Final answer:
The mass of the CH4 sample with 7.28 x 10^22 molecules is approximately 1.94 grams. This is found by calculating the number of moles and then using the molar mass of methane.
Step-by-step explanation:
To calculate the mass of a sample of CH4 when there are 7.28 x 1022 molecules, we first need to find the number of moles in the sample. Since 1 mole of any substance contains approximately 6.022 x 1023 molecules (Avogadro's number), the number of moles of CH4 is calculated by dividing the number of molecules by Avogadro's number:
(7.28 x 1022) ÷ (6.022 x 1023) = 0.1209 moles of CH4
Next, we need to know the molar mass of CH4. Carbon has an atomic mass of about 12.01 grams per mole, and hydrogen has an atomic mass of about 1.01 grams per mole. Therefore, for methane (CH4), the molar mass is (12.01 + (4 x 1.01)) = 16.05 grams per mole. To find the mass of our sample in grams, we multiply the number of moles by the molar mass of CH4:
0.1209 moles x 16.05 g/mole = 1.94145 grams
Therefore, a sample of CH4 containing 7.28 x 1022 molecules has a mass of approximately 1.94 grams.