Question

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

Short answer

The balanced half-reaction is \(6e^- + 14\text{H}^+ + \text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\).

Step-by-step solution

Identify the Reactants and Products

The half-reaction involves converting dichromate ions, \(\text{Cr}_2\text{O}_7^{2-}\), into chromium ions, \(\text{Cr}^{3+}\). Identify these as the reactants and products in your half-reaction equation.

Write the Unbalanced Half-reaction

Start with the basic unbalanced equation: \[\text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}^{3+}\] Remember, chromium is in the +6 oxidation state in the dichromate ion and needs to be reduced to the +3 state in the chromium ion.

Balance the Chromium Atoms

Since there are two chromium atoms in the dichromate ion, ensure that the same number of chromium ions appears in the products:\[\text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+}\]

Balance the Oxygen Atoms

There are seven oxygen atoms in \(\text{Cr}_2\text{O}_7^{2-}\). Add seven water molecules to the other side to balance the oxygens:\[\text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Balance the Hydrogen Atoms

Balance hydrogen molecules by adding 14 hydrogen ions (\(\text{H}^+\)) to the left side, because each water molecule has two hydrogen atoms:\[14\text{H}^+ + \text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Balance the Charges

The total charge on the left side is \(+12\) (14 from \(\text{H}^+\) minus 2 from \(\text{Cr}_2\text{O}_7^{2-}\)), while the right side is \(+6\) from the two \(\text{Cr}^{3+}\) ions. Add 6 electrons (\(6e^-\)) to the left side to balance the charges:\[6e^- + 14\text{H}^+ + \text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\]

Review the Balanced Equation

Verify the half-reaction equation has the same number of each type of atom on both sides and that the charge is balanced. The balanced equation:\[6e^- + 14\text{H}^+ + \text{Cr}_2\text{O}_7^{2-} \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}\] is correct.

Key concepts

Half-reaction Balancing

Balancing a chemical equation may seem tricky at first, but with a methodical approach, it becomes much simpler. In the context of Chemical Oxygen Demand (COD) titration, the goal is to create a balanced half-reaction. This involves dichromate ions transforming into chromium ions. The half-reaction focuses on the piece of the overall reaction where reduction or oxidation happens.

Here’s how you do it:

• Identify your initial reactants and final products. In this exercise, dichromate (\(\text{Cr}_2\text{O}_7^{2-}\)) turns into chromium (\(\text{Cr}^{3+}\)).
• Start with writing an unbalanced equation. At this stage, align only the key reactants and products in equation form like: \(\text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}^{3+}\).
• Balance each type of atom present in your equation. This includes chromium, oxygen, and hydrogen atoms.
• Finally, balance the charge by adding electrons to the appropriate side of the half-reaction.

This systematic progression helps ensure all elements and charges are accounted for in the equation.

Dichromate Ion Reduction

The reduction of the dichromate ion is a central part of the COD titration process. This refers to the gain of electrons by the dichromate ion in a chemical reaction.

Let's break it down:

• Dichromate ions (\(\text{Cr}_2\text{O}_7^{2-}\)) are reduced to chromium ions (\(\text{Cr}^{3+}\)).
• The reduction occurs when these ions undergo a change in their oxidation state from +6 in dichromate to +3 in chromium ion.
• This involves adding electrons to the reaction, as electrons are essential for the reduction process.

During Reduction, oxygen from the dichromate is generally not involved directly but is catered to by balancing through water molecules and the addition of hydrogen ions as needed.

Oxidation States

Oxidation states, or oxidation numbers, are critical in understanding both oxidation and reduction reactions. They help track how many electrons an atom gains or loses. Here in our dichromate half-reaction:

• The oxidation state of chromium in \(\text{Cr}_2\text{O}_7^{2-}\) starts at +6.
• As the reaction progresses, chromium is transformed to \(\text{Cr}^{3+}\), reducing its oxidation state to +3.
• This change represents a gain of electrons, which is the hallmark of a reduction process.

Using oxidation states, we can clearly identify and follow the electron transfer process throughout the reaction, making it easier to balance chemical equations.

Electron Transfer

Electron transfer is at the heart of redox reactions, including the reaction in COD titrations. It helps in changing the oxidation states, dictating whether a species is reduced or oxidized. Here's how it shapes the reduction of the dichromate ion:

• In the transition from dichromate to chromium ions, 6 electrons are added to balance the equation.
• This transfer is essential as it reduces chromium from the +6 to the +3 state, indicating the reduction aspect of the reaction.
• Electrons are added to the left side of the equation to offset any charge differences.

Tracking electron transfer is crucial for understanding the reaction’s mechanism and for correctly balancing chemical equations during analysis.

Charge Balance

Balancing charge is the final step in creating a balanced chemical equation. This ensures that both sides of an equation have equal charge, reflecting a correct and thorough balance. Here's how it works for this half-reaction:

• Initially, the left side might have a positive charge surplus due to added ions or electrons, such as 14 positive charges from hydrogen ions and offset by the -2 charge of the dichromate ion.
• The right side comprises mainly of chromium ions with a total charge of +6.
• Adding 6 electrons (each with a charge of -1) to the left side balances the charges, ensuring both sides equal out.

After ensuring balanced atoms, balancing charge is an indispensable check to confirm that the chemical reaction adheres to the conservation of charge principle.