# What is the sum of the coefficients when the following equation is balanced with the simplest whole numbers? If a substance has an understood 1 as the coefficient, do not forget to add it in. Fe2O3 (s) + C (s) → Fe (s) + CO2 (g)

Dec 21, 2017

$12$

#### Explanation:

$F {e}_{2} {O}_{3} \left(s\right) + C \left(s\right) \rightarrow F e \left(s\right) + C {O}_{2} \left(g\right)$

Number of iron (Fe) atoms: 2 on the LHS, 1 on the RHS.
Number of carbon (C) atoms: 1 on the LHS, 1 on the RHS.
Number of oxygen (O) atoms: 3 on the LHS, 2 on the RHS.

Since we have an odd number of oxygens, we should probably balance that first.

Multiply by $2$: $2 F {e}_{2} {O}_{3} \left(s\right) + C \left(s\right) \rightarrow F e \left(s\right) + C {O}_{2} \left(g\right)$

Let's balance the oxygen on the other side by multiplying by $3$: $2 F {e}_{2} {O}_{3} \left(s\right) + C \left(s\right) \rightarrow F e \left(s\right) + 3 C {O}_{2} \left(g\right)$

Balance the carbon by multiplying by $3$ on the LHS: $2 F {e}_{2} {O}_{3} \left(s\right) + 3 C \left(s\right) \rightarrow F e \left(s\right) + 3 C {O}_{2} \left(g\right)$

Finally, balance the iron by multiplying by $4$ on the LHS: $2 F {e}_{2} {O}_{3} \left(s\right) + 3 C \left(s\right) \rightarrow 4 F e \left(s\right) + 3 C {O}_{2} \left(g\right)$

This is our balanced equation in its simplest form.

The sum of the coefficients is $2 + 3 + 4 + 3 = 12$.