Question

How to balance an equation in easiest way?

Answer 1

by the method of transposing.
it's too easy.

Answer 2

Let's see the example.

KNO3 + C12H22O11 --> N2 + CO2 + H2O + K2CO3

Assume a set of variables for each of involved compounds. Like this:

a1 KNO3 + a2 C12H22O11 --> a3 N2 + a4 CO2 + a5 H2O + a6 K2CO3

Then count the number of moles for each element and write an equation.

K: a1 = 2a6
N: a1 = 2a3
O: 3a1 + 11a2 = 2a4 + a5 + 3a6
C: 12a2 = a4 + a6
H: 22a2 = 2a5

Now you get five equations of six variables. Usually, these equations will have infinite solution sets which you can multiply any number to all solutions to get the new set, but we need just one of them. So, let's choose the probably best one. In most cases, there are at least one equation which is in the form of ax = by. We'll use this equation as an assumption point.

I choose H equation. From 22a2 = 2a5 (or in fact, 11a2 = a5), I will assume that a2 is 1 and a5 is 11.

Next, substitute values of a2 and a5 in all five equations. You'll get this:

K: a1 = 2a6
N: a1 = 2a3
O: 3a1 + 11 = 2a4 + 11 + 3a6
(rewrite O: 3a1 = 2a4 + 3a6)
C: 12 = a4 + a6
H: 22 = 22 (so we don't need this anymore)

The set are reduced to this.

K: a1 = 2a6
N: a1 = 2a3
O: 3a1 = 2a4 + 3a6
C: 12 = a4 + a6

From K and N equation, you can get that a1 = 2a3 and a6 = a3. Replacing a1 with 2a3 and a6 with a3 will bring you to here:

K: 2a3 = 2a3
N: 2a3 = 2a3
O: 6a3 = 2a4 + 3a3
C: 12 = a4 + a3

You can discard K and N and rewrite O right now.

O: 3a3 = 2a4
C: 12 = a4 + a3

We have already reduced things to just two two-variable equations. You can solve it easily and get that a3 is 24/5 and a4 is 36/5. As we know that a6 equals to a3 and a1 is twice as much as a3, you will eventually get that a6 is 24/5 and a1 is 48/5.

In conclusion, we now have already got all six values.

a1 = 48/5
a2 = 1
a3 = 24/5
a4 = 36/5
a5 = 11
a6 = 24/5

However, this set does not look good, as we need all coefficients of all compounds to be integers and unable to reduce further. In this case, just multiply with 5.

a1 = 48
a2 = 5
a3 = 24
a4 = 36
a5 = 55
a6 = 24

Looks ridiculous, you might think, but let's check it.

48 KNO3 + 5 C12H22O11 --> 24 N2 + 36 CO2 + 55 H2O + 24 K2CO3

K: 48 = 48
N: 48 = 48
O: 144 + 55 = 72 + 55 + 72 (= 199)
C: 60 = 36 + 24
H: 110 = 110

Yes, that's it!

Tips: 1. Make value assumption only once, or your two assumptions will contradict with each other.
2. If your equation involves charges, include one equation for charges as well.

Hope this helps.