Balancing Redox Equations

Balancing Redox Equations

It is not always possible to balance redox equations using the simple “inspection” technique. The following unbalanced net ionic equation provides an example.

Au³⁺(aq) + I⁻(aq) ® Au(s) + I₂(s)

At first glance, it seems that this equation can be balanced by placing a 2 in front of the I⁻.

Au³⁺(aq) + 2I⁻(aq) ® Au(s) + I₂(s)

Note, however, that although the atoms are now balanced, the charge is not. The sum of the charges on the left is +1, and the sum of the charges on the right is zero, as if the products could somehow have one more electron than the reactants. To correctly balance this equation, it helps to look more closely at the oxidation and reduction that occur in the reaction. The iodine atoms are changing their oxidation number from −1 to 0, so each iodide ion must be losing one electron. The Au³⁺ is changing to Au, so each gold(III) cation must be gaining three electrons. The half-reactions are:

I⁻(aq)    ® ½I₂(s) + e⁻

Au³⁺(aq) + 3e⁻    ®    Au(s)

We know that in redox reactions, the number of electrons lost by the reducing agent must be equal to the number of electrons gained by the oxidizing agent; thus, for each Au³⁺ that gains three electrons, there must be three I⁻ ions that each lose one electron. If we place a 3 in front of the I⁻ and balance the iodine atoms with a 3/2 in front of the I₂, both the atoms and the charge will be balanced.

Au³⁺(aq) + 3I⁻(aq) ® Au(s) + 3/2I₂(s)

or     2Au³⁺(aq) + 6I⁻(aq) ® 2Au(s) + 3I₂(s)

Balancing Redox Equations Using the Oxidation Number Method

In most situations that call for balancing an equation, you are not told whether the reaction is redox or not. In these circumstances, you can use a procedure called the oxidation number method, which is outlined below.

Sample Study Sheet: Balancing Redox Equations Using the Oxidation Number Technique

Tip-off – If you are asked to balance an equation and if you are not told whether the reaction is a redox reaction or not, you can use the following procedure.
General Steps

Step 1:  Try to balance the atoms in the equation by inspection, that is, by the standard technique for balancing non-redox equations. (Many equations for redox reactions can be easily balanced by inspection.) If you successfully balance the atoms, go to Step 2. If you are unable to balance the atoms, go to Step 3.

Step 2:  Check to be sure that the net charge is the same on both sides of the equation. If it is, you can assume that the equation is correctly balanced. If the charge is not balanced, go to Step 3.

Step 3:  If you have trouble balancing the atoms and the charge by inspection, determine the oxidation numbers for the atoms in the formula, and use them to decide whether the reaction is a redox reaction. If it is not redox, return to Step 1 and try again. If it is redox, go to Step 4.

Step 4:  Determine the net increase in oxidation number for the element that is oxidized and the net decrease in oxidation number for the element that is reduced.

Step 5:  Determine a ratio of oxidized to reduced atoms that would yield a net increase in oxidation number equal to the net decrease in oxidation number (a ratio that makes the number of electrons lost equal to the number of electrons gained).

Step 6:  Add coefficients to the formulas so as to obtain the correct ratio of the atoms whose oxidation numbers are changing. (These coefficients are usually placed in front of the formulas on the reactant side of the arrow.)

Step 7:  Balance the rest of the equation by inspection.

EXAMPLE 1 – Balancing Redox Reactions Using the Oxidation Number Method

Balance the following redox equation using either the “inspection” technique or the “oxidation number” method. Be sure to check that the atoms and the charge are balanced.

      HNO₃(aq) + H₃AsO₃(aq)  ®  NO(g) + H₃AsO₄(aq) + H₂O(l)

Solution:

Step 1:  Try to balance the atoms by inspection.

The H and O atoms are difficult to balance in this equation. You might arrive at the correct balanced equation using a “trial and error” technique, but if you do not discover the correct coefficients fairly quickly, proceed to Step 3.

Step 3: Is the reaction redox?

The N atoms change from +5 to +2, so they are reduced. This information is enough to tell us that the reaction is redox. (The As atoms, which change from +3 to +5, are oxidized.)

Step 4: Determine the net increase in oxidation number for the element that is oxidized and the net decrease in oxidation number for the element that is reduced.

As +3 to +5 Net Change = +2

N +5 to +2 Net Change = −3

Step 5: Determine a ratio of oxidized to reduced atoms that would yield a net increase in oxidation number equal to the net decrease in oxidation number.

As atoms would yield a net increase in oxidation number of +6. (Six electrons would be lost by three arsenic atoms.) 2 N atoms would yield a net decrease of −6. (Two nitrogen atoms would gain six electrons.) Thus the ratio of As atoms to N atoms is 3:2.

Step 6: To get the ratio identified in Step 5, add coefficients to the formulas which contain the elements whose oxidation number is changing.

   2HNO₃(aq) + 3H₃AsO₃(aq) ®  NO(g) + H₃AsO₄(aq) + H₂O(l)

Step 7:  Balance the rest of the equation by inspection.

2HNO₃(aq) + 3H₃AsO₃(aq)
                                  ® 2NO(g) + 3H₃AsO₄(aq) + H₂O(l)
EXAMPLE 2 - Balancing Redox Reactions Using the Oxidation Number Method:

Balance the following redox equation using either the “inspection” technique or the “oxidation number” method. Be sure to check that the atoms and the charge are balanced.

      Cu(s) + HNO₃(aq)  ®  Cu(NO₃)₂(aq) + NO(g) + H₂O(l)

Solution:

The nitrogen atoms and the oxygen atoms are difficult to balance by inspection, so we will go to Step 3. The copper atoms are changing their oxidation number from 0 to +2, and some of the nitrogen atoms are changing from +5 to +2. These changes indicate that this reaction is a redox reaction. We next determine the changes in oxidation number for the atoms oxidized and reduced.

Cu 0 to +2      Net Change = +2

Some N +5 to +2     Net Change = −3

We need three Cu atoms (net change of +6) for every 2 nitrogen atoms that change (net change of −6). Although the numbers for the ratio determined in Step 5 are usually put in front of reactant formulas, this equation is somewhat different. Because some of the nitrogen atoms are changing and some are not, we need to be careful to put the 2 in front of a formula in which all of the nitrogen atoms are changing or have changed. We therefore place the 2 in front of the NO(g) on the product side. The 3 for the copper atoms can be placed in front of the Cu(s).

3Cu(s) + HNO₃(aq)  ®  Cu(NO₃)₂(aq) + 2NO(g) + H₂O(l)

We balance the rest of the atoms using the technique described in Chapter 4, being careful to keep the ratio of Cu to NO 3:2.

3Cu(s) + 8HNO₃(aq) ® 3Cu(NO₃)₂(aq) + 2NO(g) + 4H₂O(l)

EXAMPLE Balancing Redox Reactions Using the Oxidation Number Method Balance the following redox equation using either the “inspection” technique or the “oxidation number” method. Be sure to check that the atoms and the charge are balanced.

NO₂(g) + H₂(g)   ®   NH₃(g) + H₂O(l)

Solution:

The atoms in this equation can be balanced by inspection. (You might first place a 2 in front of the H₂O to balance the O’s, then 7/2 in front of the H₂ to balance the H’s, and then multiply all the coefficients by 2 to get rid of the fraction.)

   2NO₂(g) + 7H₂(g)  ®  2NH₃(g) + 4H₂O(l)

We therefore proceed to Step 2. For the reaction between NO₂ and H₂, the net charge on both sides of the equation in Step 1 is zero. Because the charge and the atoms are balanced, the equation is correctly balanced.

Balancing Redox Equations for Reactions in Acidic Conditions Using the Half-reaction Method

Redox reactions are commonly run in acidic solution, in which case the reaction equations often include H₂O(l) and H⁺(aq). This page will show you how to write balanced equations for such reactions even when you do not know whether the H₂O(l) and H⁺(aq) are reactants or products. For example, you may know that dichromate ions, Cr₂O₇²⁻, react with nitrous acid molecules, HNO₂, in acidic conditions to form chromium ions, Cr³⁺, and nitrate ions, NO₃⁻. Because the reaction requires acidic conditions, you assume that H₂O(l) and H⁺(aq) participate in some way, but you do not know whether they are reactants or products, and you do not know the coefficients for the reactants and products. An unbalanced equation for this reaction might be written

      Cr₂O₇²⁻(aq) + HNO₂(aq)   ®  Cr³⁺(aq) + NO₃⁻(aq)   (acidic)

In order to balance equations of this type, we need a special technique called the half-reaction method or the ion-electron method.

Sample Study Sheet: Balancing Redox Equations Run in Acidic Conditions Using the Half-reaction Technique

Tip-off – If you are asked to balance a redox equation and told that it takes place in an acidic solution, you can use the following procedure.
General Steps

Step 1:   Write the skeletons of the oxidation and reduction half-reactions. (The skeleton reactions contain the formulas of the compounds oxidized and reduced, but the atoms and electrons have not yet been balanced.) See Example.

Step 2:    Balance all elements other than H and O.

Step 3:    Balance the oxygen atoms by adding H₂O molecules where needed.

Step 4:    Balance the hydrogen atoms by adding H⁺ ions where needed.

Step 5:    Balance the charge by adding electrons, e^-.

Step 6:    If the number of electrons lost in the oxidation half-reaction is not equal to the number of electrons gained in the reduction half-reaction, multiply one or both of the half- reactions by a number that will make the number of electrons gained equal to the number of electrons lost.

Step 7:    Add the 2 half-reactions as if they were mathematical equations. The electrons will always cancel. If the same formulas are found on opposite sides of the half-reactions, you can cancel them. If the same formulas are found on the same side of both half-reactions, combine them.

Step 8:    Check to make sure that the atoms and the charges balance.

EXAMPLE – Balancing Redox Equations for Reactions Run in Acidic Conditions: Balance the following redox equation using the “half-reaction” method.

    Cr₂O₇²⁻(aq) + HNO₂(aq)  ® Cr³⁺(aq) + NO₃⁻(aq)   (acidic)

Solution:

Step 1:   Write the skeletons of the oxidation and reduction half-reactions.

You will usually be given formulas for two reactants and two products. In such cases, one of the reactant formulas is used in writing one half-reaction, and the other reactant formula is used in writing the other half-reaction. (In most cases, you do not need to know which reactant is oxidized and which is reduced.) The product formula in each half-reaction must include all of the elements in the reactant formula except hydrogen and oxygen. There are circumstances that make this step more complicated, but we will stick to simpler examples at this stage.

Cr₂O₇²⁻   ®  Cr³⁺

HNO₂   ®    NO₃⁻

Step 2:    Balance all elements other than H and O.

To balance the chromium atoms in our first half-reaction, we need a two in front of Cr³⁺.

Cr₂O₇²⁻  ®    2Cr³⁺

HNO₂   ®   NO₃⁻

Step 3:    Balance the oxygen atoms by adding H₂O molecules on the side of the arrow where O atoms are needed.

The first half-reaction needs seven oxygen atoms on the right, so we add seven H₂O molecules.

Cr₂O₇²⁻  ®   2Cr³⁺ + 7H₂O

The second half-reaction needs one more oxygen atom on the left, so we add one H₂O molecule.

HNO₂+ H₂O   ®    NO₃⁻

Step 4:    Balance the hydrogen atoms by adding H⁺ ions on the side of the arrow where H atoms are needed.

The first half-reaction needs 14 hydrogen atoms on the left to balance the 14 hydrogen atoms in the 7 H₂O molecules, so we add 14 H⁺ ions to the left.

    Cr₂O₇²⁻ + 14H⁺   ®   2Cr³⁺ + 7H₂O

The second half-reaction needs three hydrogen atoms on the right to balance the three hydrogen atoms on the left, so we add 3 H⁺ ions to the right.

       HNO₂+ H₂O   ®   NO₃⁻ + 3H⁺

Step 5:    Balance the charge by adding electrons, e-.

The electrons go on the side of the equation with the highest charge (most positive or least negative). We add enough electrons make the charge on that side of the equation equal to the charge on the other side of the equation.

The sum of the charges on the left side of the chromium half-reaction is +12 (-2 for the Cr₂O₇²⁻ plus +14 for the 14 H⁺). The sum of the charges on the right side of the chromium half-reaction is +6 (for the 2 Cr³⁺). If we add six electrons to the left side, the sum of the charges on each side of the equation becomes +6.

6e⁻ + Cr₂O₇²⁻ + 14H⁺ ® 2Cr³⁺ + 7H₂O

The sum of the charges on the left side of the nitrogen half‑reaction is zero. The sum of the charges on the right side of the nitrogen half-reaction is +2 (−1 for the nitrate plus +3 for the 3 H⁺). If we add two electrons to the right side, the sum of the charges on each side of the equation becomes zero.

HNO₂+ H₂O   ®   NO₃⁻ + 3H⁺ + 2e⁻

(Although it is not necessary, you can check that you have added the correct number of electrons by looking to see whether the net change in oxidation number for each half-reaction is equal to the number of electrons gained or lost. Because the two Cr atoms in Cr₂O₇²⁻ are changing from +6 to +3, the net change in oxidation number is 2(−3) or −6. This would require six electrons, so we have added the correct number of electrons to the first half-reaction. The N atom in HNO₂ changes from +3 to +5, so the net change is +2. Two electrons would be lost in this change, so we have added the correct number of electrons to the second half-reaction.)

Step 6:    If the number of electrons lost in the oxidation half-reaction is not equal to the number of electrons gained in the reduction half-reaction, multiply one or both of the half- reactions by a number that will make the number of electrons gained equal to the number lost.

For the chromium half-reaction to gain six electrons, the nitrogen half-reaction must lose six electrons. Thus we multiply the coefficients in the nitrogen half-reaction by 3.

6e⁻ + Cr₂O₇²⁻ + 14H⁺ ® 2Cr³⁺ + 7H₂O

3(HNO₂+ H₂O   ®   NO₃⁻ + 3H⁺ + 2e⁻)

or

6e⁻ + Cr₂O₇²⁻ + 14H⁺ ® 2Cr³⁺ + 7H₂O

3HNO₂+ 3H₂O   ®   3NO₃⁻ + 9H⁺ + 6e⁻

Step 7:    Add the 2 half-reactions as if they were mathematical equations.

The 3 H₂O in the second half-reaction cancel three of the 7 H₂O in the first half-reaction to yield 4 H₂O on the right of the final equation.

The 9 H⁺ on the right of the second half-reaction cancel nine of the 14 H⁺ on the left of the first half-reaction leaving 5 H⁺ on the left of the final equation.

     Cr₂O₇²⁻ + 3HNO₂ + 5H⁺ ® 2Cr³⁺ + 3NO₃⁻ + 4H₂O

Step 8:    Check to make sure that the atoms and the charge balance.

The atoms in our example balance and the sum of the charges is +3 on each side, so our equation is correctly balanced.

Cr₂O₇²⁻(aq)    + 3HNO₂(aq)    + 5H⁺(aq)
              ® 2Cr³⁺(aq)    + 3NO₃⁻ (aq)    + 4H₂O(l)

Balancing Redox Equations for Reactions in Basic Conditions Using the Half-reaction Method

Redox reactions are also commonly run in basic solution, in which case, the reaction equations often include H₂O(l) and OH⁻(aq). You may know the formulas for the reactants and products for your reaction, but you may not know whether the H₂O(l) and OH⁻(aq) are reactants or products. For example, you may know that solid chromium(III) hydroxide, Cr(OH)₃, reacts with aqueous chlorate ions, ClO₃⁻, in basic conditions to form chromate ions, CrO₄²⁻, and chloride ions, Cl⁻. Because the reaction requires basic conditions, you assume that H₂O(l) and OH⁻(aq) participate in some way, but you do not know whether they are reactants or products, and you do not know the coefficients for the reactants and products. An unbalanced equation for this reaction might be written

Cr(OH)₃(s) + ClO₃⁻( aq) ® CrO₄²⁻(aq) + Cl⁻(aq) (basic)

The process for balancing a redox reaction run in basic solution is very similar to the steps for balancing redox equations for acidic solutions. We first balance the equation as if it were in acidic solution, and then we make corrections for the fact that it is really in basic solution.

Sample Study Sheet: Balancing Redox Equations Run in Basic Conditions Using the Half-reaction Technique

Tip-off – If you are asked to balance a redox equation and told that it takes place in a basic solution, you can use the following procedure.
General Steps

Steps 1-7: Begin by balancing the equation as if it were in acid solution. If you have H⁺ ions in your equation at the end of these steps, proceed to Step 8. Otherwise, skip to Step 11.

Step 8:   Add enough OH⁻ ions to each side to cancel the H⁺ ions. (Be sure to add the OH⁻ ions to both sides to keep the charge and atoms balanced.)

Step 9:  Combine the H⁺ ions and OH⁻ ions that are on the same side of the equation to form water.

Step 10:  Cancel or combine the H₂O molecules.

Step 11:  Check to make sure that the atoms and the charge balance. If they do balance, you are done. If they do not balance, re-check your work in Steps 1-10.

EXAMPLE – Balancing Redox Reactions Using the Half-Reaction Method:     Balance the following redox equation using the “half-reaction” method.

Cr(OH)₃(s) + ClO₃⁻(aq)  ®  CrO₄²⁻(aq) + Cl⁻(aq)   (basic)

Solution:

Step 1:

Cr(OH)₃   ® CrO₄²⁻

ClO₃⁻    ®    Cl⁻

Step 2: (Not necessary for this example)

Cr(OH)₃    ®   CrO₄²⁻

ClO₃⁻    ®    Cl⁻

Step 3:

Cr(OH)₃ + H₂O    ®   CrO₄²⁻

ClO₃⁻    ®    Cl⁻ + 3H₂O

Step 4:

Cr(OH)₃ + H₂O    ®   CrO₄²⁻ + 5H⁺

ClO₃⁻ + 6H⁺    ®    Cl⁻ + 3H₂O

Step 5:

Cr(OH)₃ + H₂O   ®  CrO₄²⁻ + 5H⁺ + 3e⁻

ClO₃⁻ + 6H⁺ + 6e⁻    ®    Cl⁻ + 3H₂O

Step 6:

2(Cr(OH)₃ + H₂O   ®   CrO₄²⁻ + 5H⁺ + 3e⁻ )

ClO₃⁻ + 6H⁺ + 6e⁻    ®    Cl⁻ + 3H₂O

or

2Cr(OH)₃ + 2H₂O   ®  2CrO₄²⁻ + 10H⁺ + 6e⁻

ClO₃⁻ + 6H⁺ + 6e⁻    ®    Cl⁻ + 3H₂O

Step 7:

2Cr(OH)₃(s) + ClO₃^-(aq)
®    2CrO₄²⁻(aq)  + Cl⁻(aq)  + H₂O(l) + 4H⁺(aq)

Step 8: Because there are 4 H⁺ on the right side of our equation above, we add 4 OH^- to each side of the equation.

2Cr(OH)₃ + ClO₃⁻ +   4OH⁻
   ®    2CrO₄²⁻ + Cl⁻ + H₂O + 4H⁺ + 4OH⁻

Step 9: Combine the 4 H⁺ ions and the 4 OH^- ions on the right of the equation to form 4 H₂O.

2Cr(OH)₃ + ClO₃⁻   +   4OH^- ®    2CrO₄²⁻ + Cl⁻ + H₂O + 4H₂O

Step 10:  Cancel or combine the H₂O molecules.

2Cr(OH)₃(s) + ClO₃⁻(aq) + 4OH⁻(aq)
                   ® 2CrO₄²⁻(aq) + Cl⁻(aq) + 5H₂O(l)

Step 11: The atoms in our equation balance, and the sum of the charges in each side is −5. Our equation is balanced correctly.