A sample of propane, \rm C_3H_8, contains 12.8 moles of carbon atoms. How many total moles of atoms does the sample contain?

Write the equation and balance it. Calculate moles of each of the products, the products, then add moles products to moles of any reactants remaining unreacted to obtain the total number of moles.

To find the total number of moles of atoms in the sample, we need to consider the molecular formula of propane, which is \rm C_3H_8.

From the given information, we know that the sample contains 12.8 moles of carbon atoms (\rm C).

Let's break down the molecular formula of propane:
- \rm C_3H_8 indicates that there are 3 carbon atoms (\rm C) in each molecule.
- Additionally, there are 8 hydrogen atoms (\rm H) in each molecule.

So, for every molecule of propane, we have a total of 3 carbon atoms and 8 hydrogen atoms.

Since the sample contains 12.8 moles of carbon atoms and there are 3 carbon atoms in each molecule, we can find the number of moles of propane molecules by dividing the number of moles of carbon atoms by 3:

12.8 moles C / 3 = 4.27 moles of C3H8

Now, we can calculate the total number of moles of atoms in the sample by multiplying the number of moles of propane molecules (4.27 moles) by the total number of atoms in each molecule (3 carbon atoms + 8 hydrogen atoms):

4.27 moles C3H8 * (3 + 8) = 42.7 moles of atoms

Therefore, the sample of propane contains a total of 42.7 moles of atoms.