Understanding the Reaction
The reaction provided is the combustion of carbon:
$C + O_2 \rightarrow CO_2$
From the balanced chemical equation, we can see that 1 mole of $O_2$ is required to produce 1 mole of $CO_2$.
Step-by-Step Calculation
To find the number of oxygen molecules needed to produce $220\ \text{mg}$ of $CO_2$, follow these steps:
1. Convert mass of $CO_2$ to grams
$220\ \text{mg} = 0.22\ \text{g}$
2. Calculate the Molar Mass of $CO_2$
- Carbon (C): $12.01\ \text{g/mol}$
- Oxygen (O): $16.00\ \text{g/mol} \times 2 = 32.00\ \text{g/mol}$
- Molar Mass of $CO_2 = 12.01 + 32.00 = 44.01\ \text{g/mol}$ (approximated as $44\ \text{g/mol}$ for calculation).
3. Find the number of moles of $CO_2$
$n(CO_2) = \frac{\text{mass}}{\text{molar mass}} = \frac{0.22\ \text{g}}{44\ \text{g/mol}} = 0.005\ \text{moles}$
4. Determine moles of $O_2$ required
Since the stoichiometric ratio of $O_2$ to $CO_2$ is 1:1, we need $0.005\ \text{moles}$ of $O_2$.
5. Convert moles to molecules
Using Avogadro's number ($N_A = 6.022 \times 10^{23}\ \text{molecules/mol}$): $\text{Number of molecules} = n \times N_A$ $\text{Number of molecules} = 0.005 \times 6.022 \times 10^{23}$ $\text{Number of molecules} = 3.011 \times 10^{21}\ \text{molecules}$
Summary
To produce $220\ \text{mg}$ of $CO_2$, you need exactly $3.011 \times 10^{21}$ molecules of oxygen.