Final answer:
To find the number of atoms of nitrogen in 34.5g of caffeine (C8H10N4O2), we calculate moles of caffeine and multiply by 4 (for nitrogen atoms per molecule) and Avogadro's number. The closest answer to our calculation is option (b) 6.02 × 10²³ atoms of nitrogen.
Step-by-step explanation:
To determine how many atoms of nitrogen are present in 34.5g of caffeine (C8H10N4O2), we first need to calculate the number of moles of caffeine. Using the molecular formula C8H10N4O2, we find the molar mass of caffeine to be (8 × 12.01 g/mol for carbon) + (10 × 1.01 g/mol for hydrogen) + (4 × 14.01 g/mol for nitrogen) + (2 × 16.00 g/mol for oxygen) = 194.19 g/mol. Dividing the mass of caffeine by its molar mass gives us the number of moles:
34.5 g ÷ 194.19 g/mol = 0.1777 mol
Each molecule of caffeine contains 4 nitrogen atoms. To find the total number of nitrogen atoms, we multiply the number of moles of caffeine by 4 (for the nitrogen atoms in each molecule) and then by Avogadro's number (6.022 × 10²³ atoms/mol):
0.1777 mol × 4 atoms/mol × 6.022 × 10²³ atoms/mol = 4.28 × 10²³ atoms of nitrogen
Since none of the answer choices exactly match this value, we can conclude that there may have been an error in the question. Based on the calculation method, however, option (b) 6.02 × 10²³ atoms, would be the answer closest to the calculated number of nitrogen atoms.