Half equations in electrolysis

During electrolysis, ions react at electrodes by gaining or losing electrons. A half equation represents the change at one electrode. It shows the particles before and after the change, including the electrons transferred.

At the cathode, positive ions gain electrons.
At the anode, negative ions lose electrons.

A half equation must balance both the number of each type of atom and the total charge on its two sides.

Half equation at the cathode

For example, a magnesium ion gains two electrons to form a magnesium atom:

\ce{Mg^{2+} + 2e- -> Mg}

The electrons are on the left because the ion gains them. There is one magnesium atom on each side. The total charge on the left is $$$+2 - 2 = 0$$$ , matching the zero charge on the right.

Half equation at the anode

Chloride ions lose electrons to form chlorine molecules. Each chlorine molecule contains two chlorine atoms, so two chloride ions are needed:

\ce{2Cl- -> Cl2 + 2e-}

The electrons are on the right because the ions lose them. There are two chlorine atoms on each side. The total charge is $$$-2$$$ on the left and $$$-2$$$ on the right.

Balancing a half equation

To write or complete a half equation, use the formulas of the particles involved, then check atoms and charge:

Balance the atoms by placing numbers in front of the particle formulas where needed. Do not change the formulas themselves.
Balance the charge by adding electrons to the appropriate side. Each electron has a charge of $$$-1$$$ .
Check that the number of each type of atom and the total charge are the same on both sides.

For the chloride half equation, balancing chlorine atoms first gives two chloride ions on the left and one chlorine molecule on the right. The left side then has a charge of $$$-2$$$ , while the chlorine molecule has no charge. Adding two electrons to the right makes the charges equal.

Electrolysis

Electrolysis uses electrical energy to break down an ionic substance. It works when the substance contains ions that are free to move, such as when it is molten or dissolved in water. A substance that conducts electricity through moving ions and is decomposed by the current is called an electrolyte.

Two electrodes are placed in the electrolyte and connected to an electrical supply. The supply makes one electrode negative and the other positive. When current flows, ions move through the electrolyte towards the electrode with the opposite charge:

Positive ions move towards the negative electrode, called the cathode. There they gain electrons and are discharged.
Negative ions move towards the positive electrode, called the anode. There they lose electrons and are discharged.

Discharge means that ions gain or lose electrons at an electrode, producing particles that can form elements. For example, positive metal ions can gain electrons at the cathode to form metal atoms.

The electrical supply drives these changes: ions carry charge through the electrolyte, while electrons are supplied to or removed from the electrodes. The result is chemical decomposition of the electrolyte.

Electrolytes

An ionic compound conducts electricity only when its charged particles, or ions, can move. Mobile ions carry charge from place to place through the substance.

In a solid ionic compound, the ions are held in fixed positions in a lattice. Although the ions are charged, they cannot move through the solid, so it does not conduct electricity.

When the compound is melted or dissolved in water, its ions are no longer fixed in the lattice. They can move through the liquid or solution and carry charge, so the substance conducts electricity.

A liquid or solution that contains ions free to move and can therefore conduct electricity is called an electrolyte.