To balance the chemical equation for the combustion of methane [tex]\((CH_4)\)[/tex], we must balance the number of each type of atom on both sides of the equation. The initial unbalanced equation is:
[tex]\[ CH_4 + O_2 \rightarrow CO_2 + H_2O \][/tex]
Let's proceed step-by-step to find the correct coefficients.
1. Balance Carbon (C) atoms:
There is 1 carbon atom in [tex]\(CH_4\)[/tex] and 1 carbon atom in [tex]\(CO_2\)[/tex]. So, the coefficients for [tex]\(CH_4\)[/tex] and [tex]\(CO_2\)[/tex] should remain as 1.
[tex]\[ 1CH_4 + O_2 \rightarrow 1CO_2 + H_2O \][/tex]
2. Balance Hydrogen (H) atoms:
There are 4 hydrogen atoms in [tex]\(CH_4\)[/tex] and 2 hydrogen atoms in [tex]\(H_2O\)[/tex]. To balance hydrogen, the coefficient of [tex]\(H_2O\)[/tex] should be 2:
[tex]\[ 1CH_4 + O_2 \rightarrow 1CO_2 + 2H_2O \][/tex]
3. Balance Oxygen (O) atoms:
There are 2 oxygen atoms in [tex]\(O_2\)[/tex]. On the product side, there are 2 oxygen atoms in [tex]\(CO_2\)[/tex] and 2 oxygen atoms in the 2 [tex]\(H_2O\)[/tex] (since each [tex]\(H_2O\)[/tex] molecule contains 1 oxygen atom). So, there are a total of 4 oxygen atoms needed on the reactant side. Therefore, the coefficient for [tex]\(O_2\)[/tex] should be 2:
[tex]\[ 1CH_4 + 2O_2 \rightarrow 1CO_2 + 2H_2O \][/tex]
So, each coefficient of the balanced equation is:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
The coefficients are 1 for [tex]\(CH_4\)[/tex], 2 for [tex]\(O_2\)[/tex], 1 for [tex]\(CO_2\)[/tex], and 2 for [tex]\(H_2O\)[/tex].
Based on the options provided:
A. 0
B. 1
C. 2
D. 3
E. 4
The solution shows that the correct answer for the missing coefficient in the reactants and products, which makes the reaction balanced, is:
C. 2
