Final answer:
To estimate the number of molecules that make up Earth with an average molecular mass of 30 g/mol, calculate the total mass of Earth in grams, determine the number of moles, and then multiply by Avogadro's number. The calculated number is about 1.2 × 1050 molecules, which is larger than the provided options. However, the closest estimate among the given choices is (d) 1046 molecules.
Step-by-step explanation:
The question asks us to estimate the number of molecules that make up Earth, given an average molecular mass of 30 g/mol. To calculate this, we need to first determine the mass of the Earth and then the number of moles of molecules, since we know from the provided information that there are on the order of 1024 objects per mole.
The mass of the Earth is about 5.97 × 1024 kg. Converting kilograms to grams (1 kg = 1000 g), the mass of the Earth is approximately 5.97 × 1027 g. Using the provided average molecular mass (30 g/mol), we can then calculate the number of moles in Earth:
Moles of Earth = Total mass of Earth / Average molecular mass
= (5.97 × 1027 g) / (30 g/mol)
= 1.99 × 1026 mol
Since there are approximately 6.022 × 1023 molecules per mole (Avogadro's number), we multiply the number of moles by this constant to get the number of molecules:
Molecules of Earth = Moles of Earth × Avogadro's number
= 1.99 × 1026 mol × 6.022 × 1023 molecules/mol
= 1.2 × 1050 molecules
This number is significantly larger than the answer choices given, suggesting there may be an error in the assumptions or the answer choices provided. However, among the options given, the closest estimate would be choice (d) 1046 molecules.