Balance the following equations by inserting the appropriate coefficients

Balance the following equations by inserting the appropriate coefficients.

• P₄ + O₂ —–> P₂O₅
• C₂H₆ + O₂ —–> CO₂ + H₂O

The correct answer and explanation is :

Balanced Equations:

1. Phosphorus and Oxygen Reaction
   Unbalanced:
   [
   P_4 + O_2 \rightarrow P_2O_5
   ]
   Balanced:
   [
   P_4 + 5O_2 \rightarrow 2P_2O_5
   ]
2. Ethane Combustion
   Unbalanced:
   [
   C_2H_6 + O_2 \rightarrow CO_2 + H_2O
   ]
   Balanced:
   [
   2C_2H_6 + 7O_2 \rightarrow 4CO_2 + 6H_2O
   ]

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Explanation:

1. Balancing Phosphorus and Oxygen Reaction

• The given equation contains P₄ (tetraphosphorus) and O₂ (oxygen gas), producing P₂O₅ (diphosphorus pentoxide).
• Since each P₂O₅ molecule contains 2 P atoms, we need 2 molecules to account for all 4 phosphorus atoms in P₄.
• Oxygen balance: Each P₂O₅ contains 5 oxygen atoms, and 2 molecules contribute 10 oxygen atoms in total.
• Since O₂ molecules each contain 2 oxygen atoms, we need 5 O₂ molecules to provide 10 oxygen atoms.

Thus, the balanced equation is:
[
P_4 + 5O_2 \rightarrow 2P_2O_5
]

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2. Balancing the Combustion of Ethane

• Ethane (C₂H₆) reacts with oxygen (O₂) to form carbon dioxide (CO₂) and water (H₂O).
• Carbon: C₂H₆ has 2 carbon atoms, so we need 2 CO₂ molecules.
• Hydrogen: C₂H₆ has 6 hydrogen atoms, so we need 3 H₂O molecules to balance the hydrogen.
• Oxygen: The right side contains 4 oxygens from CO₂ and 3×1 = 3 oxygens from H₂O, totaling 7 oxygens.
• Since O₂ molecules contribute 2 oxygen atoms each, we need 7 O₂ molecules to balance.

Thus, the balanced equation is:
[
2C_2H_6 + 7O_2 \rightarrow 4CO_2 + 6H_2O
]

Balancing chemical equations ensures that the law of conservation of mass is satisfied, meaning atoms are neither created nor destroyed.