Edvantage Science AP Chemistry 2 WorkbookPLUS Chapter 7.2 by Edvantage Science

7.2

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7.2 Balancing Oxidation-Reduction Equations Warm Up Examine the following equation:

Zn(s) +

Cu+(aq) →

Zn2+(aq) +

Cu(s)

1. Which species acts as a reducing agent and consequently is oxidized? __________________________ 2. Which species acts as an oxidizing agent and consequently is reduced? _________________________ 3. How many electrons are lost by each atom of the reducing agent as it is oxidized? ________________ 4. A Cu+ ion accepts only one electron to become a neutral Cu atom. How many Cu+ ions does it take to accept two electrons? _____________________ 5. Add coefficients to the equation so that the number of electrons donated by the reducing agent equals the number of electrons received by the oxidizing agent. 6. Does the net charge of the reactants now equal the net charge of the products? _________________

The Conservation of Mass and Charge

Oxidation Is Loss of electrons Reduction Is Gain of electrons

For the past several years, you’ve been applying Antoine Lavoisier’s law of conservation of mass to every chemical reaction you’ve encountered. This law states that the mass of the products equals the mass of the reactants in any chemical reaction. This is because no atoms are gained or lost during a chemical reaction. In junior science, you learned to place coefficients in front of various chemical species to make sure that the total number of atoms of each type on the reactant side would equal the total number of atoms of the same type on the product side of the equation. In previous years, you learned to write net ionic equations for a variety of reaction types. In these equations, it was necessary to balance the charge as well as the number of each type of each atom. In oxidation-reduction reactions, charge is balanced by making certain that the number of electrons lost equals the number gained. This is sometimes done by simple inspection. An example is the reduction of copper(I) ion by zinc metal in the Warm Up question above. Examination reveals that two Cu+ ions are reduced for every Zn atom oxidized, so the balanced equation is: Zn(s) + 2 Cu+(aq) → Zn2+(aq) + 2 Cu(s) As luck would have it, there are many oxidation-reduction reactions that are considerably more complex than this simple example. For these more complicated cases, we require a system to help us determine the number of electrons lost and gained so we can balance not only the number of atoms of each type, but also the number of electrons transferred.

Figure 7.2.1 Remember the

OIL RIG.

Half-Reactions

It is possible to separate out the reduction and oxidation portions of a redox reaction and to represent them as two separate half-reactions. For example, the sample reaction from the Warm Up may be broken into the following half-reactions: Zn → Zn2+ + 2e− (oxidation) and Cu+ + e− → Cu (reduction)

Chapter 7 Oxidation-Reduction and Its Applications 441

Notice that the half-reactions include the number of electrons lost, in the case of oxidation, or gained, in the case of reduction. A half-reaction is an equation representing either an oxidation or a reduction, including the number of electrons lost or gained.

Balancing questions usually specify whether the reaction is occurring under acidic or basic conditions. Sometimes this will be readily apparent from the chemical reactants. If this isn’t obvious or isn’t stated, the conditions are likely acidic. It is possible, however, that it is occurring under neutral conditions. This means that when you balance it, you find that any H+ or OH− ions will cancel out and not appear in the final reaction statement. Balancing a half-reaction requires the application of the following steps:

Balancing HalfReactions

OTHER atoms — Balance atoms other than H and O. All atoms except oxygen and hydrogen should be balanced first. This is not always necessary, so people tend to forget to balance the “other” atoms. Do not forget this step and watch the way coefficients affect charges. OXYGEN atoms — Balance oxygen atoms by adding H2O. Redox reactions occur in aqueous solution. Consequently, you may add as many water molecules as required to balance the number of oxygen atoms. HYDROGEN atoms — Balance hydrogen atoms by adding H+ ions. As most reactions occur in an acidic environment, you may add as many hydrogen ions, H+, as are needed. CHARGE — Balance the charge by adding electrons. Always add the electrons to the more positive (or less negative) side. Add the number of electrons needed to ensure that the charge is the same on both sides of the equation. This is a good time to check that the total number of atoms of each type is in fact the same on both sides, so the equation is indeed balanced in terms of mass and charge.

442 Chapter 7 Oxidation-Reduction and Its Applications

Sample Problem 7.2.1(a) — Balancing Half-Reactions in Acidic Conditions Balance the following half-reaction occurring under acidic conditions: ClO4− → Cl2 Does this represent an oxidation or a reduction?

What to Think About

How to Do It

1. Balance atoms other than O and H. This requires a coefficient 2 in front of the perchlorate ion, ClO4−. Because the “other” atoms are often already balanced, students frequently do not need to balance them and as a result they tend to forget to apply the first step. Always check the “other” atoms first. 2. Balance oxygen atoms by adding H2O molecules. As there are now 8 oxygen atoms on the reactant side, add 8 water molecules to the products.

2 ClO4− → Cl2

2 ClO4− → Cl2 + 8 H2O

3. Balance hydrogen atoms by adding H+ions. As there are now 16 hydrogen atoms on the product side, add 16 H+ ions on the reactant side.

16 H+ + 2 ClO4− → Cl2 + 8 H2O

4. Balance the charge by adding the e− to the more positive side. As the total charge on the reactant side is +14 and there is no charge on the product side, add 14 electrons on the reactant side.

14 e− + 16 H+ + 2 ClO4− → Cl2 + 8 H2O An oxidation number check is helpful to perform on half-reactions. Note that the number of electrons gained matches the oxidation number change. +7 0 ✓ 2 ClO4− → Cl2 [Gain of 7e− (×2) = 14e− gained.] This is a reduction.

Electrons are gained (they are “reactants”).

While all redox reactions occur in aqueous solution, some occur in basic, rather than acidic conditions. When balancing a reaction that is occurring under basic conditions, chemists simply add a step to our sequence to convert from an acidic to a basic environment. When a redox reaction is to be balanced in base, the hydrogen ions must be neutralized. This is accomplished by adding hydroxide ions, OH−, to cancel any H+ ions. If hydroxide ions are added to one side of the equation, the same number must be added to the other side. Thus, complete the first four steps and then… BASE — Add OH− ions to both sides to neutralize all H+ Ions. The number of OH− ions added to neutralize the H+ must be balanced by adding the same number of OH− ions to the other side of the reaction. Free H+ and OH− ions on the same side of the equation should be combined to form the corresponding number of H2O molecules. This step may result in water molecules showing up on both sides of the equation. Be sure to cancel so that H2O appears on one side of the equation only. It is critically important to pay close attention to all charges during the balancing process. Dropping the charge from an ion or inadvertently changing a charge will lead to a wrong answer every time!

Chapter 7 Oxidation-Reduction and Its Applications 443

Sample Problem 7.2.1(b) — Balancing Half-Reactions in Basic Conditions Balance the following half-reaction: I2 → IO4− in base. Does this represent an oxidation or a reduction?

What to Think About

How to Do It

1. Balance atoms other than O and H. A coefficient 2 is needed in front of IO4−.

I2 → 2 IO4−

2. Balance oxygen atoms by adding H2O molecules. As there are 8 oxygen atoms on the product side, add 8 H2O molecules as reactants.

8 H2O + I2 → 2 IO4−

3. Balance hydrogen atoms by adding H+ions to the product side. As there are now 16 hydrogen atoms on the reactant side, add 16 H+ to the product side. 4. Add the e− to the more positive side. As the total charge on the product side is +14 and there is no charge on the reactant side, add 14 electrons on the product side. 5. The objective for balancing a reaction in base is to neutralize the H+ions. As there are 16 H+ ions on the product side, add 16 OH− ions to both sides. Each combination of H+ with OH− forms an H2O molecule. Water molecules present on both sides of the equation algebraically cancel. NEVER leave H2O molecules on both sides.

Electrons are produced-hence they are lost.

8 H2O + I2 → 2 IO4− + 16 H+

8 H2O + I2 → 2 IO4− + 16 H+ + 14e−

8 H2O + I2 → 2 IO4− + 16 H+ + 14e− 16 OH− 16 OH− 16 OH− + I2 → 2 IO4− + 8 H2O + 14 e− Oxidation number check: 0 +7 ✓ I2 →2 IO4− [Loss of 7e− (×2) = 14e− lost] This process is an oxidation.

Practice Problems 7.2.1 — Balancing Half-Reactions in Acidic and Basic Conditions Balance the following half-reactions. Assume the reactions occur in acid unless specified otherwise. In each case, indicate whether the half-reaction is an oxidation or a reduction.

→

Sm3+

NO3−

IO4−

S2O32–

→

SO42–

BrO3−

→

Br2 (basic)

→ →

NH4+ IO3− (basic)

444 Chapter 7 Oxidation-Reduction and Its Applications

Redox Reactions

The equation for an oxidation-reduction reaction is a combination of two of the half-reactions we have just finished balancing (an oxidation and a reduction). When a reducing agent is oxidized, the electrons are not actually lost in the usual sense of the word. In fact, chemists know exactly where those electrons go. They are, of course, gained by an oxidizing agent that will become reduced. The goal of balancing a redox reaction is to ensure the number of electrons lost by a reducing agent (as it becomes oxidized) exactly equals the number of electrons gained by the oxidizing agent (as it becomes reduced). Oxidation-reduction (redox) reactions are characterized by a balanced loss and gain of electrons.

There are two common methods for balancing redox reactions. We will begin by focusing on the method that involves balancing two half-reactions. This method is appropriately called the halfreaction method. It consists of the following steps: SEPARATE the redox equation into its half-reactions. In most cases, it is easy to identify the two half-reactions by noting species in the reactants that contain atoms in common with species in the products. BALANCE each half-reaction. Give yourself plenty of room and don’t forget to compare the change in oxidation numbers with the electron gain or loss. MULTIPLY each half-reaction by an integer to balance the transfer of electrons. Take the time and space to rewrite each reaction and take care as you transcribe the formulas and coefficients to avoid errors. ADD the half-reactions together. Algebraically cancel those species that appear on both sides of the equation. Again: be careful — not careless! No common species should remain on both sides of the equation. If the equation is basic, ADD OH− to both sides to neutralize the H+ ions only after recombining the equations. Balancing redox equations can seem tedious at times, as there are many steps involved. Errors made early will lead to a series of mistakes but even one late error will result in the wrong answer. Taking care in transcribing steps and checking each process as you go will lead to consistent success.

Chapter 7 Oxidation-Reduction and Its Applications 445

Sample Problem 7.2.2 — Balancing Redox Reactions: Acidic Balance the following redox reaction: IO3− + HSO3−

→

SO42– + I2

What to Think About

How to Do It

IO3− → I2 HSO3− → SO42–

1. Separate the redox equation Into its two halfreactions. Look for common atoms to assist you. IO3− and I2 both contain iodine. HSO3− and SO42– both contain sulfur.

10e− + 12 H+ + 2 IO3− → I2 + 6 H2O H2O + HSO3− → SO42– + 3 H+ + 2e−

2. Balance each half-reaction. Note: There must be an electron gain on one side and loss on the other. If not, you have made an error!

Don’t forget to do a quick check of oxidation numbers at this point. +5

2 IO3− → I2 HSO3− → SO42– (–5 × 2 = 10e− gain) (+2 = 2e− lost) ✓

3. Balance the electron loss and gain. Look for the lowest common multiple. Multiply the second halfreaction by 5 and rewrite both equations.

1(10e– + 12 H+ + 2 IO3− → I2 + 6 H2O) 5(H2O + HSO3− → SO42– + 3 H+ + 2e−) 4. Add the balanced half-reactions together, cancelling where appropriate.

10e– + 12 H+ + 2 IO3− → I2 + 6 H2O 5 H2O + 5 HSO3− → 5 SO42– + 15 H+ + 10e− 5 HSO3− + 2 IO3− → 5 SO42– + 3 H+ + I2 + H2O

Once you have balanced a full redox reaction, it is worth taking the time to do a full balancing check. You may have performed similar checks when balancing standard equations at some point in your chemistry past. A table is a helpful tool: Species

Reactants

Products

Hydrogen Sulfur

Oxygen

Iodine

Charge

–7

✔ The charge is perhaps the most important part of the check. Be sure to take care with your counting and as mentioned earlier, don’t drop or change ion charges during the transcribing. More than one student has done a wonderful job of correctly balancing an equation that wasn’t assigned to them because they changed one of the species.

446 Chapter 7 Oxidation-Reduction and Its Applications

Practice Problems 7.2.2 — Balancing Redox Reactions in Acid Balance each of the following equations in acidic solution. Perform a check for each. 1. H3AsO4 + Zn

→

2. C2H5OH + NO3−

AsH3 + Zn2+

→

CH3COOH + N2O4

Disproportionation Reactions

Some redox reactions can be rather difficult to break into half-reactions. One of the most troublesome almost appears, at first glance, to be a half-reaction. Take the reaction, Sn2+

→

Sn4+ + Sn

The tin(II) ion is both oxidized (to form the tin(IV) ion) and reduced (to form tin metal). A reaction such as this is called a disproportionation reaction. A disproportionation reaction is a redox reaction in which the same species is both oxidized and reduced. Occasionally, multiple reactants form only one product. A chemical change of this sort is called a comproportionation reaction. This may be the reverse of a disproportionation in which one species is reduced to form a product and a different species is oxidized to give the same product.

Chapter 7 Oxidation-Reduction and Its Applications 447

Sample Problem 7.2.3 — Balancing Disproportionation Reactions: Basic Balance the following in base: IAsO4→ AsO43– + I2 + IO3−

What to Think About 1. Separate the half-reactions. Both halfreactions must contain the same reactant, so this is a disproportionation reaction. Arsenic must be a product in both half-reactions. Hence the remaining two iodine-containing species must be split between the two halfreactions.

2. Balance each half-reaction and check the oxidation numbers with the electron loss and gain.

How to Do It

IAsO4 → AsO43– + I2 IAsO4→ AsO43– + IO3− 6e− + 2 IAsO4→ 2 AsO43– + I2 3 H2O + IAsO4→ AsO43– + IO3− + 6 H+ + 2e− +3

2 IAsO4→ AsO43– + I2 (–3 x 2 = gain 6e−) +3

IAsO4→

3. Multiply the second half-reaction by 3. 4. Sum the two halves with appropriate cancelling.

+ IO3− (+2 = loss of 2e−) ✓

6e− + 2 IAsO4→ 2 AsO43– + I2 9 H2O + 3 IAsO4→ 3 AsO43–+ 3 IO3− + 18 H+ + 6e− 9 H2O + 5 IAsO4 → 5 AsO43– + 3 IO3− + I2 + 18 H+ (+ 18 OH−) (+ 18 OH−) 18 OH− + 5 IAsO4 → 5 AsO43– + 3 IO3− + I2 + 9 H2O

5. To balance in base, add 18 OH− ions to each side; then cancel 9 H2O’s.

AsO43–

Species Hydrogen Arsenic Oxygen Iodine Charge

A final check is always a good idea.

448 Chapter 7 Oxidation-Reduction and Its Applications

Products 18 5 38 5 –18

Reactants 18 5 38 5 –18

✔

Practice Problems 7.2.3 — Balancing Disproportionation Reactions Balance the following reactions in a basic environment. Perform a check for each. 1. HXeO4−

→

−

2. BrO3− + Br

XeO64– + Xe + O2

→

Br2 (a comproportionation)

3. CH3COO−

→

CH4 + CO2

OOHe — Other atoms, Oxygen (with H2O), Hydrogen (with H+), electrons

Chapter 7 Oxidation-Reduction and Its Applications 449