Concept:Before identifying a molar ratio, an equation must obey the Law of Conservation of Mass by balancing the number of atoms of each element on both sides.
Formula:$$ 2\text{Al}_2\text{O}_3 \rightarrow 4\text{Al} + 3\text{O}_2 $$
Solution:- Look at Oxygen first. There are 3 on the left and 2 on the right. To balance, cross-multiply by placing a 2 in front of \( \text{Al}_2\text{O}_3 \) and a 3 in front of \( \text{O}_2 \).
- Now you have \( 2\text{Al}_2\text{O}_3 \rightarrow \text{Al} + 3\text{O}_2 \).
- This creates 4 Aluminum atoms on the left (\( 2 \times 2 = 4 \)).
- Place a 4 in front of Al on the right: \( 2\text{Al}_2\text{O}_3 \rightarrow 4\text{Al} + 3\text{O}_2 \).
- The question asks for the specific molar ratio of Aluminum (Al) to Oxygen gas (\( \text{O}_2 \)).
- The coefficient for Al is 4. The coefficient for \( \text{O}_2 \) is 3. The ratio is 4:3.
Why other options are incorrect:- 2:3: This is the ratio of Aluminum Oxide (reactant) to Oxygen gas (product), not Al to \( \text{O}_2 \).
- 3:4: This inverses the ratio, presenting \( \text{O}_2 \) : Al instead of the requested Al : \( \text{O}_2 \).
- 1:1: Completely unbalanced equation.
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