Question

Give the stoichiometric coefficient for oxygen when the following equation is balanced using the lowest, whole-number coefficients: ___CH4O(l) ___O2(g) -> ___CO2(g) ____H2O(l)

Answer 1

Answer: $2 \cdot CH_{4} O (l)+3 \cdot O_{2}(g) \rightharpoonup 2 \cdot CO_{2}(g) + 4 \cdot H_{2}O(l)$

Explanation:

Let consider that one mole of diatomic oxygen is used. So, the stoichometric can be modelled by using three variables:

$x \cdot CH_{4} O (l)+O_{2}(g) \rightharpoonup y \cdot CO_{2}(g) + z \cdot H_{2}O(l)$

Where $x,y,z$ are the required variables.

Now, three equations are constructed from the number of elements involved (Carbon, Hydrogen and Oxygen):

Carbon

$x=y$

Oxygen

$x+2=2\cdot y + z$

Hydrogen

$4\cdot x = 2 \cdot z$

The coefficients can be found by solving the abovementioned 3 x 3 Linear System:

$x = \frac{2}{3}, y = \frac{2}{3}, z = \frac{4}{3}$

The whole-number coefficients are determined by multiplying every coefficient by 3, then:

$2 \cdot CH_{4} O (l)+3 \cdot O_{2}(g) \rightharpoonup 2 \cdot CO_{2}(g) + 4 \cdot H_{2}O(l)$