Solve with half equation reaction SO3 2- + MnO4 -=SO4 2- + Mn2+

To solve this question, you need to balance the redox reaction using half-equations. Here's the step-by-step process:

Step 1: Assign oxidation states.
In the given equation, the oxidation state of sulfur (S) changes from +6 in SO3 2- to +6 in SO4 2-. The oxidation state of manganese (Mn) changes from +7 in MnO4 - to +2 in Mn2+.

Step 2: Write the half-equation for the oxidation reaction.
Since sulfur is getting oxidized from +6 to +6, there is no change in its oxidation state. Therefore, there is no oxidation half-reaction in this equation.

Step 3: Write the half-equation for the reduction reaction.
The reduction half-reaction involves the change in oxidation state of manganese. The oxidation state of Mn changes from +7 to +2.

MnO4 - + 8H+ + 5e- -> Mn2+ + 4H2O

In this reduction half-reaction, the MnO4 - ion gains 5 electrons and combines with 8H+ ions to form Mn2+ and 4H2O.

Step 4: Balance the atoms and charges.
In the reduction half-reaction, there is an imbalance of oxygen atoms. To balance the oxygen atoms, add 4 H2O molecules on the right side.

MnO4 - + 8H+ + 5e- -> Mn2+ + 4H2O

This balances the oxygen atoms. However, there is still an imbalance in the hydrogen atoms. To balance the hydrogen atoms, add 8 H+ ions on the left side.

MnO4 - + 8H+ + 5e- -> Mn2+ + 4H2O

Now, the hydrogen atoms are balanced.

Next, balance the charge by adding 5 electrons (e-) on the left side.

MnO4 - + 8H+ + 5e- -> Mn2+ + 4H2O

Now, both the atoms and the charges are balanced in the reduction half-reaction.

Step 5: Multiply the half-equations to balance the electrons.
Since there are 5 electrons in the reduction half-reaction, multiply the oxidation half-reaction by 5 to balance the electrons.

5(SO3 2-) -> 5(SO4 2-)

Now, we have the balanced oxidation half-reaction and the balanced reduction half-reaction.

Step 6: Combine the half-equations.
To combine the half-equations, multiply each half-reaction by the necessary coefficients so that the total number of electrons gained in the reduction equals the total number of electrons lost in the oxidation.

5(SO3 2-) + 2(MnO4 -) + 16H+ -> 5(SO4 2-) + 2(Mn2+) + 8H2O

This is the balanced redox reaction for the given equation, SO3 2- + MnO4 - -> SO4 2- + Mn2+.