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Balancing Symbolic Equations/Reactions
simple inspection
PRELIMINARY UNDERSTANDINGS
Before an equation is balanced, the mathematical meaning of formulas must be
understood. For example, NaCl represents 1 atom of sodium and 1 atom of chlorine
bonded together in a particle called a molecule. In AlCl3, there is 1 atom of aluminum
bonded with 3 atoms of chlorine in a particle called a molecule. Once atoms are locked
together in a molecule, that ratio is not able to be changed without another chemical
reaction. In more complicated molecules this ratio still holds true. For example the
formula (NH4)2CO3 contains 2 ion particles of NH4 and 1 ion particle of CO3. In NH4,
there is 1 atom of N and 4 atoms of H bonded together, and in CO3, there is 1 atom of C
and 3 atoms of O bonded together. Again, once the 2 ion particles of NH 4 and 1 ion
particle of CO3. are bonded, the ratio is fixed and cannot change unless another
reaction takes place. Overall there are a total of 2 N atoms, 8 H atoms, 1 C atom and 3
O atoms.
In order to indicate more than one molecule, no super or subscripts are used.
Instead, full sized numbers are used and placed immediately to the left side of the
molecule symbol. These numbers are called COEFFICIENTS. For example, to
symbolize 4 molecules of NaCl, the correct written expression would be 4 NaCl. This
means that there are a total of 4 Na atoms and 4 Cl atoms, although they are still rigidly
bound in NaCl pairs. To symbolize 5 molecules of AlCl3, the correct expression would
be 5 AlCl3 This means that there are a total of 5 Al atoms and 15 Cl atoms, although
they are still rigidly bound in AlCl3 groups. Finally, to symbolize 3 molecules of
(NH4)2CO3, the correct written expression would be 3 (NH4)2CO3. This means that there
are a total of 3 (NH4)2 ion particle groups or 6 NH4 ion particle groups, and 3 CO3 ion
particle groups. This means that there are a total of 6 N atoms, 24 H atoms, 3 C atoms,
and 9 O atoms, although they are still rigidly bound into molecule groups of (NH4)2CO3.
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Example A
1. First look at the equation:
Na2CO3 + CaCl2
→
CaCO3 +
NaCl
The total number of symbols for each element or ion depicted on the left side of the
arrow MUST be equal to the total number of symbols for each element or ion depicted
on the right side of the arrow.
→
Na2CO3 + CaCl2
CaCO3 +
NaCl
left side
right side
>two Na
>one Na
one CO3
one CO3
one Ca
one Ca
>two Cl
>one Cl
The small wedges mark the parts of the equation that are NOT balanced. The number
of symbols of Na and Cl are NOT the same on both sides of the arrow. There not
enough symbols for Na or Cl on the right side.
2. To balance this equation, coefficients are placed in the equation immediately to the
left of the formula for the molecule containing the symbols needing to be balanced. The
coefficient has the effect of multiplying all elements or ions in the formula by the amount
of the coefficient.
→
Na2CO3 + CaCl2
CaCO3 +
2
NaCl
left side
right side
>two Na
one CO3
one Ca
2 x >one Na = two Na
>two Cl
2 x >one Cl = two Cl
one CO3
one Ca
This equation is now balanced. All components have the same amount on both sides of
the arrow. Final answer:
Na2CO3 + CaCl2
→
CaCO3 +
2
NaCl
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Example B
1. First look at the equation:
Na2CO3 +
AlCl3
→
Al2(CO3)3 +
NaCl
The total number of symbols for each element or ion MUST be the same on both sides
of the arrow.
→
Na2CO3 + AlCl3
Al2(CO3)3 +
NaCl
left side
right side
>two Na
>one Na
>one CO3
>three CO3
>one Al
>two Al
>three Cl
>one Cl
Notice in this equation, that NOTHING is balanced.
2. To balance this equation, pick a place to start, such as Al. Place a coefficient in front
of the entire molecule where Al is deficient. Although the Al is now balanced on both
sides, notice that the coefficient changes the Cl total.
Na2CO3 +
2x
2x
→
2 AlCl3
Al2(CO3)3 +
NaCl
left side
>two Na
>one CO3
right side
>one Na
>three CO3
>one Al = two Al
>two Al
>three Cl = six Cl
>one Cl
3. Since balancing Al changed the Cl as well, add a coefficient on the right side to
balance the Cl. Again notice the effect this new coefficient has on Na.
Na2CO3 +
2 AlCl3
→
Al2(CO3)3 +
left side
NaCl
right side
6 x >one Na = six Na
>two Na
>one CO3
2x
2x
6
>three CO3
>one Al = two Al
>two Al
6 x >one Cl = six Cl
>three Cl = six Cl
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4. Since adding the coefficient of 6 to NaCl changed the Na as well as the Cl, go to the
left side and add the coefficient of 3 that will bring the Na back into balance. Again
notice the effect that this new coefficient has on the CO3.
3 Na2CO3
+
2 AlCl3
left side
3x
3x
2x
>two Na = six Na
>one CO3 = three CO3
>one Al = two Al
→
Al2(CO3)3 +
6
NaCl
right side
6 x >one Na = six Na
>three CO3
>two Al
2x
>three Cl = six Cl
6 x >one Cl = six Cl
5. The last coefficient has completed the process. All amounts of element
symbols/ions are now equal. This equation is balanced. Final answer:
3 Na2CO3
2 AlCl3
+
→
6
Al2(CO3)3 +
NaCl
WARNING ! ! !
**Coefficients are NEVER placed in the middle of a formula. They are always
and only placed on the left side of a formula, and they apply ONLY to the whole
formula immediately to the right of the coefficient.
**When finished balancing an equation, make sure that the coefficients are the
smallest possible set of coefficients that will balance the equation.
ie:
Na2CO3 +
2 Na2CO3
+
CaCl2
2 CaCl2
→
CaCO3 +
→ 2 CaCO
3
+
2
NaCl
4
NaCl
Both equations are balanced, but the equation with the smaller set of coefficients is
correct. Final correct answer is :
Na2CO3 +
CaCl2
→
CaCO3 +
2
NaCl