Molecules Count C75Cf5

1. **State the problem:** Calculate the number of molecules in 229 mg of aspirin (C$_9$H$_8$O$_4$). 2. **Formula and constants:** - Number of molecules = moles $\times$ Avogadro's number ($6.022 \times 10^{23}$ molecules/mol). - Moles = mass (g) / molar mass (g/mol). 3. **Calculate molar mass of aspirin (C$_9$H$_8$O$_4$):** - Carbon (C): 12.01 g/mol $\times 9 = 108.09$ g/mol - Hydrogen (H): 1.008 g/mol $\times 8 = 8.064$ g/mol - Oxygen (O): 16.00 g/mol $\times 4 = 64.00$ g/mol - Total molar mass = $108.09 + 8.064 + 64.00 = 180.154$ g/mol 4. **Convert mass to grams:** $$229\ \text{mg} = 0.229\ \text{g}$$ 5. **Calculate moles of aspirin:** $$\text{moles} = \frac{0.229}{180.154} \approx 0.001271\ \text{mol}$$ 6. **Calculate number of molecules:** $$\text{molecules} = 0.001271 \times 6.022 \times 10^{23} \approx 7.65 \times 10^{20}$$ --- 1. **State the problem:** Calculate the number of molecules in 229 mg of acetaminophen (C$_8$H$_9$NO$_2$). 2. **Calculate molar mass of acetaminophen:** - Carbon (C): 12.01 g/mol $\times 8 = 96.08$ g/mol - Hydrogen (H): 1.008 g/mol $\times 9 = 9.072$ g/mol - Nitrogen (N): 14.01 g/mol $\times 1 = 14.01$ g/mol - Oxygen (O): 16.00 g/mol $\times 2 = 32.00$ g/mol - Total molar mass = $96.08 + 9.072 + 14.01 + 32.00 = 151.162$ g/mol 3. **Convert mass to grams:** $$229\ \text{mg} = 0.229\ \text{g}$$ 4. **Calculate moles of acetaminophen:** $$\text{moles} = \frac{0.229}{151.162} \approx 0.001515\ \text{mol}$$ 5. **Calculate number of molecules:** $$\text{molecules} = 0.001515 \times 6.022 \times 10^{23} \approx 9.13 \times 10^{20}$$ **Final answers:** - 229 mg aspirin contains approximately $7.65 \times 10^{20}$ molecules. - 229 mg acetaminophen contains approximately $9.13 \times 10^{20}$ molecules.