Question

Alcohols can be oxidized very easily by potassium dichromate. This fact formed the basis for many of the early breathalyzers used by law eaforcement officers to determine the approximate blood alcohol levels of suspected drunk drivers. The unbalanced equation for the reaction is $$ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cr}_{2} \mathrm{O}^{2} \rightarrow \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{Cr}^{3} $$ In this reaction, the potassium dichromate is orange and the chromium(III) jons are blue. The bluer a solution of potassium dichromate becomes, the greater the concentration of alcohol in the breath. Write a balanced ionic cquation for this reaction in an acidic cnvironment.

Short answer

Balanced equation: \[3\text{CH}_3\text{CH}_2\text{OH} + 2\text{Cr}_2\text{O}_7^{2-} + 16H^+ \rightarrow 3\text{CH}_3\text{COOH} + 4\text{Cr}^{3+} + 11H_2O\]

Step-by-step solution

Write the Unbalanced Ionic Equation

Start with the unbalanced ionic equation: \[\text{CH}_3\text{CH}_2\text{OH} + \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{CH}_3\text{COOH} + \text{Cr}^{3+}\]

Identify the Oxidation and Reduction Half-Reactions

Identify the oxidation half-reaction (ethanol being oxidized to acetic acid) and the reduction half-reaction (dichromate being reduced to chromium(III)). Write their half-reactions:Oxidation: \[\text{CH}_3\text{CH}_2\text{OH} \rightarrow \text{CH}_3\text{COOH} + 4H^+ + 4e^-\]Reduction: \[\text{Cr}_2\text{O}_7^{2-} + 14H^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7H_2O\]

Balance Electrons in Half-Reactions

To balance the electrons in the half-reactions, multiply the oxidation half-reaction by 3 and the reduction half-reaction by 2 so the number of electrons lost equals the number of electrons gained:Oxidation: \[3(\text{CH}_3\text{CH}_2\text{OH} \rightarrow \text{CH}_3\text{COOH} + 4H^+ + 4e^-)\]Result: \[3\text{CH}_3\text{CH}_2\text{OH} \rightarrow 3\text{CH}_3\text{COOH} + 12H^+ + 12e^-\]Reduction: \[2(\text{Cr}_2\text{O}_7^{2-} + 14H^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7H_2O)\]Result: \[2\text{Cr}_2\text{O}_7^{2-} + 28H^+ + 12e^- \rightarrow 4\text{Cr}^{3+} + 14H_2O\]

Combine and Simplify the Reactions

Combine the two balanced half-reactions and simplify to form the balanced overall reaction:\[3\text{CH}_3\text{CH}_2\text{OH} + 2\text{Cr}_2\text{O}_7^{2-} + 16H^+ \rightarrow 3\text{CH}_3\text{COOH} + 4\text{Cr}^{3+} + 11H_2O\]

Key concepts

Breathalyzer Chemistry

Breathalyzers work by detecting the presence of ethanol (the alcohol in alcoholic drinks) in a person's breath. When a person breathes into a breathalyzer, any ethanol in their breath reacts with chemicals inside the device. One common chemical used in early breathalyzers is potassium dichromate.
The reaction between ethanol and potassium dichromate changes the color of the solution from orange to blue. The more alcohol present, the bluer the solution gets.
This color change is due to a redox reaction, where ethanol is oxidized to acetic acid and dichromate ions are reduced to chromium(III) ions. Essentially, the breathalyzer is measuring the amount of ethanol through an oxidation-reduction reaction.

Chemical Equations

A chemical equation represents a chemical reaction where reactants are transformed into products. In our alcohol oxidation reaction, the unbalanced equation is: \(\text{CH}_3\text{CH}_2\text{OH} + \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{CH}_3\text{COOH} + \text{Cr}^{3+}\).
Chemical equations must be balanced to obey the Law of Conservation of Mass, meaning the number of atoms for each element must be the same on both sides of the equation.
To balance this, we use ionic and half-reaction methods. We write separate equations for the oxidation (loss of electrons) and reduction (gain of electrons) processes, then combine and adjust them so that the total number of electrons lost equals the total number of electrons gained.

Alcohol Oxidation

Alcohol oxidation is when an alcohol reacts to form a carbonyl group like an aldehyde or a carboxylic acid. In our reaction, ethanol (CH3CH2OH) is oxidized to acetic acid (CH3COOH) through different steps.
During oxidation, ethanol loses electrons and hydrogen ions, forming acetic acid and protons: \(\text{CH}_3\text{CH}_2\text{OH} \rightarrow \text{CH}_3\text{COOH} + 4H^+ + 4e^-\).
Simultaneously, the dichromate ion is reduced by gaining electrons and reacting with protons to form chromium(III) ions and water: \(\text{Cr}_2\text{O}_7^{2-} + 14H^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7H_2O\).
This process results in a color change from orange to blue, indicating the presence of alcohol due to the production of blue chromium(III) ions.