Questions: Balance the following reaction: C9H20O2 + O2 → CO2 + H2O

Transcript text: Balance the following reaction: $\mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2}+$ $\mathrm{O}_{2} \rightarrow$ $\mathrm{CO}_{2}+$ $\mathrm{H}_{2} \mathrm{O}$

Solution

Solution Steps

Step 1: Write the Unbalanced Equation

First, write down the unbalanced chemical equation: \[ \mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \]

Step 2: Balance Carbon Atoms

Balance the carbon atoms by ensuring the number of carbon atoms on both sides of the equation is equal. There are 9 carbon atoms in $\mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2}$, so we need 9 $\mathrm{CO}_{2}$ molecules: \[ \mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2} + \mathrm{O}_{2} \rightarrow 9 \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \]

Step 3: Balance Hydrogen Atoms

Next, balance the hydrogen atoms. There are 20 hydrogen atoms in $\mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2}$, so we need 10 $\mathrm{H}_{2} \mathrm{O}$ molecules: \[ \mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2} + \mathrm{O}_{2} \rightarrow 9 \mathrm{CO}_{2} + 10 \mathrm{H}_{2} \mathrm{O} \]

Step 4: Balance Oxygen Atoms

Finally, balance the oxygen atoms. On the right side, we have:

$9 \times 2 = 18$ oxygen atoms from $\mathrm{CO}_{2}$
$10 \times 1 = 10$ oxygen atoms from $\mathrm{H}_{2} \mathrm{O}$

This gives a total of $18 + 10 = 28$ oxygen atoms on the right side. On the left side, we have 2 oxygen atoms from $\mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2}$, so we need $28 - 2 = 26$ oxygen atoms from $\mathrm{O}_{2}$, which means we need $ \frac{26}{2} = 13 $ $\mathrm{O}_{2}$ molecules: \[ \mathrm{C}_{9} \mathrm{H}_{20} \mathrm{O}_{2} + 13 \mathrm{O}_{2} \rightarrow 9 \mathrm{CO}_{2} + 10 \mathrm{H}_{2} \mathrm{O} \]