Question

when the following equation is balanced using the smallest set of whole number coefficients, what is the coefficient for o₂? c₈h₁₈o₃(l) + o₂(g) → h₂o(g) + co₂(g) 13 17 22 11 8

Explanation:

Step1: Balance carbon atoms

Let the coefficient of \(C_8H_{18}O_3\) be \(1\). For carbon atoms, since there are \(8\) carbon atoms in \(C_8H_{18}O_3\), the coefficient of \(CO_2\) is \(8\) (\(C_8H_{18}O_3+\ O_2
ightarrow\ H_2O + 8CO_2\)).

Step2: Balance hydrogen atoms

There are \(18\) hydrogen atoms in \(C_8H_{18}O_3\). So the coefficient of \(H_2O\) is \(9\) (\(C_8H_{18}O_3+\ O_2
ightarrow9H_2O + 8CO_2\)).

Step3: Balance oxygen atoms

On the right - hand side, the number of oxygen atoms in \(9H_2O\) is \(9\) and in \(8CO_2\) is \(16\), so the total number of oxygen atoms on the right - hand side is \(9 + 16=25\). On the left - hand side, there are \(3\) oxygen atoms in \(C_8H_{18}O_3\). Let the coefficient of \(O_2\) be \(x\). Then \(3 + 2x=25\). Solving for \(x\):

$$
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$$

The balanced equation is \(C_8H_{18}O_3+11O_2
ightarrow9H_2O + 8CO_2\)

Answer:

11