1. Determine the number of molecules:

* One mole of any substance contains Avogadro's number of particles (6.022 x 10^23).

* So, 6.75 moles of C2H6 contain 6.75 moles * (6.022 x 10^23 molecules/mole) = 4.06 x 10^24 molecules of C2H6.

2. Calculate the total number of atoms:

* Each molecule of C2H6 contains 2 carbon atoms and 6 hydrogen atoms, for a total of 8 atoms.

* Therefore, 4.06 x 10^24 molecules of C2H6 contain (4.06 x 10^24 molecules) * (8 atoms/molecule) = 3.25 x 10^25 atoms.

Answer: There are 3.25 x 10^25 atoms in 6.75 moles of C2H6.