We are presented with the molecular formula C₂H₆O. To determine the amount of carbon atoms present, we must first determine how many moles of carbon are present. The question states that there are 0.92 moles of C₂H₆O. However, there are 2 carbon atoms per molecule of this structure, therefore:
0.92 moles C₂H₆O x 2 moles C/1 mole C₂H₆O = 1.84 moles C
There are 1.84 moles of carbon atoms per 0.92 moles of C₂H₆O. Now we must determine the total number of carbon atoms present and we can do this using a value called Avogadro's constant. Avogadro's number is the value designating how many atoms or molecules are present in a mole of that substance. The value of this constant is roughly 6.022 x 10²³ atoms/mole. We can calculate the amount of carbon atoms present as follows:
1.84 moles C x 6.022 x 10²³ atoms/mole = 1.11 x 10²⁴ atoms.
Therefore, there are roughly 1.11 x 10²⁴ carbon atoms in 0.92 moles of C₂H₆O.