

Smart
Balance is a
free online tool for balancing
chemical equations. Almost any kind of chemical reaction can be balanced
using this program. This includes halfcell
reactions, oxidationreduction
(redox) reactions, and net ionic
reactions. Think of Smart Balance as a chemistry
calculator for balancing chemical reactions. Although it will balance
equations for you, a basic understanding of chemistry is still required by
the user to interpret the validity of the results. The mathematics behind the
balancer program are described below and can be used by
anyone with an understanding of algebra to balance complex chemical equations
quickly and reliably. How to Balance an Equation 

1 
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 oxidationreduction
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. 

2 
Click
on the balance
button to see the result. The input text box can now be cleared and the next equation can
be entered. 

3 
If you
received an error message or unexpected result see the common
mistakes section before posting in the guest book.
When done, please feel free to leave anonymous feedback in my guest book or
visit one of my useful links. I
appreciate feedback on suggestions for improvements, problems you encountered
or your thoughts and ideas. 

New: Useful Links to free, browserfriendly balancers, powerful online
chemistry tools and calculators, and help for making your own balancer. 







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]Fe_{2}O_{3
}+ [B]Al → [C]Al_{2}O_{3 }+ [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 breakdown 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 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 byhand 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.
All
that is left to do to get the lowest whole number ratio of coefficients is to
multiple through by 2.
What if you had mistakenly
tried to balance the following equation using the exact same method?
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. 





Updated January 25, 2012 by Jeff Larsen 