Understanding the Concept
In chemistry, the mole is the standard unit for measuring the amount of substance. One mole of any substance contains exactly $6.022 \times 10^{23}$ particles (atoms or molecules), a value known as Avogadro's constant ($N_A$).
To solve this problem, we need to connect three fundamental concepts:
- Mass to Moles conversion: Using the molar mass.
- Molecules to Moles conversion: Using Avogadro's number.
- Difference: Subtracting the removed moles from the initial moles.
Step-by-Step Solution
1. Identify Given Values
- Initial mass of Carbon Monoxide (CO) = $0.28\text{ g}$
- Molecules removed = $2 \times 10^{21}$
- Molar mass of CO = $12.01 \text{ (C)} + 16.00 \text{ (O)} \approx 28\text{ g/mol}$
- Avogadro's number ($N_A$) = $6.022 \times 10^{23}\text{ molecules/mol}$
2. Calculate Initial Moles of CO
Using the formula $\text{n} = \frac{\text{mass}}{\text{molar mass}}$: $\text{n}_{\text{initial}} = \frac{0.28\text{ g}}{28\text{ g/mol}} = 0.01\text{ moles}$
3. Calculate Moles Removed
Using the formula $\text{n} = \frac{\text{number of molecules}}{N_A}$: $\text{n}{\text{removed}} = \frac{2 \times 10^{21}}{6.022 \times 10^{23}}$ $\text{n}{\text{removed}} \approx 0.332 \times 10^{-2} = 0.00332\text{ moles}$
4. Calculate Remaining Moles
$\text{n}{\text{remaining}} = \text{n}{\text{initial}} - \text{n}{\text{removed}}$ $\text{n}{\text{remaining}} = 0.01 - 0.00332 = 0.00668\text{ moles}$
Conclusion
After removing $2 \times 10^{21}$ molecules of carbon monoxide from the initial $0.28\text{ g}$ sample, you are left with approximately $0.00668\text{ moles}$ of CO.
Quick Tips
- Check units: Always ensure your mass is in grams and your molar mass is in g/mol.
- Precision: Keep at least 3-4 significant figures during intermediate steps to avoid rounding errors in the final answer.