Final answer:
The mass of a C₃H₈ sample with 7.68 x 10²⁴ H atoms is approximately 7.03495 grams, calculated by first finding the number of moles of H, then the number of moles of C₃H₈, and finally multiplying by the molar mass of C₃H₈.
Step-by-step explanation:
A sample of C₃H₈ has 7.68 x 10²⁴ H atoms. To calculate the mass of the sample in grams, we must first determine the number of moles of hydrogen atoms. Since there are 6.02 x 10² atoms in 1 mole, we can use this to find the moles of H atoms:
- Number of moles of H = (7.68 x 10²⁴ atoms) / (6.02 x 10² atoms/mol) = 1.276 moles H
Since C₃H₈ has 8 H atoms per molecule, we divide the number of moles of H by 8 to find the number of moles of C₃H₈:
- Number of moles of C₃H₈ = 1.276 moles H / 8 = 0.1595 moles C₃H₈
Now, we multiply the number of moles of C₃H₈ by its molar mass, 44.1 g/mol, to get the mass:
- Mass of C₃H₈ = 0.1595 moles * 44.1 g/mol = 7.03495 grams
Therefore, the mass of the C₃H₈ sample is approximately 7.03495 grams.