When suspected drunk drivers are tested with a Breathalyzer, the alcohol (ethanol) in the exhaled breath is oxidized to acetic acid with an acidic solution of potassium dichromate: The color of the solution changes because some of the orange Cr₂O₇^2- is converted to the green Cr³⁺ The Breathalyzer measures the color change and produces a meter reading calibrated in blood alcohol content. (a) What is E° for the reaction if the standard half-cell potential for the reduction of acetic acid to ethanol is 0.058 V?

Verified step by step guidance

1. Identify the half-reactions involved in the Breathalyzer reaction. The oxidation half-reaction is the conversion of ethanol to acetic acid, and the reduction half-reaction is the conversion of Cr_{2}O_{7}^{2-} to Cr^{3+}.
2. Write the standard reduction potential for each half-reaction. The given standard reduction potential for the reduction of acetic acid to ethanol is 0.058 V. You will need to find the standard reduction potential for the Cr_{2}O_{7}^{2-} to Cr^{3+} reaction from a standard reduction potential table.
3. Reverse the oxidation half-reaction to represent the oxidation of ethanol to acetic acid. Remember to change the sign of the standard reduction potential for this half-reaction since it is now an oxidation reaction.
4. Add the standard potentials of the two half-reactions to find the standard cell potential (E°) for the overall reaction. E° = E°(reduction) + E°(oxidation).
5. Ensure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction. If necessary, multiply the half-reactions by appropriate coefficients to balance the electrons before adding the potentials.

Key Concepts

Standard Electrode Potentials

Standard electrode potentials (E°) are measured voltages that indicate the tendency of a chemical species to be reduced, under standard conditions. Each half-reaction has a specific E° value, which can be used to calculate the overall cell potential for redox reactions. In this context, knowing the E° for the reduction of acetic acid to ethanol helps in determining the E° for the oxidation of ethanol to acetic acid.

Redox Reactions

Redox reactions involve the transfer of electrons between two species, where one is oxidized (loses electrons) and the other is reduced (gains electrons). In the Breathalyzer reaction, ethanol is oxidized to acetic acid, while potassium dichromate is reduced, leading to a color change. Understanding the oxidation and reduction processes is crucial for calculating the overall cell potential and interpreting the results.

Nernst Equation

The Nernst equation relates the cell potential of an electrochemical reaction to the concentrations of the reactants and products. It allows for the calculation of the actual cell potential under non-standard conditions. In this scenario, the Nernst equation can be applied to find the E° for the reaction by considering the standard potentials and the stoichiometry of the involved species.