Balance half equation for SO2 = SO4^2- , show step by step working out?

The balanced half equation for the conversion of SO2 to SO4^2- is as follows:

SO2 + 2H2O -> SO4^2- + 4H+ + 2e-

To balance this half equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

Step 1: Balance the sulfur atoms by adding 1 SO4^2- ion on the right side:

SO2 + 2H2O -> SO4^2- + 4H+ + 2e-

Step 2: Balance the oxygen atoms by adding 4 H2O molecules on the left side:

SO2 + 2H2O -> SO4^2- + 4H+ + 2e-

Step 3: Balance the hydrogen atoms by adding 8 H+ ions on the left side:

SO2 + 2H2O + 8H+ -> SO4^2- + 4H+ + 2e-

Step 4: Balance the charge by adding 2 electrons on the left side:

SO2 + 2H2O + 8H+ + 2e- -> SO4^2- + 4H+ + 2e-

The balanced half equation for the conversion of SO2 to SO4^2- is:

SO2 + 2H2O + 8H+ + 2e- -> SO4^2- + 4H+ + 2e-

Step 1: Balance the sulfur atoms.

SO2 → SO4^2-

We have one sulfur atom on the left side and one sulfur atom on the right side. The equation is already balanced in terms of sulfur atoms.

Step 2: Balance the oxygen atoms.

SO2 → SO4^2-

We have two oxygen atoms on the left side and four oxygen atoms on the right side. To balance the oxygen atoms, we add two water molecules to the left side:

SO2 + 2H2O → SO4^2-

Now we have four oxygen atoms on both sides.

Step 3: Balance the hydrogen atoms.

SO2 + 2H2O → SO4^2-

We have four hydrogen atoms on the left side and zero hydrogen atoms on the right side. To balance the hydrogen atoms, we add four hydrogen ions to the right side:

SO2 + 2H2O → SO4^2- + 4H+

Now we have four hydrogen atoms on both sides.

Step 4: Check the overall charge.

The overall charge on the left side is 0, and the overall charge on the right side is -2. To balance the charges, we add two electrons to the left side:

SO2 + 2H2O → SO4^2- + 4H+ + 2e-

Now the overall charge on both sides is -2.

The balanced half equation is:

SO2 + 2H2O → SO4^2- + 4H+ + 2e-