Concept:First establish the stoichiometric molar ratio between the reactant and the product from a balanced equation, then convert the resulting product moles into grams.
Formula:$$ \text{ZnCO}_3 \rightarrow \text{ZnO} + \text{CO}_2 $$
Solution:- Write the balanced decomposition equation: \( \text{ZnCO}_3 \rightarrow \text{ZnO} + \text{CO}_2 \).
- The ratio is 1:1. Exactly 1 mole of zinc carbonate decomposes to produce exactly 1 mole of carbon dioxide.
- Therefore, thermally decomposing 10 moles of \( \text{ZnCO}_3 \) will produce exactly 10 moles of \( \text{CO}_2 \).
- Convert 10 moles of \( \text{CO}_2 \) to mass. (Molar mass of \( \text{CO}_2 = 12 + 32 = 44 \text{ g/mol} \)).
- Mass = \( 10 \text{ moles} \times 44 \text{ g/mol} = 440 \text{ grams} \).
Why other options are incorrect:- 320, 360, 400: These masses correlate to incorrect mole amounts (e.g. producing 7, 8, or 9 moles of \( \text{CO}_2 \) instead of 10) or utilizing an incorrect molar mass for \( \text{CO}_2 \).
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