Questions: Calculate the mass of forsterite (Mg2SiO4) that contains a million (1.000 x 10^6) magnesium atoms. Be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.

Solution Steps

First, we need to find the number of moles of magnesium atoms in \(1.000 \times 10^6\) atoms. Using Avogadro's number (\(N_A = 6.022 \times 10^{23}\) atoms/mol):

\[ \text{Number of moles of Mg} = \frac{1.000 \times 10^6 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 1.6605 \times 10^{-18} \text{ mol} \]

Forsterite (\(\mathrm{Mg}_2\mathrm{SiO}_4\)) contains 2 magnesium atoms per formula unit. Therefore, the number of moles of forsterite is half the number of moles of magnesium atoms:

\[ \text{Number of moles of forsterite} = \frac{1.6605 \times 10^{-18} \text{ mol}}{2} = 8.3025 \times 10^{-19} \text{ mol} \]

The molar mass of forsterite (\(\mathrm{Mg}_2\mathrm{SiO}_4\)) is calculated by summing the molar masses of its constituent elements:

• Mg: \(24.305 \text{ g/mol}\)
• Si: \(28.085 \text{ g/mol}\)
• O: \(16.00 \text{ g/mol}\)

\[ \text{Molar mass of } \mathrm{Mg}_2\mathrm{SiO}_4 = 2 \times 24.305 + 28.085 + 4 \times 16.00 = 140.69 \text{ g/mol} \]

Finally, we calculate the mass of forsterite by multiplying the number of moles of forsterite by its molar mass:

\[ \text{Mass of forsterite} = 8.3025 \times 10^{-19} \text{ mol} \times 140.69 \text{ g/mol} = 1.168 \times 10^{-16} \text{ g} \]

Final Answer