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The equation provided is:

\[
C_2H_6O(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)
\]

We need to balance it by determining the correct coefficients for each compound, particularly the coefficient for \( O_2 \).

### Step-by-step process:

1. **Count atoms on both sides:**
   - **Left side:**
     - \( C_2H_6O \): 2 carbon (C), 6 hydrogen (H), 1 oxygen (O).
     - \( O_2 \): 2 oxygen (O) atoms per molecule.
   - **Right side:**
     - \( CO_2 \): 1 carbon (C), 2 oxygen (O).
     - \( H_2O \): 2 hydrogen (H), 1 oxygen (O).

2. **Balance carbon atoms:**
   - There are 2 carbon atoms in \( C_2H_6O \), so we need 2 \( CO_2 \) molecules on the right:
   \[
   C_2H_6O + O_2 \rightarrow 2 CO_2 + H_2O
   \]

3. **Balance hydrogen atoms:**
   - There are 6 hydrogen atoms in \( C_2H_6O \), so we need 3 \( H_2O \) molecules on the right to balance the hydrogens:
   \[
   C_2H_6O + O_2 \rightarrow 2 CO_2 + 3 H_2O
   \]

4. **Balance oxygen atoms:**
   - Left side: \( C_2H_6O \) contributes 1 oxygen atom.
   - Right side: There are \( 2 \times 2 = 4 \) oxygen atoms from \( CO_2 \) and \( 3 \times 1 = 3 \) oxygen atoms from \( H_2O \), giving a total of 7 oxygen atoms on the right.
   - To balance, we need \( \frac{7 - 1}{2} = 3 \) \( O_2 \) molecules on the left:
   \[
   C_2H_6O + 3 O_2 \rightarrow 2 CO_2 + 3 H_2O
   \]

Thus, the coefficient in front of \( O_2 \) is **3**.

### Final Balanced Equation:
\[
C_2H_6O + 3 O_2 \rightarrow 2 CO_2 + 3 H_2O
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do we balance combustion reactions in general?
2. What is the significance of using whole numbers in balancing equations?
3. Why is oxygen balanced last in combustion reactions?
4. How would you balance a more complex organic compound combustion reaction?
5. What happens if you have fractional coefficients—how do you eliminate them?

**Tip:** Always start by balancing elements that appear in only one reactant and one product before moving to elements like oxygen that appear in multiple compounds.

What is the coefficient in front of the O2 when the equation below is balanced (using only whole numbers and the lowest whole number ratio)? C2H6O(g) + O2(g) -> CO2(g) + H2O(g)

Discover how to balance the chemical equation C2H6O(g) + O2(g) -> CO2(g) + H2O(g) with a focus on determining the coefficient of oxygen (O2). This guide provides a step-by-step approach using the conservation of mass principle, ideal for high school chemistry students.

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