Question

carbon dioxide and water are produced when pentane ($c_5h_{12}$) reacts with oxygen. what is the balanced equation for this reaction?
$c_5h_{12}(g) + o_2(g) \
ightarrow co_2(g) + h_2o(g)$
$c_5h_{12}(g) + o_2(g) \
ightarrow 5co_2(g) + h_2o(g)$
$c_5h_{12}(g) +8o_2(g) \
ightarrow 5co_2(g) + 6h_2o(g)$
$5co_2(g) + 6h_2o(g) \
ightarrow c_5h_{12}(g) + 8o_2(g)$

Explanation:

To balance the combustion reaction of pentane ($\ce{C5H12}$) with oxygen, we start by balancing carbon, then hydrogen, and finally oxygen.

1. Carbon Balance: There are 5 C atoms in $\ce{C5H12}$, so we need 5 $\ce{CO2}$ molecules (since each $\ce{CO2}$ has 1 C).
2. Hydrogen Balance: There are 12 H atoms in $\ce{C5H12}$. Each $\ce{H2O}$ has 2 H, so we need $\frac{12}{2} = 6$ $\ce{H2O}$ molecules.
3. Oxygen Balance: On the product side, 5 $\ce{CO2}$ has $5 \times 2 = 10$ O, and 6 $\ce{H2O}$ has $6 \times 1 = 6$ O, totaling $10 + 6 = 16$ O. Since $\ce{O2}$ is diatomic, we need $\frac{16}{2} = 8$ $\ce{O2}$ molecules.

The balanced equation is $\ce{C5H12(g) + 8O2(g) -> 5CO2(g) + 6H2O(g)}$.

Answer:

C. $\ce{C5H12(g) + 8O2(g) -> 5CO2(g) + 6H2O(g)}$