Question

The blood alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) level can be determined by titrating a sample of blood plasma with an acidic potassium dichromate solution, resulting in the production of \(\mathrm{Cr}^{3+}(a q)\) and carbon dioxide. The reaction can be monitored because the dichromate ion \(\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)\) is orange in solution, and the \(\mathrm{Cr}^{3+}\) ion is green. The balanced equation is \(16 \mathrm{H}^{+}(a q)+2 \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \longrightarrow\) $$ 4 \mathrm{Cr}^{3+}(a q)+2 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(i) $$ This reaction is an oxidation-reduction reaction. What species is reduced, and what species is oxidized? How many electrons are transferred in the balanced equation above?

Short answer

In the given oxidation-reduction reaction, the dichromate ion \(\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)\) is reduced to \(\mathrm{Cr}^{3+}(a q)\), and ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) is oxidized to \(\mathrm{CO}_{2}\). A total of 6 electrons are transferred in the balanced equation.

Step-by-step solution

Assign Oxidation Numbers

Let's assign the oxidation numbers to each element involved in the reaction: \(16 \mathrm{H}^{+}(a q)+2 \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \longrightarrow 4 \mathrm{Cr}^{3+}(a q)+2 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l)\) Oxidation numbers: H: +1 O: -2 C (in ethanol, C2H5OH): -2 Cr (in Cr2O7^(2-)): +6 Cr (in Cr^(3+)): +3

Identify the Reduced Species

In the reaction, we need to find out which species has its oxidation number decreased. When comparing the reactants and products, we can see that the oxidation number of Cr changes from +6 to +3. This means the dichromate ion \(\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)\) is reduced to \(\mathrm{Cr}^{3+}(a q)\).

Identify the Oxidized Species

Next, we need to find out which species has its oxidation number increased. Comparing the reactants and products, the oxidation number of carbon in ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) changes from -2 to +4 in carbon dioxide (\(\mathrm{CO}_{2}\)). This means that ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) is oxidized to \(\mathrm{CO}_{2}\).

Determine the Number of Electrons Transferred

Finally, we have to find the total number of electrons transferred in the balanced equation. Let's look at the changes in oxidation numbers of the reduced and oxidized species: Cr: +6 to +3 (reduced, decrease of 3 oxidation numbers) C (in ethanol): -2 to +4 (oxidized, increase of 6 oxidation numbers) Since there are 2 Cr atoms in each dichromate ion, the total decrease in oxidation numbers for chromium is 2 × 3 = 6. For carbon, the increase in oxidation number is 6, the same as chromium. Thus, 6 electrons are transferred in the balanced equation.

Key concepts

Oxidation Numbers

Understanding oxidation numbers is essential for solving redox reactions, which involve changes in the oxidation states of elements involved. An oxidation number is a value assigned to an element in a chemical compound that represents its actual or hypothetical charge, reflecting its degree of oxidation. Here's how we use these numbers:

• We consider elements in their standard state to have an oxidation number of zero.
• In compounds, the sum of oxidation numbers equals the charge on the compound. For neutral compounds, this sum is zero.
• For monoatomic ions, the oxidation number is equal to the ion's charge.
• Oxygen usually has an oxidation number of -2 and hydrogen is typically +1, except in hydrides where it's -1.

By diligently assigning oxidation numbers to the elements in a reaction, we're laying the groundwork for identifying which species are oxidized and reduced.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions are the backbone of many chemical processes, including energy production in batteries and metabolic reactions in biology. In a redox reaction, one species undergoes oxidation while another undergoes reduction, essentially a simultaneous transfer of electrons from the oxidized species to the reduced one.

Oxidation

Occurs when an element increases its oxidation number, indicating a loss of electrons.

Reduction

Refers to the decrease in oxidation number, reflecting a gain of electrons.
In the case of blood alcohol determination by potassium dichromate, the ethanol in the blood is oxidized to carbon dioxide, while the dichromate ion is reduced to chromium(III) ions. Recognizing which species is oxidized and which is reduced is crucial in understanding redox reactions.

Chemical Titration

Chemical titration is an analytical technique used to determine the concentration of an unknown substance in a solution. It involves the gradual addition of a solution of known concentration, called the titrant, to the solution containing the unknown substance, until the reaction reaches an endpoint. This endpoint can be detected in various ways, such as a color change with an indicator as seen in redox titrations involving blood alcohol determination.

Dichromate titrations exploit the distinct color change from the orange of dichromate ions to the green of chromium(III) ions as a visible endpoint. By measuring the volume of titrant required to reach this point, we can calculate the amount of the substance being tested—ethanol in this particular case—using stoichiometry and molarity concepts.

Electron Transfer

The principle of electron transfer is at the heart of redox reactions. It explains how atoms or molecules lose or gain electrons, thereby changing their oxidation states. In redox titrations, the electron transfer quantitates how much reducing or oxidizing agent is present.

In the example of blood alcohol titration, chromium in the dichromate ion accepts electrons when it is reduced from an oxidation state of +6 to +3. At the same time, the carbon in ethanol contributes electrons as its oxidation state increases from -2 to +4. These changes correspond to a net transfer of electrons—six in our example. Counting the number of electrons transferred helps to balance redox reactions and is essential for correctly interpreting the results of a titration.