Final answer:
To find the mass of forsterite containing a million magnesium atoms, calculate the average atomic mass of Mg from its isotopes, find the number of moles corresponding to a million atoms, and then multiply by the molar mass of forsterite.
Step-by-step explanation:
To calculate the mass of forsterite that contains a million magnesium atoms, we need to first calculate the average mass of a magnesium (Mg) atom by taking into account the different isotopes of magnesium and their relative abundances. The average mass of a Mg atom can be calculated by summing the products of the mass of each isotope and its relative abundance. The average atomic mass (amu) of Mg can be expressed as:
(0.7870 × 23.98 amu) + (0.1013 × 24.99 amu) + (0.1117 × 25.98 amu)
Once we have the average atomic mass of Mg, we need to know the number of Mg atoms in a mole (…Avogadro's number, 6.022×10²³ atoms per mole). Finally, we multiply the number of moles by the molar mass of forsterite, which is 140.7 g/mol, to find the mass of forsterite containing that many Mg atoms. The calculation should yield a result with a unit of grams (g) and the answer must be rounded to the appropriate number of significant figures based on the least precise measurement in the calculation, as per the steps for accurate scientific calculations.