To determine the mass of carbon atoms present in the 2.750 gram sample of the compound, we need to follow these steps, assuming we have sufficient data about the combustion reaction (like the amount of $CO_2$ and $H_2O$ produced):

Step-by-Step Solution:

1. Write the balanced equation for the combustion reaction:

   $C_x H_y O_z + O_2 \longrightarrow CO_2 + H_2O$

   Here, $C_x H_y O_z$ represents the unknown compound containing carbon, hydrogen, and oxygen.

2. Determine the moles of $CO_2$ produced:

   Since carbon atoms from the compound will end up in the $CO_2$ produced, we can use the mass of $CO_2$ to determine the mass of carbon.

   • The molar mass of $CO_2$ is: $\text{Molar mass of } CO_2 = 12.01 \, \text{g/mol (C)} + 2 \times 16.00 \, \text{g/mol (O)} = 44.01 \, \text{g/mol}.$

3. Relate carbon in the sample to the amount of $CO_2$ produced:

   Each mole of $CO_2$ contains 1 mole of carbon atoms. Thus, we calculate the number of moles of $CO_2$ and multiply by the molar mass of carbon to get the mass of carbon.

To proceed, we need the exact mass of $CO_2$ produced during the combustion.

Could you provide the mass of $CO_2$ produced, or any additional details? That will allow us to calculate the mass of carbon precisely.

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Here are 5 related questions to further your understanding:

1. How can the mass of $H_2O$ produced help in finding the amount of hydrogen in the compound?
2. Why does every mole of $CO_2$ represent 1 mole of carbon atoms?
3. What role does excess oxygen play in combustion reactions?
4. How can we determine the molecular formula of the compound from this data?
5. Why is it important to burn the compound in excess oxygen?

Tip: Always check units carefully when converting between moles and grams to avoid calculation errors.