reaction to the concentrations of the species involved. However, we need to know the balanced equation for the reaction involving Cu(III) and Cu(II).
Let's start by examining the given data:
1) Cu^+3 + 2e^- -> Cu^+, E°1 = 1.28 V
2) Cu^+2 + e^- -> Cu^+, E°2 = 0.15 V
3) Cu^+2 + 2e^- -> Cu(s), E°3 = 0.34 V
4) Cu^+ + e^- -> Cu(s), E°4 = 0.52 V
The equations with the lowest oxidation states involve the formation of solid copper (Cu), which means we cannot directly obtain information about the reaction involving Cu(III) to Cu(II) from the given data.
To solve this, we can combine the equations in a way that cancels out the species we don't need. By summing the equations 1) and 2), we can cancel out the Cu^+ species:
Cu^+3 + 2e^- -> Cu^+ (Equation 1)
Cu^+2 + e^- -> Cu^+ (Equation 2)
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Cu^+3 + 3e^- -> Cu^+ (Combined equation)
Now, we have an equation involving Cu^+3 and Cu^+. However, we need to convert Cu^+3 to Cu(III) and Cu^+ to Cu(II). To do this, we multiply the equation by 1/3, which allows us to manipulate the stoichiometry:
(1/3) Cu^+3 + e^- -> (1/3) Cu^+ (Combined equation)
Now, the equation represents the reaction of Cu(III) to Cu(II). We can assign the reduction potential for this reaction by multiplying the reduction potential of the combined equation by 1/3:
E° (Cu^+3 + e^- -> Cu^+) = (1/3) * (E°1 + E°2)
= (1/3) * (1.28 V + 0.15 V)
= (1/3) * 1.43 V
= 0.477 V
Therefore, the standard reduction potential for the reaction of Cu(III) to Cu(II) is 0.477 V.