A given sample of caffeine, \( \mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} \), has \( 6.47 \times 10^{22} \) atoms of carbon. How many atoms of hydrogen in the same sample? a \( 6.47 \times 10^{22} \mathrm{H} \) atoms b \( 6.47 \times 10^{23} \mathrm{H} \) atoms c \( 5.18 \times 10^{22} \mathrm{H} \) atoms d \( 8.09 \times 10^{22} \mathrm{H} \) atoms

To find the number of hydrogen atoms in the sample of caffeine (\( \mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2} \)), we start with the information given: the sample has \( 6.47 \times 10^{22} \) atoms of carbon. Since caffeine has 8 carbon atoms for every molecule, we can find the number of caffeine molecules in the sample: \[ \text{Number of molecules} = \frac{6.47 \times 10^{22}}{8} = 8.09 \times 10^{21} \text{ molecules} \] Each caffeine molecule contains 10 hydrogen atoms. Therefore, the total number of hydrogen atoms is: \[ \text{Total H atoms} = 8.09 \times 10^{21} \, \text{molecules} \times 10 \, \text{H/molecule} = 8.09 \times 10^{22} \text{ H atoms} \] Thus, the correct answer is: d \( 8.09 \times 10^{22} \mathrm{H} \) atoms For a little extra fun with caffeine: Did you know that caffeine is not just a popular pick-me-up? It's also a fascinating substance with a history that dates back centuries. Originally derived from coffee beans, caffeine has been consumed in various forms by different cultures, allowing humans to boost their alertness and productivity long before energy drinks were a thing! And speaking of productivity, remember to stay hydrated! Caffeine is a diuretic, which means it makes you urinate more frequently. While it's fantastic for that jolt of energy, it also leads to increased fluid loss. So, make sure to balance your caffeine intake with plenty of water to keep your hydration levels up. Cheers (to your health)!