Questions: Select the coefficients that would correctly balance the equation. C5H8 + O2 -> CO2 + H2O 1,14,5,8 1,7,5,4 2,14,10,8 1,7,5,8

Transcript text: Select the coefficients that would correctly balance the equation. \[ \mathrm{C}_{5} \mathrm{H}_{8}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \] $1,14,5,8$ $1,7,5,4$ $2,14,10,8$ $1,7,5,8$

Solution

Solution Steps

Step 1: Write the Unbalanced Equation

The given chemical equation is: \[ \mathrm{C}_{5} \mathrm{H}_{8} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \]

Step 2: Identify the Number of Atoms on Each Side

On the left side:
- Carbon (C): 5
- Hydrogen (H): 8
- Oxygen (O): 2 (from $\mathrm{O}_{2}$)
On the right side:
- Carbon (C): 1 (from $\mathrm{CO}_{2}$)
- Hydrogen (H): 2 (from $\mathrm{H}_{2}\mathrm{O}$)
- Oxygen (O): 3 (1 from $\mathrm{CO}_{2}$ and 2 from $\mathrm{H}_{2}\mathrm{O}$)

Step 3: Balance the Carbon Atoms

To balance the carbon atoms, we need 5 $\mathrm{CO}_{2}$ molecules on the right side: \[ \mathrm{C}_{5} \mathrm{H}_{8} + \mathrm{O}_{2} \rightarrow 5 \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \]

Step 4: Balance the Hydrogen Atoms

To balance the hydrogen atoms, we need 4 $\mathrm{H}_{2}\mathrm{O}$ molecules on the right side: \[ \mathrm{C}_{5} \mathrm{H}_{8} + \mathrm{O}_{2} \rightarrow 5 \mathrm{CO}_{2} + 4 \mathrm{H}_{2}\mathrm{O} \]

Step 5: Balance the Oxygen Atoms

Now, we count the oxygen atoms on the right side:

From $\mathrm{CO}_{2}$: $5 \times 2 = 10$
From $\mathrm{H}_{2}\mathrm{O}$: $4 \times 1 = 4$
Total oxygen atoms needed: $10 + 4 = 14$

To balance the oxygen atoms, we need 7 $\mathrm{O}_{2}$ molecules on the left side: \[ \mathrm{C}_{5} \mathrm{H}_{8} + 7 \mathrm{O}_{2} \rightarrow 5 \mathrm{CO}_{2} + 4 \mathrm{H}_{2}\mathrm{O} \]