What if it is a complete molecular equation?

Fifteen Examples

Problems 1-10 | Only the examples and problems |

Problems 11-25 | Return to Redox menu |

Problems 26-60 |

If you don't have a net ionic equation to balance, that means you have what is usually called a molecular equation (or a complete molecular equation). These are harder to balance because the elements being oxidized and reduced are mixed in with substances that are are not being reduced or oxidized.

The solution is to, as much as possible, remove the "extraneous" substances: the ones that are neither oxidized or reduced. This gives you an unbalanced net ionic equation, which you proceed to balance. You then add back in the substances you had removed.

The problem? There is no explicit set of steps for how to do this. So, I will just let the technique evolve through some examples.

Comment: one thing that frustrates students learning the technique discussed in this tutorial is knowing how to decide what to eliminate and what not to. The easy answer to that is to advise you to eliminate everything but that which gets oxidized and reduced. For example, this equation:

CuCl_{2}+ KI --> CuI + I_{2}+ KCl

You must be able to see that the Cu is reduced from +2 to +1 and that the I goes from -1 to zero. That means that the chloride and the potassium ion are spectator ions and we arrive at this:

Cu^{2+}+ I¯ ---> Cu^{+}+ I_{2}

and eventually this:

2CuThe problem then is that, to a large degree, knowing what to do to take it back to the complete molecular equation is experience-based. You have to see (and do) a number of examples before the ideas begin to set in.^{2+}+ 2I¯ ---> 2Cu^{+}+ I_{2}

That is why it must seem to a student that the teacher just magically knows what to do and the proper order of steps to follow. This is the experience factor. In the ChemTeam's case, high school chemistry was taken in the late 60's, well before many of you were born. Much experience has transpired since then!

**Example #1:** NaIO_{3} + H_{2}SO_{3} ---> NaI + H_{2}SO_{4}

**Solution:**

1) The sodium ion never changes its oxidation state. It's a +1 in NaIO_{3} and a +1 in NaI. We can eliminate it on our way to the net ionic equation:

IO_{3}¯ + H_{2}SO_{3}---> I¯ + H_{2}SO_{4}

2) The hydrogen never changes its oxidation state. I will choose to remove it from the equation:

IO_{3}¯ + SO_{3}^{2}¯ ---> I¯ + SO_{4}^{2}¯I actually could have left the hydrogen ion and still got to the final answer. My personal opinion is to take them out.

3) I have run across teachers that will say to drop the oxygens from the sulfite and the sulfate. My preference is to keep them. The reason is that sulfate and sulfate ions exist as discrete species in solution, so I choose to keep them that way. That leaves the equation in step 2 as the net ionic.

4) Separate into half reactions:

IO_{3}¯ ---> I¯

SO_{3}^{2}¯ ---> SO_{4}^{2}¯

5) Balance:

6e¯ + 6H^{+}+ IO_{3}¯ ---> I¯ + 3H_{2}O

H_{2}O + SO_{3}^{2}¯ ---> SO_{4}^{2}¯ + 2H^{+}+ 2e¯

6) Equalize electrons:

6e¯ + 6H^{+}+ IO_{3}¯ ---> I¯ + 3H_{2}O

3H_{2}O + 3SO_{3}^{2}¯ ---> 3SO_{4}^{2}¯ + 6H^{+}+ 6e¯

7) Add:

IO_{3}¯ + 3SO_{3}^{2}¯ ---> I¯ + 3SO_{4}^{2}¯

8) Put spectator ions back in:

NaIO_{3}+ 3H_{2}SO_{3}---> NaI + 3H_{2}SO_{4}I added one Na

^{+}and six H^{+}back in.

**Example #2:** SeCl_{2} ---> H_{2}SeO_{3} + Se + HCl

**Solution:**

1) Here is what can be removed:

a) the SeCl_{2}can be changed to Se^{2+}

b) the H_{2}SeO_{3}can be changed to SeO_{3}^{2}¯

c) the HCl.

I dropped the chlorine and hydrogen because neither was oxidized or reduced. The prime skill needed in changing a molecular equation to a net ionic is recognizing which elements have had their oxidation states changed.

I will discuss the SeO_{3}^{2}¯ a bit more below. Also, the HCl tells me that this solution is to be balanced in acidic solution.

2) We now have this unbalanced net ionic equation:

Se^{2+}---> SeO_{3}^{2}¯ + Se

3) Here are the two half-reactions:

Se^{2+}---> SeO_{3}^{2}¯

Se^{2+}---> Se

4) Balance the two half-reactions (in acidic solution):

3H_{2}O + Se^{2+}---> SeO_{3}^{2}¯ + 6H^{+}+ 2e¯

Se^{2+}+ 2e¯ ---> Se

5) Add the two half-reactions and eliminate electrons:

3H_{2}O + 2Se^{2+}---> Se + SeO_{3}^{2}¯ + 6H^{+}

6) Restore items that were removed (shown in two steps). This gives the final answer:

a) 3H_{2}O + 2SeCl_{2}---> Se + SeO_{3}^{2}¯ + 4HCl + 2H^{+}

b) 3H_{2}O + 2SeCl_{2}---> Se + H_{2}SeO_{3}+ 4HCl

Why not drop the oxygen and get this half-reaction?

Se^{2+}---> Se^{4+}+ 2e¯

It does work because you get this balanced net ionic equation as an answer:

2Se^{2+}---> Se^{4+}+ Se

However, it seems to me to be a bit of a hassle to get back to the final answer. You might wish to try that on your own. Also, H_{2}SeO_{3} is a weak acid. You might want to keep the full formula in its half-reaction and then balance. You can also get to the correct answer that way.

**Example #3:** H_{2}SO_{3} + KMnO_{4} ---> MnSO_{4} + H_{2}SO_{4} + K_{2}SO_{4} + H_{2}O

**Solution:**

You must be able to see that it is the Mn that gets reduced (from +7 to +2) and that the S gets oxidized (from +4 to +6).

1) Here is what I will remove:

a) the H_{2}O (it will get back in via both half-reactions)

b) the H in H_{2}SO_{3}and H_{2}SO_{4}

c) the potassium ion

Here is the unbalanced net-ionic equation that results:

SO_{3}^{2}¯ + MnO_{4}¯ ---> MnSO_{4}

In order to make the half-reactions, I going to allow the MnSO_{4} to ionize. Why?

I know that the sulfate will play no role in balancing the reduction half-reaction, so I don't need it. How did I know? I know because the sulfur in the sulfate is being oxidized. I can't have an oxidation occuring in a reduction half-reaction. I will recombine the Mn^{2+} and the sulfate when I recover the balanced, molecular equation.

Also, suppose I keep the MnSO_{4} unionized. That means I would have to include the permanganate in the equation, to keep Mn present on both sides. That means I have to balance the net-ionic equation. Ah, no, I won't do that!

2) Here are the half-reactions that result:

SO_{3}^{2}¯ ---> SO_{4}^{2}¯

MnO_{4}¯ ---> Mn^{2+}

3) Here are the balanced half-reactions (note that it is acidic solution and that I have equalized the electrons):

5 [H_{2}O + SO_{3}^{2}¯ ---> SO_{4}^{2}¯ + 2H^{+}+ 2e¯]

2 [5e¯ + 8H^{+}+ MnO_{4}¯ ---> Mn^{2+}+ 4H_{2}O]

4) The final, balanced net ionic equation (extra water and hydrogen ion have been removed):

5SO_{3}^{2}¯ + 2MnO_{4}¯ + 6H^{+}---> 5SO_{4}^{2}¯ + 2Mn^{2+}+ 3H_{2}O

5) Make some MnSO_{4}:

5SO_{3}^{2}¯ + 2MnO_{4}¯ + 6H^{+}---> 3SO_{4}^{2}¯ + 2MnSO_{4}+ 3H_{2}O

6) Make some potassium permanganate:

5SO_{3}^{2}¯ + 2KMnO_{4}+ 6H^{+}---> 2SO_{4}^{2}¯ + 2MnSO_{4}+ 3H_{2}O + K_{2}SO_{4}Notice how I made some potassium sulfate at the same time.

7) Make some H_{2}SO_{3}:

2SO_{3}^{2}¯ + 2KMnO_{4}+ 3H_{2}SO_{3}---> 2SO_{4}^{2}¯ + 2MnSO_{4}+ 3H_{2}O + K_{2}SO_{4}

8) Now, I will add 4 hydrogens on each side:

2KMnO_{4}+ 5H_{2}SO_{3}---> 2H_{2}SO_{4}+ 2MnSO_{4}+ 3H_{2}O + K_{2}SO_{4}

**Example #4:** HCl + KMnO_{4} ---> H_{2}O + KCl + MnCl_{2} + Cl_{2}

**Solution:**

1) We can eliminate the following:

H^{+}from the HCl

H_{2}O

K^{+}

Cl¯, but only from the right-hand sideWhy only from the right-hand side? It is because the Cl¯ will be oxidized. I know this because there is Cl

_{2}on the right-hand side as well. This tells me the chlorine is going from a -1 oxidation state to zero. It is being oxidized. So, I need Cl¯ on the left-hand side, but not the right-hand side.

2) Here is the net-ionic equation:

Cl¯ + MnO_{4}¯ ---> Mn^{2+}+ Cl_{2}

3) From this, we get the half-reactions:

MnO_{4}¯ ---> Mn^{2+}

Cl¯ ---> Cl_{2}

4) The balanced half-reactions:

2 [5e¯ + 8H^{+}+ MnO_{4}¯ ---> Mn^{2+}+ 4H_{2}O]

5 [2Cl¯ ---> Cl_{2}+ 2e¯]Note the addition of the factors 2 and 5, which will balance the electrons.

5) The balanced equation, in net-ionic form:

16H^{+}+ 2MnO_{4}¯ + 10Cl¯ ---> 2Mn^{2+}+ 5Cl_{2}+ 8H_{2}O

6) Now, we must re-create the molecular equation, but in balanced form. First, make some HCl:

6H^{+}+ 2MnO_{4}¯ + 10HCl ---> 2Mn^{2+}+ 5Cl_{2}+ 8H_{2}O

7) Next, add potassium ion back in:

6H^{+}+ 2KMnO_{4}+ 10HCl ---> 2Mn^{2+}+ 2K^{+}+ 5Cl_{2}+ 8H_{2}O

8) To both sides, add in six chlorine ions:

2KMnO_{4}+ 16HCl ---> 2MnCl_{2}+ 2KCl + 5Cl_{2}+ 8H_{2}OWhere did they go? On the left-hand side, they hooked up with the hydrogen ion to make 6 HCl, giving a total of 16HCl. On the right-hand side, two went with the potassium ion to make KCl and the other 4 made 2MnCl

_{2}.I can add Cl¯ back in since we know, from the starting equation, that it was always present. Some of the Cl¯ reacted, to form Cl

_{2}, and some remained as spectator ions.This equation is your answer.

**Example #5:** KMnO_{4} + KCl + H_{2}SO_{4} ---> K_{2}SO_{4} + MnSO_{4} + Cl_{2} + H_{2}O

**Solution #1:**

1) Eliminate all spectator ions (this means anything that **isn't** reduced or oxidized). The list is:

K^{+}(from the KMnO_{4}and the KCl)

H_{2}SO_{4}

K_{2}SO_{4}

SO_{4}^{2}¯ (from the MnSO_{4})

H_{2}O

That leaves this:

MnO_{4}¯ + Cl¯ ---> Mn^{2+}+ Cl_{2}

Why did I keep those? It's because they are the exact items oxidized (the Cl) or reduced (the Mn).

2) Balance the net ionic reaction (in acidic solution because of the sulfuric acid):

MnO3) Add back in the spectator ions (which I will do in a step-wise fashion):_{4}¯ ---> Mn^{2+}

Cl¯ ---> Cl_{2}5e¯ + 8H

^{+}+ MnO_{4}¯ ---> Mn^{2+}+ 4H_{2}O

2Cl¯ ---> Cl_{2}+ 2e¯16H

^{+}+ 2MnO_{4}¯ + 10Cl¯ ---> 2Mn^{2+}+ 5Cl_{2}+ 8H_{2}O (this is the balanced, net ionic equation)

a) add back in 8 sulfates:

8H_{2}SO_{4}+ 2MnO_{4}¯ + 10Cl¯ ---> 2MnSO_{4}+ 5Cl_{2}+ 8H_{2}O + 6K_{2}SO_{4}b) This added 12 potassium ions to the right side, so add 12 K

^{+}to the left:8H_{2}SO_{4}+ 2KMnO_{4}+ 10KCl ---> 2MnSO_{4}+ 5Cl_{2}+ 8H_{2}O + 6K_{2}SO_{4}

The last equation is the balanced, molecular equation.

**Solution #2:**

1) Identify the atoms being oxidized and reduced:

Mn goes from +7 to +2; it is reduced

Cl goes from -1 to zero; it is oxidized

2) Write the two half-reactions, showing ONLY the items reduced/oxidized:

Mn^{7+}+ 5e¯ ---> Mn^{2+}

2Cl¯ ---> Cl_{2}+ 2e¯

3) Multiply the first reaction by 2 and the second by 5, and add them to get:

2Mn^{7+}+ 10Cl¯ ---> 2Mn^{2+}+ 5Cl_{2}

4) Since this a complete redox reaction and the number of electrons are equal on both sides, we can now use these coefficients in the molecular equation to balance it:

2KMnO5) Balancing the other atoms can now be done by 'trial and error' method:_{4}+ 10KCl + H_{2}SO_{4}---> K_{2}SO_{4}+ 2MnSO_{4}+ 5Cl_{2}+ H_{2}O

This is left to the reader.

**Example #6:** CH_{3}CH_{2}OH + K_{2}Cr_{2}O_{7} + H_{2}SO_{4} ---> HC_{2}H_{3}O_{2} + Cr_{2}(SO_{4})_{3} + K_{2}SO_{4} + H_{2}O

1) Write the net ionic equation:

CH_{3}CH_{2}OH + Cr_{2}O_{7}^{2}¯ ---> Cr^{3+}+ HC_{2}H_{3}O_{2}

2) Half-reactions and balance:

CH_{3}CH_{2}OH ---> HC_{2}H_{3}O_{2}

Cr_{2}O_{7}^{2}¯ ---> Cr^{3+}H

_{2}O + CH_{3}CH_{2}OH ---> HC_{2}H_{3}O_{2}+ 4H^{+}+ 4e¯

6e¯ + 14H^{+}+ Cr_{2}O_{7}^{2}¯ ---> 2Cr^{3+}+ 7H_{2}OTop half-reaction by 3, bottom by 2; then add and eliminate water and hydrogen ion.

16H

^{+}+ 3CH_{3}CH_{2}OH + 2Cr_{2}O_{7}^{2}¯ ---> 4Cr^{3+}+ 3HC_{2}H_{3}O_{2}+ 11H_{2}O

3) Add 4 K^{+} to the left, then the right. Add two sulfate to the right (thus making the potassium sulfate), then to the left:

12H^{+}+ 2H_{2}SO_{4}+ 3CH_{3}CH_{2}OH + 2K_{2}Cr_{2}O_{7}---> 4Cr^{3+}+ 3HC_{2}H_{3}O_{2}+ 11H_{2}O + 2K_{2}SO_{4}

4) Add six sulfates to the Cr(III) ion, then make the rest of the sulfuric acid. Result:

8H_{2}SO_{4}+ 3CH_{3}CH_{2}OH + 2K_{2}Cr_{2}O_{7}---> 2Cr_{2}(SO_{4})_{3}+ 3HC_{2}H_{3}O_{2}+ 11H_{2}O + 2K_{2}SO_{4}

**Example #7:** PbCrO_{4} + HCl + FeSO_{4} ---> PbCl_{2} + Cr_{2}(SO_{4})_{3} + FeCl_{3} + H_{2}O + Fe_{2}(SO_{4})_{3}

**Solution:**

1) Half-reactions:

CrO_{4}^{2}¯ ---> Cr^{3+}

Fe^{2+}---> Fe^{3+}

2) Balance in acidic solution:

3e¯ + 8H^{+}+ CrO_{4}^{2}¯ ---> Cr^{3+}+ 4H_{3}O

Fe^{2+}---> Fe^{3+}+ e¯

3) Equalize electrons:

3e¯ + 8H^{+}+ CrO_{4}^{2}¯ ---> Cr^{3+}+ 4H_{3}O

3Fe^{2+}---> 3Fe^{3+}+ 3e¯

4) Add:

8H^{+}+ CrO_{4}^{2}¯ + 3Fe^{2+}---> Cr^{3+}+ 3Fe^{3+}+ 4H_{3}O

5) Inspection of Cr_{2}(SO_{4})_{3} leads us to double the balanced equation before turning it into a molecular equation:

16H^{+}+ 2CrO_{4}^{2}¯ + 6Fe^{2+}---> 2Cr^{3+}+ 6Fe^{3+}+ 8H_{3}O

6) Restore the full formulas on the reactant side:

16HCl + 2PbCrO_{4}+ 6FeSO_{4}---> 2Cr^{3+}+ 6Fe^{3+}+ 8H_{3}O16 chloride ions, two Pb(II) ions and six sulfate ions were added.

7) Add sulfates to the product side:

16HCl + 2PbCrO_{4}+ 6FeSO_{4}---> Cr_{2}(SO_{4})_{3}+ 4Fe^{3+}+ Fe_{2}(SO_{4})_{3}+ 8H_{3}O

8) Add Pb(II) to the product side:

16HCl + 2PbCrO_{4}+ 6FeSO_{4}---> 2PbCl_{2}+ Cr_{2}(SO_{4})_{3}+ 4Fe^{3+}+ Fe_{2}(SO_{4})_{3}+ 8H_{3}ONote how four chorides were also added.

9) Add twelve more chlorides to finish:

16HCl + 2PbCrO_{4}+ 6FeSO_{4}---> 2PbCl_{2}+ Cr_{2}(SO_{4})_{3}+ 4FeCl_{3}+ Fe_{2}(SO_{4})_{3}+ 8H_{3}O

**Example #8:** C_{6}H_{12}O_{6} + KMnO_{4} + H_{2}SO_{4} ---> CO_{2} + K_{2}SO_{4} + MnSO_{4} + H_{2}O

**Solution:**

1) Half-reactions:

C_{6}H_{12}O_{6}---> CO_{2}

MnO_{4}¯ ---> Mn^{2+}

2) Balance:

6H_{2}O + C_{6}H_{12}O_{6}---> 6CO_{2}+ 24H^{+}+ 24e¯

5e¯ + 8H^{+}+ MnO_{4}¯ ---> Mn^{2+}+ 4H_{2}O

3) Equalize electrons:

30H_{2}O + 5C_{6}H_{12}O_{6}---> 30CO_{2}+ 120H^{+}+ 120e¯

120e¯ + 192H^{+}+ 24MnO_{4}¯ ---> 24Mn^{2+}+ 96H_{2}O

4) Add:

72H^{+}+ 5C_{6}H_{12}O_{6}+ 24MnO_{4}¯ ---> 30CO_{2}+ 24Mn^{2+}+ 66H_{2}O

5) Complete the reactant side only:

36H_{2}SO_{4}+ 5C_{6}H_{12}O_{6}+ 24KMnO_{4}---> 30CO_{2}+ 24Mn^{2+}+ 66H_{2}O36 sulfates and 24 potassium ions were added.

6) Add 24 sulfates to the product side:

36H_{2}SO_{4}+ 5C_{6}H_{12}O_{6}+ 24KMnO_{4}---> 30CO_{2}+ 24MnSO_{4}+ 66H_{2}OThis leaves 24 potassium ions and 12 sulfate ions left over. Imagine that!

7) Finish:

36H_{2}SO_{4}+ 5C_{6}H_{12}O_{6}+ 24KMnO_{4}---> 30CO_{2}+ 24MnSO_{4}+ 12K_{2}SO_{4}+ 66H_{2}O

**Example #9:** KMnO_{4} + KOH + FeSO_{4} ---> K_{2}MnO_{4} + Fe(OH)_{3} + K_{2}SO_{4}

**Solution:**

1) Net ionic:

MnO_{4}¯ + OH¯ + Fe^{2+}---> MnO_{4}^{2}¯ + Fe(OH)_{3}

2) Half reactions:

e¯ + MnO_{4}¯ ---> MnO_{4}^{2}¯

3OH¯ + Fe^{2+}---> Fe(OH)_{3}+ e¯

3) Add (since electrons are already equalized):

MnO_{4}¯ + 3OH¯ + Fe^{2+}---> MnO_{4}^{2}¯ + Fe(OH)_{3}

4) Add four potassium ion and one sulfate to the left:

KMnO_{4}+ 3KOH + FeSO_{4}---> MnO_{4}^{2}¯ + Fe(OH)_{3}

5) Add the same to the right side:

KMnO_{4}+ 3KOH + FeSO_{4}---> K_{2}MnO_{4}+ Fe(OH)_{3}+ K_{2}SO_{4}

6) I wrote Fe(OH)_{3} because I know, from experience, that it is an insoluble precipitate. Let us suppose you did not know that and wrote this:

MnO_{4}¯ + OH¯ + Fe^{2+}---> MnO_{4}^{2}¯ + Fe^{3+}Could this be balanced correctly? The answer, of course is yes.

7) Here are the revised half-reactions:

e¯ + MnO_{4}¯ ---> MnO_{4}^{2}¯

Fe^{2+}---> Fe^{3+}+ e¯

8) Add (since electrons are already equalized):

MnO_{4}¯ + Fe^{2+}---> MnO_{4}^{2}¯ + Fe^{3+}

9) Four potassiums and one sulfate, just as above. The only other thing is to add three hydroxides to each side.

**Example #10:** K_{2}Cr_{2}O_{7} + KI + H_{2}SO_{4} ---> Cr_{2}(SO_{4})_{3} + K_{2}SO_{4} + I_{2} + H_{2}O

**Solution:**

1) Identify the net ionic:

Cr_{2}O_{7}^{2}¯ + I¯ ---> Cr^{3+}+ I_{2}

2) Balanced half-reactions:

6e¯ + 14H^{+}+ Cr_{2}O_{7}^{2}¯ ---> 2Cr^{3+}+ 7H_{2}O

2I¯ ---> I_{2}+ 2e¯

3) Equalize electrons and add:

14H^{+}+ Cr_{2}O_{7}^{2}¯ + 6I¯ ---> 2Cr^{3+}+ 3I_{2}+ 7H_{2}O

4) Add seven sulfates and eight potassium ions to the left-hand side:

7H_{2}SO_{4}+ K_{2}Cr_{2}O_{7}+ 6KI ---> 2Cr^{3+}+ 3I_{2}+ 7H_{2}O

5) Add three sulfates to the right-hand side:

7H_{2}SO_{4}+ K_{2}Cr_{2}O_{7}+ 6KI ---> Cr_{2}(SO_{4})_{3}+ 3I_{2}+ 7H_{2}O

6) There are eight potassium ions and four sulfates. Whatever shall we do with them?

7H_{2}SO_{4}+ K_{2}Cr_{2}O_{7}+ 6KI ---> Cr_{2}(SO_{4})_{3}+ 3I_{2}+ 7H_{2}O + 4K_{2}SO_{4}

**Example #11:** C_{6}H_{4}(CH_{3})_{2} + K_{2}Cr_{2}O_{7} + H_{2}SO_{4} ---> C_{6}H_{4}(COOH)_{2} + Cr_{2}(SO_{4})_{3} + H_{2}O

**Solution:**

Comment: this is the reaction to change xylene [C_{6}H_{4}(CH_{3})_{2}] to terephthalic acid [C_{6}H_{4}(COOH)_{2}]. I won't bother with the fact that each compound name actually has three different isomers since that does not affect the redox balancing.

1) Write half-reactions in net-ionic form:

C_{6}H_{4}(CH_{3})_{2}---> C_{6}H_{4}(COOH)_{2}

Cr_{2}O_{7}^{2}¯ ---> Cr_{2}^{6+}

2) Balance:

4H_{2}O + C_{6}H_{4}(CH_{3})_{2}---> C_{6}H_{4}(COOH)_{2}+ 12H^{+}+ 12e¯

6e¯ + 14H^{+}+ Cr_{2}O_{7}^{2}¯ ---> Cr_{2}^{6+}+ 7H_{2}OComment: when I balanced this equation for posting on the website, I initially put a 2 in front of the H

_{2}O in the first half-reaction. I finally saw the mistake but, even so, even veterans can still make mistakes (and miss them for a few moments).

3) Equalize electrons:

4H_{2}O + C_{6}H_{4}(CH_{3})_{2}---> C_{6}H_{4}(COOH)_{2}+ 12H^{+}+ 12e¯

12e¯ + 28H^{+}+ 2Cr_{2}O_{7}^{2}¯ ---> 2Cr_{2}^{6+}+ 14H_{2}O

4) Add:

16H^{+}+ C_{6}H_{4}(CH_{3})_{2}+ 2Cr_{2}O_{7}^{2}¯ ---> C_{6}H_{4}(COOH)_{2}+ 2Cr_{2}^{6+}+ 10H_{2}O

5) Add eight sulfates and 4 potassium ion to the left-hand side:

8H_{2}SO_{4}+ C_{6}H_{4}(CH_{3})_{2}+ 2K_{2}Cr_{2}O_{7}---> C_{6}H_{4}(COOH)_{2}+ 2Cr_{2}^{6+}+ 10H_{2}O

6) Only six sulfates are used to restore chromium(III) sulfate:

8H_{2}SO_{4}+ C_{6}H_{4}(CH_{3})_{2}+ 2K_{2}Cr_{2}O_{7}---> C_{6}H_{4}(COOH)_{2}+ 2Cr_{2}(SO_{4})_{3}+ 10H_{2}O

7) Add two potassium sulfate to the right-hand side to finish the balancing:

8H_{2}SO_{4}+ C_{6}H_{4}(CH_{3})_{2}+ 2K_{2}Cr_{2}O_{7}---> C_{6}H_{4}(COOH)_{2}+ 2Cr_{2}(SO_{4})_{3}+ 2K_{2}SO_{4}+ 10H_{2}O

8) You could write the first half-reaction like this:

(CH_{3})_{2}^{2}¯ ---> (COOH)_{2}^{2}¯and add the C

_{6}H_{4}back in at the end. You are welcome to try that on your own.

**Example #12:** H_{2}SeO_{3} + HBr ---> Se + Br_{2} + H_{2}O

**Solution:**

1) I'm going to not write a net ionic equation. Here are the half-reactions:

H_{2}SeO_{3}---> Se + H_{2}O

HBr ---> Br_{2}

2) Do the balancing!

4e¯ + 4H^{+}+ H_{2}SeO_{3}---> Se + 3H_{2}O

2HBr ---> Br_{2}+ 2H^{+}+ 2e¯

3) Equalize electrons:

4e¯ + 4H^{+}+ H_{2}SeO_{3}---> Se + 3H_{2}O

4HBr ---> 2Br_{2}+ 4H^{+}+ 4e¯

4) Add:

H_{2}SeO_{3}+ 4HBr ---> Se + 2Br_{2}+ 3H_{2}O

**Example #13:** KI + CoSO_{4} + KIO_{3} + H_{2}O ---> Co(OH)_{2} + K_{2}SO_{4} + I_{2}

**Solution:**

1) Examine the equation for what gets oxidized and reduced and we find this:

I¯ ---> I_{2}

IO_{3}¯ ---> I_{2}There are a number of rections in which cobalt is either oxidized or reduced. Not in this example.

2) Balance in acidic solution:

2I¯ ---> I_{2}+ 2e¯

10e¯ + 12H^{+}+ 2IO_{3}¯ ---> I_{2}+ 6H_{2}O

3) Equalize electrons:

10I¯ ---> 5I_{2}+ 10e¯

10e¯ + 12H^{+}+ 2IO_{3}¯ ---> I_{2}+ 6H_{2}O

4) Add:

12H^{+}+ 10I¯ + 2IO_{3}¯ ---> 6I_{2}+ 6H_{2}O

5) Divide through by 2, then convert to basic:

6H^{+}+ 5I¯ + IO_{3}¯ ---> 3I_{2}+ 3H_{2}O6H

_{2}O + 5I¯ + IO_{3}¯ ---> 3I_{2}+ 3H_{2}O + 6OH¯3H

_{2}O + 5I¯ + IO_{3}¯ ---> 3I_{2}+ 6OH¯

6) Add three cobalt(II) ion back into the equation:

3H_{2}O + 3Co^{2+}+ 5I¯ + IO_{3}¯ ---> 3I_{2}+ 3Co(OH)_{2}I added three because I knew I had to use six hydroxides.

7) Add six potassium ion and three sulfate to the left-hand side:

3H_{2}O + 3CoSO_{4}+ 5KI + KIO_{3}---> 3I_{2}+ 3Co(OH)_{2}

7) Add six potassium ion and three sulfate to the right-hand side:

3H_{2}O + 3CoSO_{4}+ 5KI + KIO_{3}---> 3I_{2}+ 3Co(OH)_{2}+ 3K_{2}SO_{4}Done!

**Example #14:** NaCl + H_{2}SO_{4} + MnO_{2} ---> Na_{2}SO_{4} + MnCl_{2} + H_{2}O + Cl_{2}

**Solution:**

1) What to remove?

NaCl: sodium ion is a classic spectator ion and it will be removed.

H_{2}SO_{4}; notice how only sulfate is present on the right-hand side. It will be removed.

MnO_{2}: this stays since Mn is reduced in the reaction.

Cl_{2}: it stays since the chloride from the left-hand side is oxidized.Here is what remains: Cl¯ + H

^{+}+ MnO_{2}---> Mn^{2+}+ H_{2}O + Cl_{2}That's the net ionic.

Notice I kept the MnO

_{2}intact.

2) Now for the half-reactions:

Cl¯ ---> Cl_{2}

MnO_{2}---> Mn^{2+}

3) Balance them:

2Cl¯ ---> Cl_{2}+ 2e¯

2e¯ + 4H^{+}+ MnO_{2}---> Mn^{2+}+ 2H_{2}O

4) Since the electrons are already balanced, we add:

2Cl¯ + 4H^{+}+ MnO_{2}---> Cl_{2}+ Mn^{2+}+ 2H_{2}O

5) We add in two more chloride to make MnCl_{2}:

4Cl¯ + 4H^{+}+ MnO_{2}---> Cl_{2}+ MnCl_{2}+ 2H_{2}O

6) We add in 4 sodium ion to make NaCl:

4NaCl + 4H^{+}+ MnO_{2}---> 4Na^{+}+ Cl_{2}+ MnCl_{2}+ 2H_{2}O

7) Add in four sulfate ions:

4NaCl + 2H_{2}SO_{4}+ MnO_{2}---> 2Na_{2}SO_{4}+ Cl_{2}+ MnCl_{2}+ 2H_{2}O

**Example #15:** Fe(s) + NO_{3}¯(aq) ---> Fe^{3+}(aq) + NO_{2}(g)

**Solution:**

Notice that that reaction is already in net ionic form. I propose to balance it and then put it into molecular form.

1) Balance by half-reactions in acidic solution:

Fe(s) ---> Fe^{3+}(aq) + 3e¯

e¯ + 2H^{+}+ NO_{3}¯(aq) ---> NO_{2}(g) + H_{2}OFe(s) ---> Fe

^{3+}(aq) + 3e¯

3e¯ + 6H^{+}+ 3NO_{3}¯(aq) ---> 3NO_{2}(g) + 3H_{2}O6H

^{+}+ Fe(s) + 3NO_{3}¯(aq) ---> Fe^{3+}(aq) + 3NO_{2}(g) + 3H_{2}OI knew to balance in acidic solution because of the nitrate. I needed positive ions coupled with the nitrate to give me a compound. Hydroxide did not fit my needs. Also, note that the iron(III) ion is in solution. In the presence of hydroxide, Fe(OH)

_{3}would precipitate.

2) To make a molecular equation, join up some hydrogen ion with some nitrate ion:

3H^{+}+ Fe(s) + 3HNO_{3}(aq) ---> Fe^{3+}(aq) + 3NO_{2}(g) + 3H_{2}O

3) We need more nitrate ion to combine with the rest of the hydrogen ion AND the ferric ion:

Fe(s) + 6HNO_{3}(aq) ---> Fe(NO_{3})_{3}(aq) + 3NO_{2}(g) + 3H_{2}O

It's now a fully-balanced molecular equation. Note that iron(III) nitrate is soluble, making the three nitrate ions added in this last step as the only spectator ions in the reaction.

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