Question

balance a chemical equation
balance the chemical equation for the chemical reaction of burning ethanol.
inputs/reactants outputs/products
__ c₂h₅oh + _ o₂ → __ co₂ + __ h₂o
carbon (c) =
oxygen (o) =
hydrogen (h) = carbon (c) =
oxygen (o) =
hydrogen (h) =

Explanation:

Step1: Balance Carbon (C)

In \( C_2H_5OH \), there are 2 C atoms. So, we need 2 \( CO_2 \) molecules (since each \( CO_2 \) has 1 C) to balance C. Now the equation is: \( \underline{1} C_2H_5OH + \underline{?} O_2
ightarrow \underline{2} CO_2 + \underline{?} H_2O \)

Step2: Balance Hydrogen (H)

In \( C_2H_5OH \), there are \( 5 + 1 = 6 \) H atoms. Each \( H_2O \) has 2 H, so we need \( \frac{6}{2} = 3 \) \( H_2O \) molecules. Now the equation is: \( \underline{1} C_2H_5OH + \underline{?} O_2
ightarrow \underline{2} CO_2 + \underline{3} H_2O \)

Step3: Balance Oxygen (O)

On the product side: \( 2 \times 2 + 3 \times 1 = 4 + 3 = 7 \) O atoms. On the reactant side, \( C_2H_5OH \) has 1 O, so \( O_2 \) must provide \( 7 - 1 = 6 \) O atoms. Since each \( O_2 \) has 2 O, we need \( \frac{6}{2} = 3 \) \( O_2 \) molecules. Now the balanced equation is: \( \underline{1} C_2H_5OH + \underline{3} O_2
ightarrow \underline{2} CO_2 + \underline{3} H_2O \)

Step4: Verify Atom Counts

• Carbon (C): Reactant: 2 (from \( C_2H_5OH \)), Product: \( 2 \times 1 = 2 \) (balanced).
• Oxygen (O): Reactant: \( 1 + 3 \times 2 = 1 + 6 = 7 \), Product: \( 2 \times 2 + 3 \times 1 = 4 + 3 = 7 \) (balanced).
• Hydrogen (H): Reactant: \( 6 \) (from \( C_2H_5OH \)), Product: \( 3 \times 2 = 6 \) (balanced).

Answer:

The balanced equation is \( \boldsymbol{1} \, C_2H_5OH + \boldsymbol{3} \, O_2
ightarrow \boldsymbol{2} \, CO_2 + \boldsymbol{3} \, H_2O \)
Atom counts:

• Reactant (C₂H₅OH + O₂): C = 2, O = 1 + 3×2 = 7, H = 6
• Product (CO₂ + H₂O): C = 2×1 = 2, O = 2×2 + 3×1 = 7, H = 3×2 = 6