Question

what is the stoichiometric coefficient for o₂ when the following equation is balanced using the smallest, whole - number coefficients?
__ c₇h₁₄o₂(l) + o₂(g) → co₂(g) + __ h₂o(g)
9
11
21
10
19

Explanation:

Step1: Balance carbon atoms

Let the coefficient of \(C_7H_{14}O_2\) be \(1\). Since there are \(7\) carbon atoms in \(C_7H_{14}O_2\), the coefficient of \(CO_2\) is \(7\) (because each \(CO_2\) has \(1\) carbon atom).

Step2: Balance hydrogen atoms

There are \(14\) hydrogen atoms in \(C_7H_{14}O_2\). Each \(H_2O\) has \(2\) hydrogen atoms. So the coefficient of \(H_2O\) is \(\frac{14}{2}=7\).

Step3: Balance oxygen atoms

The left - hand side: \(C_7H_{14}O_2\) has \(2\) oxygen atoms. Let the coefficient of \(O_2\) be \(x\). So the total oxygen atoms on the left - hand side is \(2 + 2x\).
The right - hand side: \(7CO_2\) has \(7\times2 = 14\) oxygen atoms and \(7H_2O\) has \(7\times1=7\) oxygen atoms. So the total oxygen atoms on the right - hand side is \(14 + 7=21\).
Set up the equation for oxygen atoms: \(2+2x=21\). Solve for \(x\): \(2x=21 - 2=19\), \(x=\frac{19}{2}\). But we need whole - number coefficients. Multiply all coefficients by \(2\).
The balanced equation is \(2C_7H_{14}O_2+19O_2
ightarrow14CO_2 + 14H_2O\)

Answer:

\(19\)