Question

What amount (moles) is represented by each of these samples? a. \(150.0 \mathrm{~g} \mathrm{Fe}_{2} \mathrm{O}_{3}\) b. \(10.0 \mathrm{mg} \mathrm{NO}_{2}\) c. \(1.5 \times 10^{16}\) molecules of \(\mathrm{BF}_{3}\)

Short answer

a. \(0.939 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) b. \(2.17 \times 10^{-4} \mathrm{~mol} \mathrm{NO}_{2}\) c. \(2.49 \times 10^{-8} \mathrm{~mol} \mathrm{BF}_{3}\)

Step-by-step solution

a. Calculate the moles of Fe₂O₃.

To calculate the moles of Fe₂O₃, use the formula: moles = mass / molar mass First, find the molar mass of Fe₂O₃: Fe = 55.85 g/mol (for 2 Fe atoms = 2 x 55.85 g/mol) O = 16.00 g/mol (for 3 O atoms = 3 x 16.00 g/mol) Molar mass of Fe₂O₃ = 2(55.85 g/mol) + 3(16.00 g/mol) = 159.7 g/mol Now, determine the moles of Fe₂O₃: moles = 150.0 g / 159.7 g/mol = 0.939 mol

b. Calculate the moles of NO₂.

To calculate the moles of NO₂, use the formula: moles = mass / molar mass First, convert the mass of NO₂ from mg to g: 10.0 mg = 0.010 g Now, find the molar mass of NO₂: N = 14.01 g/mol O = 16.00 g/mol (for 2 O atoms = 2 x 16.00 g/mol) Molar mass of NO₂ = 14.01 g/mol + 2(16.00 g/mol) = 46.01 g/mol Determine the moles of NO₂: moles = 0.010 g / 46.01 g/mol ≈ 2.17 x 10^{-4} mol

c. Calculate the moles of BF₃.

To calculate the moles of BF₃, use Avogadro's number to convert the given number of molecules to moles: number of moles = number of molecules / Avogadro's number number of moles = (1.5 x 10^16 molecules) / (6.022 x 10^23 molecules/mol) ≈ 2.49 x 10^{-8} mol