Question

Write the half-reaction, used in the COD titration, which converts dichromate ion to \(\mathrm{Cr}^{3+}\) ion, and balance it.

Short answer

\(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{e}^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\)

Step-by-step solution

Identify the Species

In the COD titration, we are dealing with the reduction of the dichromate ion, \ \(\text{Cr}_2\text{O}_7^{2-}\), to chromium ions, \(\text{Cr}^{3+}\).

Write the Unbalanced Half-Reaction

Write the unbalanced half-reaction for the conversion: \ \[\text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}^{3+}\] This indicates that each dichromate ion is converted into chromium ions.

Balance the Chromium Atoms

Ensure that the chromium atoms are balanced on both sides of the equation. Since there are two chromium atoms in \(\text{Cr}_2\text{O}_7^{2-}\) and one on the product side, we write it as: \[\text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+}\]

Balance the Oxygen Atoms

The dichromate ion contains 7 oxygen atoms. To balance the oxygen atoms, add 7 water molecules to the right side: \[\text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Balance the Hydrogen Atoms

There are 14 hydrogen atoms in the 7 water molecules, requiring 14 hydrogen ions on the left side: \[\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Balance Charges Using Electrons

The left side has a total charge of \(+12\) (14 positive charges and 2 negative charges), and the right side has a charge of \(+6\). Here, 6 electrons are added to the left side to balance the charges: \[\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{e}^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Key concepts

Understanding Dichromate Ion

The dichromate ion, represented as \(\text{Cr}_2\text{O}_7^{2-}\), is a key player in chemical reactions, especially oxidation-reduction reactions.
It is a compound with a negative two charge, consisting of two chromium atoms and seven oxygen atoms.
In solutions, the dichromate ion is orange, and its reactions are critical for processes like Chemical Oxygen Demand (COD) titrations. These ions serve as strong oxidizing agents, meaning they can accept electrons from other substances during a reaction.

Reduction Half-Reaction

Reduction half-reactions involve gaining electrons, an essential part of redox reactions.
In the case of the dichromate ion's reduction, electrons are added, converting the compound into a different form.
For COD titration, the reduction of the dichromate ion \(\text{Cr}_2\text{O}_7^{2-}\) involves its transformation into chromium ions, \(\text{Cr}^{3+}\).

• Gaining electrons changes the oxidation state of the chromium from +6 in dichromate to +3 in chromium ions.
• This shift indicates a reduction process, as there is a decrease in the oxidation state.

The balanced half-reaction helps understand the standard electron migrating process.

Crafting a Balanced Chemical Equation

To balance a chemical equation, you must ensure atoms' numbers are equal on both sides, giving the same total charge.
For the COD reaction, not only should the chromium be balanced, but you also need to consider oxygen and hydrogen atoms.
The original unbalanced equation given is:\[\text{Cr}_2\text{O}_7^{2-} \to \text{Cr}^{3+}\]
Here's how to balance it:

• Balance chromium by having two \(\text{Cr}^{3+}\) on the right, matching the two chromates.
• Balance oxygen by adding 7 water \(\text{H}_2\text{O}\) molecules to the product side.
• Supply 14 hydrogen \(\text{H}^+\) ions to the left to balance hydrogen.

Finally, add 6 electrons to the left to achieve charge balance:\[\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{e}^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Role of Chromium Ions

Chromium ions, noted as \(\text{Cr}^{3+}\), play an integral role during the conversion of dichromate ions in redox reactions.
These ions are the product of the dichromate ion's reduction, showcasing a significant change in oxidation states.
In this redox process:

• The oxidation state of chromium reduces from +6 in \(\text{Cr}_2\text{O}_7^{2-}\) to +3 in \(\text{Cr}^{3+}\).
• This indicates a substantial electron uptake, and therefore a reduction.

Chromium ions also differ in color from dichromate, often appearing as a green or blue in solution. This color change is useful for indicating reaction completion in titrations.

Understanding Electron Transfer

Electron transfer is central to redox reactions like those in COD titrations, where it's crucial for balancing equations.
Electrons move here to convert dichromate ions to chromium ions, affecting the overall charge balance.
In the balanced reaction:

• The 6 electrons added to the left tally the charge across reactants and products, supporting conservation of charge.
• It highlights the fundamental principle that electrons are transferred and not lost, sustaining chemical stability.

Understanding electron transfer is essential as it helps elucidate how reactants turn into products, maintaining equilibrium and showing how energy is involved in reactions.