How many grams of sodium carbonate (Na2CO3) contain 1.773 × 10^{17} carbon atoms?

• A. 0.0031 g
• B. 3.1 g
• C. 0.31 g
• D. 0.031 g

Answer: (A)

Verified step by step guidance

1. Identify the given information: the number of carbon atoms is \$1.773 \times 10^{17}\( atoms, and we need to find the mass of sodium carbonate (Na\)_2\(CO\)_3$) containing this number of carbon atoms.
2. Recall that one mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.), which is \$6.022 \times 10^{23}\( entities/mol. Use this to convert the number of carbon atoms to moles of carbon atoms using the formula: \)\text{moles of C} = \frac{\text{number of C atoms}}{6.022 \times 10^{23}}$.
3. Since each formula unit of sodium carbonate (Na\(_2\)CO\(_3\)) contains exactly one carbon atom, the moles of carbon atoms equal the moles of sodium carbonate. Therefore, \(\text{moles of Na}_2\text{CO}_3 = \text{moles of C}\).
4. Calculate the molar mass of sodium carbonate by summing the atomic masses: Na (22.99 g/mol) × 2 + C (12.01 g/mol) + O (16.00 g/mol) × 3. This gives the molar mass \(M\) of Na\(_2\)CO\(_3\) in grams per mole.
5. Finally, find the mass of sodium carbonate by multiplying the moles of sodium carbonate by its molar mass: \(\text{mass} = \text{moles of Na}_2\text{CO}_3 \times M\). This will give the mass in grams corresponding to the given number of carbon atoms.