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Enter the equation you want to balance following the formatting guidelines OR copy and paste an example equation to see the balanced result.

Advanced: Select "Acidic Solution" or "Basic Solution" for aqueous oxidation-reduction reactions where an excess of protons or hydroxide ions is present. When using either of these options it isn't necessary to include water, hydroxide or hydrogen ions.

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Formatting Guidelines

• Capitalization is very important (CO is different from Co)
• Spaces between compounds are optional
• Use an = sign not something else like -->
• Do not enter the phase of reactants or products
• Charges must be inside {curly brackets}. You can do this yourself or click on one of the charge buttons immediately after entering the compound.
• To balance a half-cell reaction you can enter "e" or "electron" as a reagent
• The program will automatically add the correct charges to H and OH and e

Common Mistakes

• Read the formatting guidelines and see the examples of what is and isn't OK to enter
• If you included H2O in your reaction, try removing it
• A cation or anion you entered has incorrect subscripts such that the resulting compound isn't electrically neutral (CaCl instead of CaCl2 or Mg3(PO4) instead of Mg3(PO4)2)
• If it still doesn't work, check the oxidation states of every ion and polyatomic ion that you entered to make sure you have the correct subscripts. 90% of the time this is the problem
• If you get an error message "Not all reagents necessary for balanced equation" then substitute repeated groups in chemical compounds with an X.
• C6H5C2H5+O2=C6H5OH+CO2+H2O can be balanced as
  XC2H5+O2=XOH+CO2+H2O

Unbalanced Examples

• C4H10 + O2 = H2O + CO2
• K4Fe(CN)6 + KMnO4 + H2SO4 = KHSO4 + Fe2(SO4)3 + MnSO4 + HNO3 + CO2 + H2O
• H2O2 + Cr(OH)6{-3} = OH{-1} + CrO4{-2} + H2O
• Co(NH3)6{+2} + H2O2 = Co(NH3)6{+3} + OH{-1}
• Mn{+2} + BiO3{-1} + H{+1} = MnO4{-1} + Bi{+3} + H2O
• H2+Ca(CN)2 + NaAlF4 + FeSO4 + MgSiO3 + KI + H3PO4 + PbCrO4 + BrCl + CF2Cl2 + SO2 = PbBr2 + CrCl3 + MgCO3 + KAl(OH)4 + Fe(SCN)3 + PI3 + NaSiO3 + CaF2 + H2O
• Mn{+2} + MnO4{-1} + e + H + H2O
• Al + OH{-1} + H2O = H2 + [Al(OH)4]{-1}
• [Cr(N2H4CO)6]4[Cr(CN)6]3 + KMnO4 + H2SO4 = K2Cr2O7 + MnSO4 + CO2 + KNO3 + K2SO4 + H2O

How Does It Work?

Keep in mind, this program does nothing more than a graphing calculator can do.  The process outlined below is very flexible and can be applied to just about any chemical equation regardless of its type or complexity. Take, for example, the reduction of iron oxide with the addition of aluminum (this is also known as the thermite reaction):

[A]Fe₂O₃  +  [B]Al  →  [C]Al₂O₃  +  [D]Fe

The blue letters represent the unknown coefficients to the balanced equation. To solve for these unknowns a system of equations must be generated.  The easiest way to do this is to write a matrix relating the quantity of each element found in each reagent.  The following table represents a break-down of this process, where each row represents a different element and each column represents an unknown coefficient. In this reaction there are 3 elements involved and 4 unknown coefficients.

Alternatively, this can be represented as a system of linear equations:

2A + 0B = 0C + 1D
3A + 0B = 3C + 0D
0A + 1B = 2C + 0D

This system of equations can now be solved simultaneously to find the unknowns.  This program carries out a similar process, though instead using the matrix similar to the one in the above table.  Basic linear algebra leads to the same solutions one would find by balancing this reaction in the traditional by-hand method, but in a fraction of the time!!

Keep in mind that an additional constraint is necessary to solve this system of equations because there is one degree of freedom (we have 4 unknowns but only 3 independent equations).  We are interested in finding the lowest whole number ratio of coefficients that will balance the equation. One way to find this ratio is to set one of the unknown coefficients equal to 1 and solve for the remaining coefficients.

Let D = 1

then {A = 0.5, B = 1, C = 0.5}

1/2 Fe₂O₃  + 1 Fe  →  1/2 Al₂O₃  +  1 Al

All that is left to do to get the lowest whole number ratio of coefficients is to multiple through by 2.

Fe₂O₃  + 2 Fe  →   Al₂O₃  +  2 Al

What if you had mistakenly tried to balance the following equation using the exact same method?

 [A]Fe₂O₃  +  [B]Al  +  [C]Al₂O₃  →  [D]Fe

Notice that aluminum oxide has been moved to the wrong side. Another system of equations can be generated for this proposed reaction, but the final result will still be the same as before!  Solving for the 4 unknowns as before you will find that coefficient B will be a negative 1 instead of a positive 1. This negative coefficient means that in the final solution, aluminum must be on the opposite side of the equation relative to your initial guess.

Very Useful Links

• WebQC.org - Online Chemical tools includes a molar mass calculator, periodic table and the best non-applet based chemical equation balancer I have come across. This should run in your browser if Smart Balance does not.
• values of the universal gas constant for any combination of units you want in easy to read tables.
• useful chemistry utilities including a java script balancer with even greater compatibility but less flexibility. The site also has other useful tools including calculators for finding empirical formulas, gas laws, electron configurations, unit conversions, sig figs, and more.
• Physicochemical calculators for boiling point, concentration, pressure and temperature. The coefficients calculator is an applet-based balancer that gives you the option of showing step-by-step exactly how the program balances your equation!
• Balancing Equations Using Matrices This site walks through how to balance chemical equaions using matrix algebra, specifically on the TI-82 calculator and also include some other useful online calculators.
• CHEMIX School A downloadable suite of chemistry tools for Windows including an equation balancer.
• Chemical Equation Balancer This site includes a set of chemistry calulators and an easy to use non-applet equation balancer with a description of how to use linear algebra to solve cheimcal equations.
• If you find something wrong with one of these links or think you have a useful addition please post a message in the guest book or email me. Please feel free to link to this webpage if you found it useful.