Calculate the number of carbon atoms in a 50.0g sample of camphor C10H16O.

To calculate the number of carbon atoms in a 50.0 g sample of camphor (\(\text{C}_{10}\text{H}_{16}\text{O}\)), we need to follow these steps:

1. **Calculate the molar mass of camphor (\(\text{C}_{10}\text{H}_{16}\text{O}\)):**

   - Carbon (C): \(10 \times 12.01 \, \text{g/mol} = 120.10 \, \text{g/mol}\)
   - Hydrogen (H): \(16 \times 1.008 \, \text{g/mol} = 16.128 \, \text{g/mol}\)
   - Oxygen (O): \(1 \times 16.00 \, \text{g/mol} = 16.00 \, \text{g/mol}\)

   The molar mass of camphor is:
   \[
   120.10 \, \text{g/mol} + 16.128 \, \text{g/mol} + 16.00 \, \text{g/mol} = 152.228 \, \text{g/mol}
   \]

2. **Calculate the number of moles of camphor in 50.0 g:**

   Use the formula:
   \[
   \text{moles of camphor} = \frac{\text{mass}}{\text{molar mass}}
   \]

   \[
   \text{moles of camphor} = \frac{50.0 \, \text{g}}{152.228 \, \text{g/mol}} \approx 0.328 \, \text{mol}
   \]

3. **Calculate the number of carbon atoms:**

   Since each molecule of camphor contains 10 carbon atoms, we can find the total number of carbon atoms by multiplying the number of moles of camphor by Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol) and then by 10:

   \[
   \text{Number of carbon atoms} = 0.328 \, \text{mol} \times 10 \, \text{atoms/molecule} \times 6.022 \times 10^{23} \, \text{atoms/mol}
   \]

   \[
   \text{Number of carbon atoms} \approx 1.976 \times 10^{24} \, \text{atoms}
   \]

Therefore, the 50.0 g sample of camphor contains approximately \(1.976 \times 10^{24}\) carbon atoms.

If you have any questions or need further details, feel free to ask!

Here are some related questions you might find interesting:
1. How do you determine the empirical formula of a compound?
2. What is Avogadro's number, and why is it important?
3. How do you convert between moles and grams of a substance?
4. What is the molecular formula, and how does it differ from the empirical formula?
5. How do you calculate the number of hydrogen atoms in a compound?
6. What is the difference between molecular weight and molar mass?
7. How do you determine the molar mass of a compound with multiple elements?
8. What is a mole in chemistry, and why is it used?

**Tip:** Always double-check the molecular formula of a compound to ensure the correct calculation of molar mass and subsequent conversions.

Learn how to calculate the number of carbon atoms in a 50.0 g sample of camphor (C10H16O) using chemical stoichiometry and molar mass calculations. This problem involves converting grams to moles, determining the number of moles of camphor, and applying Avogadro's number to find the total number of carbon atoms. Suitable for advanced high school chemistry students.

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