Calculate the amount of \( CO_2 \) gas produced, when \( 32 \)g of \( CH_4 \) is burned with sufficient amount of oxygen (Given atomic weight of \( C=12, O=16 \) and \( H=1 \))
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In stoichiometry, always "bridge" through moles. Convert the given mass to moles, use the coefficients from the balanced equation to find the moles of the desired product, and then convert those moles back to mass.
Step 1: Understanding the Concept:
This problem requires stoichiometry based on a balanced chemical equation for the combustion of methane. Step 2: Detailed Explanation:
Balanced equation: $CH_4 + 2O_2 \to CO_2 + 2H_2O$.
Molar mass of $CH_4 = 12 + 4(1) = 16 \text{ g/mol}$.
Molar mass of $CO_2 = 12 + 2(16) = 44 \text{ g/mol}$.
Moles of $CH_4 = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{32}{16} = 2 \text{ moles}$.
From equation, 1 mole $CH_4 \to 1$ mole $CO_2$.
So, 2 moles $CH_4 \to 2$ moles $CO_2$.
Mass of $CO_2 = 2 \times 44 = 88 \text{ g}$. Step 3: Final Answer:
The amount of $CO_2$ produced is 88g.