# Balance the following chemical equation: (CH4) + (O2) --> (H2O) + (CO2)?

a CH4 + bO2 ----->cH2O + dCO2

Multiplying each element by the coefficient gives you the following equations:

Eq'n 1:
a = c
When the equation is balanced, there will be (1 x a) Carbon atoms from methane on the reactants side and (1 x c) Carbon atoms from carbon dioxide on the products side

Eq'n 2:
4a = 2d
When the equation is balanced, there will be (4 x a) Hydrogen atoms from methane on the reactants side and (2 x d) hydrogen atoms from water on the products side

Eq'n 2(i):
2a = d
Note that Eq'n 2 can be simplified to this format

Eq'n 3:
2b = 2c + d
When the equation is balalnced, there will be (2 x b) oxygen atoms from oxygen gas on the reactant side, (2 x c) oxygen atoms from carbon dioxide on the products side and (1 x d) oxygen atoms from water on the product side.

Eq'n 3(i):
b = 2a
Note that this formula results by subsitituting Eq'n 1 and Eq'n 2(i) into Eq'n 3 and simplifying

To solve for a, b, c and d:

First take the smallest whole number that satisfies Eq'n 1, which is simply
a = c =1

Then, substitute that value into Eq'n 2(i):
2a = d
2(1) = d
d = 2

and Eqn' 3(i):
b = 2a
b = 2(1)
b = 2

Your coefficients are a = 1, b = 2, c = 1 and d = 2

When writing your balanced equation, the coefficient 1 is assumed and can be omitted, yielding the formula:

a CH4 + bO2 ----->cH2O + dCO2

1 CH4 +2bO2 ----->1H2O + 2CO2

CH4 +2bO2 ----->H2O + 2CO2

Source by : danielleamorim.tripod.com