Questions: Assign oxidation numbers to all elements in this reaction. What compound was oxidized, what compound was reduced, and balance the reaction. (15pts) Ru2 O3(s) + ... CO(g) → ... Ru(s) + ... CO2(g)

Solution Steps

First, we assign oxidation numbers to all elements in the reaction.

For \(\mathrm{Ru}_{2}\mathrm{O}_{3}\):

• Oxygen (O) typically has an oxidation number of -2.
• Let the oxidation number of Ruthenium (Ru) be \(x\).

The compound is neutral, so: \[ 2x + 3(-2) = 0 \implies 2x - 6 = 0 \implies x = +3 \] Thus, the oxidation number of Ru in \(\mathrm{Ru}_{2}\mathrm{O}_{3}\) is +3.

For \(\mathrm{CO}\):

• Carbon (C) typically has an oxidation number of +2.
• Oxygen (O) has an oxidation number of -2.

For \(\mathrm{Ru}\) (elemental form):

• The oxidation number of Ru in its elemental form is 0.

For \(\mathrm{CO}_{2}\):

• Oxygen (O) has an oxidation number of -2.
• Let the oxidation number of Carbon (C) be \(y\).

The compound is neutral, so: \[ y + 2(-2) = 0 \implies y - 4 = 0 \implies y = +4 \] Thus, the oxidation number of C in \(\mathrm{CO}_{2}\) is +4.

Next, we identify which compounds were oxidized and reduced by comparing the changes in oxidation numbers.

• Ru in \(\mathrm{Ru}_{2}\mathrm{O}_{3}\) changes from +3 to 0.
  • This indicates a reduction (gain of electrons).
• C in \(\mathrm{CO}\) changes from +2 to +4.
  • This indicates an oxidation (loss of electrons).

Thus:

• \(\mathrm{Ru}_{2}\mathrm{O}_{3}\) is reduced.
• \(\mathrm{CO}\) is oxidized.

Finally, we balance the reaction by ensuring the number of atoms and the charges are balanced on both sides.

The unbalanced reaction is: \[ \mathrm{Ru}_{2}\mathrm{O}_{3}(\mathrm{s}) + \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Ru}(\mathrm{s}) + \mathrm{CO}_{2}(\mathrm{g}) \]

Balancing the atoms:

1. Balance Ru atoms: \[ \mathrm{Ru}_{2}\mathrm{O}_{3} \rightarrow 2\mathrm{Ru} \]
2. Balance O atoms: \[ \mathrm{Ru}_{2}\mathrm{O}_{3} + 3\mathrm{CO} \rightarrow 2\mathrm{Ru} + 3\mathrm{CO}_{2} \]
3. Balance C atoms: \[ \mathrm{Ru}_{2}\mathrm{O}_{3} + 3\mathrm{CO} \rightarrow 2\mathrm{Ru} + 3\mathrm{CO}_{2} \]

The balanced reaction is: \[ \mathrm{Ru}_{2}\mathrm{O}_{3}(\mathrm{s}) + 3\mathrm{CO}(\mathrm{g}) \rightarrow 2\mathrm{Ru}(\mathrm{s}) + 3\mathrm{CO}_{2}(\mathrm{g}) \]

Final Answer