Questions: Write a balanced half-reaction for the reduction of bismuth oxide ion (BiO3-) to bismuth ion (Bi3+) in basic aqueous solution. Be sure to add physical state symbols where appropriate.

Write a balanced half-reaction for the reduction of bismuth oxide ion (BiO3-) to bismuth ion (Bi3+) in basic aqueous solution. Be sure to add physical state symbols where appropriate.

Transcript text: Write a balanced half-reaction for the reduction of bismuth oxide ion $\left(\mathrm{BiO}_{3}^{-}\right)$to bismuth ion $\left(\mathrm{Bi}^{3+}\right)$ in basic aqueous solution. Be sure to add physical state symbols where appropriate.

Solution

Solution Steps

Step 1: Identify the Oxidation States

First, identify the oxidation states of bismuth in the reactant and product. In $\mathrm{BiO}_3^-$, bismuth is in the +5 oxidation state, and in $\mathrm{Bi}^{3+}$, it is in the +3 oxidation state.

Step 2: Write the Unbalanced Half-Reaction

Write the unbalanced half-reaction for the reduction process: \[ \mathrm{BiO}_3^- (aq) \rightarrow \mathrm{Bi}^{3+} (aq) \]

Step 3: Balance the Atoms Other Than Oxygen and Hydrogen

In this case, bismuth is already balanced with one atom on each side.

Step 4: Balance the Oxygen Atoms

Add water molecules to balance the oxygen atoms. There are three oxygen atoms on the left, so add three water molecules to the right: \[ \mathrm{BiO}_3^- (aq) \rightarrow \mathrm{Bi}^{3+} (aq) + 3\mathrm{H}_2\mathrm{O} (l) \]

Step 5: Balance the Hydrogen Atoms

Add hydroxide ions ($\mathrm{OH}^-$) to balance the hydrogen atoms. There are six hydrogen atoms on the right, so add six hydroxide ions to the left: \[ \mathrm{BiO}_3^- (aq) + 6\mathrm{OH}^- (aq) \rightarrow \mathrm{Bi}^{3+} (aq) + 3\mathrm{H}_2\mathrm{O} (l) \]

Step 6: Balance the Charge

Balance the charge by adding electrons. The left side has a charge of $-7$ (one $\mathrm{BiO}_3^-$ and six $\mathrm{OH}^-$), and the right side has a charge of $+3$. Add 10 electrons to the left side to balance the charge: \[ \mathrm{BiO}_3^- (aq) + 6\mathrm{OH}^- (aq) + 10e^- \rightarrow \mathrm{Bi}^{3+} (aq) + 3\mathrm{H}_2\mathrm{O} (l) \]

Final Answer

The balanced half-reaction for the reduction of bismuth oxide ion to bismuth ion in basic aqueous solution is: \[ \boxed{\mathrm{BiO}_3^- (aq) + 6\mathrm{OH}^- (aq) + 10e^- \rightarrow \mathrm{Bi}^{3+} (aq) + 3\mathrm{H}_2\mathrm{O} (l)} \]

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