Final answer:
The total number of moles of atoms represented by one mole of (CH3)2NH is 10, since each molecule contains 10 atoms (2 carbons, 7 hydrogens, and 1 nitrogen), and one mole of the compound will have Avogadro's number of these atoms.
Step-by-step explanation:
The question asks for the total number of moles of atoms represented by one mole of (CH3)2NH. To find this, we must first determine the total number of atoms in one molecule of the compound and then use that to find the number of moles of atoms in one mole of the compound.
The molecular formula (CH3)2NH contains two CH3 groups and one NH group. Each CH3 group has 1 carbon and 3 hydrogens, so 2 CH3 groups contain 2 carbons and 6 hydrogens. The NH group has 1 nitrogen and 1 hydrogen. Therefore, one molecule of (CH3)2NH contains:
2 carbons
7 hydrogens (6 from CH3 groups + 1 from NH)
1 nitrogen
In total, there are 2 (carbons) + 7 (hydrogens) + 1 (nitrogen) = 10 atoms in one molecule of (CH3)2NH. Since one mole of any substance contains Avogadro's number of entities (in this case, molecules), one mole of (CH3)2NH will contain 10 moles of atoms.
The correct answer is therefore 3) 10.