How do I write a balanced half ionic equation of aluminium oxide at the cathode?

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http://www.gcsescience.com/ex12.htm

To write a balanced half-ionic equation for the reduction of aluminium oxide (Al2O3) at the cathode, you need to consider the species involved in the reaction.

Step 1: Identify the species at the cathode
The cathode is the electrode where reduction takes place. In the case of aluminium oxide, the cathode reaction involves the reduction of aluminium ions (Al3+) to aluminium metal (Al).

Step 2: Determine the balanced chemical equation
To write the half-ionic equation, you should first write the balanced chemical equation for the overall reaction. The reaction between aluminium oxide and carbon in an electrolytic cell is typically represented as follows:
Al2O3 + 3C → 2Al + 3CO

Step 3: Break down the balanced chemical equation into half-equations
Next, you need to split the overall balanced chemical equation into half-equations, one for the oxidation (in this case, carbon) and one for the reduction (aluminium ions to aluminium metal).
The reduction half-reaction for the reduction of Al3+ to Al is as follows:
Al3+ + 3e- → Al

Step 4: Balance the half-ionic equation
In the half-ionic equation, the number of electrons (e-) on both sides should be equal to maintain charge balance. In this case, it already appears to be balanced.

So, the balanced half-ionic equation for the reduction of Al3+ to Al at the cathode in the electrolysis of aluminium oxide would be:
Al3+ + 3e- → Al

Remember, the key steps to follow are:
1. Identify the species at the cathode.
2. Determine the balanced chemical equation.
3. Split the balanced chemical equation into half-equations.
4. Balance the half-ionic equation, if necessary.

To write a balanced half ionic equation for the reduction of aluminum oxide (Al2O3) at the cathode, we need to consider the ions involved in the reaction and make sure that the equation is balanced in terms of both atoms and charges.

Step 1: Write the balanced chemical equation for the formation of aluminum oxide.
2 Al + 3/2 O2 -> Al2O3

Step 2: Split the equation into two half-reactions, one for the oxidation (anode) and one for the reduction (cathode). In this case, we're interested in the reduction half-reaction.

Reduction half-reaction:
Al3+ + 3e- -> Al

Step 3: Balance the charges and the atoms on both sides of the half-reaction.

To balance the charges:
The Al ion on the left side has a charge of 3+, while the Al atom on the right side has no charge. Therefore, we will add 3 electrons (e-) on the right side to balance the charge.

Al3+ + 3e- -> Al

To balance the atoms:
There is one aluminum atom on both sides, so no further adjustment is needed.

Step 4: Verify that the equation is balanced by checking the charges on both sides of the half-reaction.

On the left side:
The Al3+ ion has a charge of 3+.

On the right side:
The Al atom has no charge.

The charges are balanced, so the half-ionic equation is now balanced.

Balanced half-ionic equation for the reduction of aluminum oxide at the cathode:
Al3+ + 3e- -> Al