If 71.89 g of CO_2 is decomposed, what mass of oxygen (O_2) is produced? (Use the periodic table to find molar masses.)

• A. 44.00 g
• B. 52.48 g
• C. 32.00 g
• D. 35.02 g

Answer: (D)

Verified step by step guidance

1. Write the balanced chemical equation for the decomposition of carbon dioxide: \$2\,\mathrm{CO_2} \rightarrow 2\,\mathrm{CO} + \mathrm{O_2}$.
2. Calculate the molar mass of carbon dioxide (\(\mathrm{CO_2}\)) by adding the atomic masses: \$12.01\,\mathrm{g/mol}\( for carbon and \)16.00\,\mathrm{g/mol}\( for each oxygen atom, so \)M_{\mathrm{CO_2}} = 12.01 + 2 \times 16.00$.
3. Determine the number of moles of \(\mathrm{CO_2}\) decomposed by dividing the given mass by its molar mass: \(n_{\mathrm{CO_2}} = \frac{71.89\,\mathrm{g}}{M_{\mathrm{CO_2}}}\).
4. Use the mole ratio from the balanced equation to find the moles of \(\mathrm{O_2}\) produced. According to the equation, \$2\( moles of \)\mathrm{CO_2}\( produce \)1\( mole of \)\mathrm{O_2}\(, so \)n_{\mathrm{O_2}} = \frac{1}{2} n_{\mathrm{CO_2}}$.
5. Calculate the mass of oxygen gas produced by multiplying the moles of \(\mathrm{O_2}\) by its molar mass (\(M_{\mathrm{O_2}} = 2 \times 16.00\,\mathrm{g/mol}\)): \(m_{\mathrm{O_2}} = n_{\mathrm{O_2}} \times M_{\mathrm{O_2}}\).