Question

Police often use a Breathalyzer test to determine the ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) content in a person's blood. The test involves a redox reaction that produces a color change. Potassium dichromate is reddish orange and chromium(III) sulfate is green. The balanced reaction is: \(2 \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(a q)+3 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)+8 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(2 \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+2 \mathrm{~K}_{2} \mathrm{SO}_{4}(a q)\) \(+3 \mathrm{CH}_{3} \mathrm{COOH}(a q)+11 \mathrm{H}_{2} \mathrm{O}(l)\) (a) Identify the element that gets oxidized and the element that gets reduced. (b) Give the oxidizing agent and the reducing agent.

Short answer

(a) Carbon is oxidized; chromium is reduced. (b) Potassium dichromate is the oxidizing agent; ethanol is the reducing agent.

Step-by-step solution

Identify the oxidation states in reactants

First, determine the oxidation states of key elements in the reactants. In potassium dichromate, \(\text{K}_2\text{Cr}_2\text{O}_7\), the oxidation state of chromium (Cr) is +6. In ethanol, \(\text{C}_2\text{H}_5\text{OH}\), carbon (C) in the -OH attached carbon has an oxidation state of -1.

Identify the oxidation states in products

Next, examine the oxidation states of the same elements in the products. In chromium(III) sulfate, \(\text{Cr}_2\left(\text{SO}_4\right)_3\), the oxidation state of chromium is +3. In acetic acid, \(\text{CH}_3\text{COOH}\), the carbon bonded to -OH has an oxidation state of +3.

Determine the element oxidized

Compare the oxidation states of carbon in ethanol and acetic acid. Since the oxidation state of carbon changes from -1 to +3, carbon is the element being oxidized.

Determine the element reduced

Compare the oxidation states of chromium in potassium dichromate and chromium(III) sulfate. The change from +6 to +3 means chromium is being reduced.

Identify oxidizing and reducing agents

The element that is reduced (chromium from potassium dichromate) is the oxidizing agent, and the element that is oxidized (carbon in ethanol) is part of the reducing agent (ethanol).

Key concepts

Oxidation States

Oxidation states are crucial for understanding redox reactions. They help us track how electrons are transferred during a chemical reaction. Each element in a compound has an oxidation state, indicating its electron count compared to a neutral atom.In a redox reaction, one element loses electrons and another gains them. We call these processes oxidation and reduction, respectively. To find out which element is oxidized or reduced in a reaction, we first determine their oxidation states before and after the reaction. For example:

• In potassium dichromate \(\text{K}_2\text{Cr}_2\text{O}_7\), chromium has an oxidation state of +6.
• In ethanol \(\text{C}_2\text{H}_5\text{OH}\), the carbon linked to the hydroxyl group has an oxidation state of -1.

Towards the reaction products:

• The chromium in chromium(III) sulfate \(\text{Cr}_2\left(\text{SO}_4\right)_3\) has an oxidation state of +3.
• The carbon in acetic acid \(\text{CH}_3\text{COOH}\) will show an oxidation state of +3 on the same carbon.

This change from -1 to +3 for carbon indicates oxidation, while the drop from +6 to +3 for chromium signifies reduction.

Oxidizing and Reducing Agents

In any redox reaction, we also categorize the substances involved as either oxidizing or reducing agents. These terms refer to entities in a reaction that facilitate oxidation and reduction.The oxidizing agent is the substance that gets reduced by gaining electrons. Conversely, the reducing agent gets oxidized by losing electrons.

• For our reaction, potassium dichromate (\(\text{K}_2\text{Cr}_2\text{O}_7\)) serves as the oxidizing agent. This is because the chromium within it reduces from an oxidation state of +6 to +3.
• Ethanol (\(\text{C}_2\text{H}_5\text{OH}\)) acts as the reducing agent. The carbon in ethanol oxidizes from -1 to +3.

Identifying these agents is an essential part of understanding how redox reactions work. They allow us to see which parts of the reaction contribute to electron donation and acceptance.

Balancing Chemical Equations

Balancing chemical equations in redox reactions is a meticulous process that shows the conservation of mass and charge. Each side of the reaction equation must have an equal quantity of each element and a consistent total charge.When balancing redox reactions, we apply the half-reaction method. This involves:

• Writing separate equations for the oxidation and reduction processes.
• Balancing each equation for atoms and charges separately.
• Combining and adjusting them to ensure overall balance.

For example, the breathalyzer test reaction is:\[2 \text{K}_2 \text{Cr}_2 \text{O}_7(aq) + 3 \text{C}_2 \text{H}_5 \text{OH}(g) + 8 \text{H}_2 \text{SO}_4(aq) \longrightarrow 2 \text{Cr}_2\left(\text{SO}_4\right)_3(aq) + 2 \text{~K}_2 \text{SO}_4(aq) + 3 \text{CH}_3 \text{COOH}(aq) + 11 \text{H}_2 \text{O}(l)\]This balanced equation demonstrates the precise stoichiometry needed for the color change in a breathalyzer reaction, where potassium dichromate oxidizes ethanol, illustrating a typical redox interplay.