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Wize University Chemistry Textbook > Electrochemistry

Balancing Redox Reactions

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Balancing Redox Reactions: Half-Reaction Method

The "half-reaction method" of balancing redox reactions is the most commonly used method :)

Balance the following redox reaction in basic conditions and assign oxidation numbers to all species.

Ag(s)+ Zn2+(aq) → Ag2O(aq) +Zn(s){\small \text{Ag}\left(\text{s}\right)+\ \text{Zn}^{2+}\left(\text{aq}\right)\ \rightarrow\ \text{Ag}_2\text{O}\left(\text{aq}\right)\ +\text{Zn}\left(\text{s}\right)}


Wize Tip
Balancing redox equations:

1. Check the oxidation numbers of each species by inspection (change in oxidation # means this is a redox reaction!)

2. Write the reduction and oxidation half-reactions.

3. Balance each half-reaction: start with atoms that are neither O nor H, balance oxygens with H2O, hydrogens with H+, and remaining charges with e−.

4. Multiply the reduction and oxidation half-reactions as needed so that each reaction exchanges the same number of e−.

5. Add the oxidation and reduction half reactions together and simplify.

6. Additional step in basic solution only: there can't be any H+ ions, so neutralize the H+ by adding the same # of OH- to each side.
Watch Out!
Always solve in acidic conditions first!
Then, if the question is asking for basic conditions do step #6!

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1. Check the oxidation numbers of each species by inspection (change in oxidation # means this is a redox reaction!)

Here we are told it's a redox reaction already, but we can still check oxidation #s to see what is oxidized and what is reduced:

  • Ag goes from having an oxidation # of
    0
    to
    +1
    . Therefore Ag is
    oxidized
    .
  • Zn goes from having an oxidation # of
    2+
    to
    0
    . Therefore Zn is
    reduced
    .


2. Write the reduction and oxidation half-reactions.

Oxidation Half Reaction:
Ag(s) -> Ag2O (aq)

Reduction Half Reaction:
Zn2+(aq) -> Zn(s)

3. Balance each half-reaction: start with atoms that are neither O nor H, balance oxygens with H2O, hydrogens with H+, and remaining charges with e−.

a) Balance everything that is not O and H:
ox:
2Ag(s) -> Ag2O(aq)

red:
Zn2+(aq) -> Zn(s)
(stays the same)
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ox: 2Ag(s) -> Ag2O(aq)

red: Zn2+(aq) -> Zn(s)


b) Balance O with H2O:
ox:
2Ag(s) + H2O -> Ag2O(aq)

red:
Zn2+(aq) -> Zn(s)
(stays the same since there are no Os to balance!)

c) Balance H with H+
ox:
2Ag(s) + H2O -> Ag2O(aq) + 2H+(aq)

red:
Zn2+(aq) -> Zn(s)
(stays the same since there are no Hs to balance!)

d) Balance charges with electrons!
ox:
2Ag(s) + H2O -> Ag2O(aq) + 2H+(aq) + 2e-

red:
Zn2+(aq) + 2e- -> Zn(s)


PAGE BREAK
ox:
2Ag(s) + H2O -> Ag2O(aq) + 2H+(aq) + 2e-

red:
Zn2+(aq) + 2e- -> Zn(s)

4. Multiply the reduction and oxidation half-reactions as needed so that each reaction exchanges the same number of e−.

Here, both half reactions have the same amount of electrons (2) so we don't need to multiply anything further since they already have the same # of electrons!

5. Add the oxidation and reduction half reactions together and simplify.



2Ag(s)+ H2O+Zn2+(aq)+2e−→Zn(s)+Ag2O(aq) +2H+(aq)+2e−{\small 2\text{Ag}\left(\text{s}\right)+\ \text{H}_2\text{O} + \text{Zn}^{2+} (aq)+\sout{2e^-}\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +2\text{H}^+(\text{aq})+\sout{2e^-}}

Answer for acidic conditions:

2Ag(s)+ H2O+Zn2+(aq)→Zn(s)+Ag2O(aq) +2H+(aq){\small 2\text{Ag}\left(\text{s}\right)+\ \text{H}_2\text{O} + \text{Zn}^{2+} (aq)\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +2\text{H}^+(\text{aq})}
If we selected this as our answer we'd be incorrect because the question is asking us to balance the redox reaction in basic conditions!

PAGE BREAK
2Ag(s)+ H2O+Zn2+(aq)→Zn(s)+Ag2O(aq) +2H+(aq){\small 2\text{Ag}\left(\text{s}\right)+\ \text{H}_2\text{O} + \text{Zn}^{2+} (aq)\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +2\text{H}^+(\text{aq})}

6. Additional step in basic solution only: there can't be any H+ ions, so neutralize the H+ by adding the same # of OH- to each side.



2OH−(aq)+2Ag(s)+ H2O+Zn2+(aq)→Zn(s)+Ag2O(aq) +2H+(aq)+2OH−(aq){\small 2\text{OH}^-\text{(aq)}+ 2\text{Ag}\left(\text{s}\right)+\ \text{H}_2\text{O} + \text{Zn}^{2+} (aq)\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +\fbox{2\text{H}$^+(\text{aq})+2\text{OH}^-\text{(aq)}$}}

2OH−(aq)+2Ag(s)+ H2O+Zn2+(aq)→Zn(s)+Ag2O(aq) +2H2O{\small 2\text{OH}^-\text{(aq)}+ 2\text{Ag}\left(\text{s}\right)+\ \sout{\text{H}_2\text{O} }+ \text{Zn}^{2+} (aq)\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +\sout{2}\text{H}_2\text{O}}

2OH−(aq)+2Ag(s)+ Zn2+(aq)→Zn(s)+Ag2O(aq) +H2O{\small 2\text{OH}^-\text{(aq)}+ 2\text{Ag}\left(\text{s}\right)+\ \text{Zn}^{2+} (aq)\rightarrow\text{Zn(s)}+\text{Ag}_2\text{O}\left(\text{aq}\right)\ +\text{H}_2\text{O}}
This last equation is the correct answer! We have fully balanced the redox reaction in BASIC conditions!


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Practice: Balancing Redox Reactions

Balance the following redox reaction in an acidic solution.

HCOOH + MnO4- --> CO2 + Mn2+
Extra Practice
Electrochemistry: Redox
Balance the following redox reaction in basic solution:
Cr(OH)3 + Br2 → CrO42- + Br- in basic solution
Electrochemistry: Redox
Balance the following redox reaction in an acidic solution.
HCOOH + MnO4- --> CO2 + Mn2+
Aqua regia is a mixture of concentrated HNO3 and HCl developed to dissolve gold. The process is a redox reaction as follows:
Au(s)+NO3(aq)−+Cl(aq)−→AuCl4(aq)−+NO2(g)Au_{(s)}+NO^-_{3(aq)}+Cl^-_{(aq)} \to AuCl^-_{4(aq)}+NO_{2(g)}
Balance this reaction under acidic conditions and identifying the oxidized and reduced species.
Thermodynamics: Work Done During Acid Digestion of Magnesium
A 10.0 g piece of Mg(s) is deposited in a container with a vast excess of HCl(aq). A reaction takes place forming hydrogen gas and Magnesium Chloride.
a) Write a balanced chemical reaction for the transformation
b) Calculate the work done by the system as a consequence of the reaction, if Pex = 1.1 atm and T = 298.15 K. You may assume ideal behaviour.
Balance the following redox reaction in basic solution:
Cr(OH)3 + Br2 --> CrO42- + Br- in basic solution
Balance the following redox reaction in an acidic solution.
HCOOH + MnO4- --> CO2 + Mn2+
Electrochemistry: Balancing Redox Reactions (Basic)
Balance the following redox reaction under basic condition:
Sn(OH)3− (aq) + Bi(OH)3 (s) → Sn(OH)62− (aq) + Bi (s)
Balance the following redox reaction:
HBrO (aq) → Br− (aq) + O2 (g) under acidic condition
Balancing Redox Reactions (Basic)
Balance the following redox reactions under basic condition:
Cl2 (aq) → ClO3− (aq) + Cl− (aq)
Sn(OH)3− (aq) + Bi(OH)3 (s) → Sn(OH)62− (aq) + Bi (s)
Balancing Redox Reactions (Acidic)
Balance the following redox reactions under acidic condition:
H2S (aq) + H2O2 (aq) → S (s) (acidic solution)
P4 (s) + NO3− (aq) → H3PO4 (aq) + NO (g) (acidic solution)
Balance the following redox reaction in acidic conditions. What is the coefficient on H+?
Cr2O9 2−(aq)+HNO2(aq)→Cr3+(aq)+NO3 −(aq){\small \text{Cr}_2\text{O}_9\ ^{2-}\text{(aq)} + \text{HNO}_2\text{(aq)} \rightarrow \text{Cr}^{3+}\text{(aq)} + \text{NO}_3\ ^-\text{(aq)}}
Consider the following unbalanced equation:
Zn (s) + NO3− (aq) + H+ (aq) → Zn2+ (aq) + NH4+ (aq) + H2O (l)
Write the net ionic and complete molecular reaction
Redox Balance
Consider the unbalanced redox reaction shown below.
IO3− (aq) + HSO3−(aq) → I−(aq) + SO42−(aq) (in acidic solution)
When the equation is balanced with the smallest whole number coefficients, what is the coefficient of SO42− ?