Calculate the mass of vanadium(V) oxide (V2O5) that contains a million (1.000 × 106) vanadium atoms. Be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.
The Correct Answer and Explanation is:
Correct Answer:
The mass of vanadium(V) oxide (V₂O₅) that contains 1.000 × 10⁶ vanadium atoms is:
2.517 × 10⁻¹⁷ g
Detailed Explanation
To calculate the mass of vanadium(V) oxide (V₂O₅) containing 1.000 × 10⁶ vanadium atoms, we can follow a step-by-step method using stoichiometry, atomic masses, and Avogadro’s number.
Step 1: Understand the Composition of V₂O₅
- The chemical formula V₂O₅ tells us that:
- 1 mole of V₂O₅ contains 2 moles of vanadium (V) atoms.
- 1 mole of V₂O₅ contains 5 moles of oxygen (O) atoms.
So, if we know the number of vanadium atoms, we can determine how many moles of V₂O₅ they belong to.
Step 2: Use Avogadro’s Number
Avogadro’s number = 6.022 × 10²³ atoms/mol
So, the number of moles of vanadium atoms is: mol V=1.000×106 atoms6.022×1023 atoms/mol=1.661×10−18 mol\text{mol V} = \frac{1.000 \times 10^6 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 1.661 \times 10^{-18} \text{ mol}
Since each mole of V₂O₅ contains 2 mol V, the number of moles of V₂O₅ is: mol V₂O₅=1.661×10−182=8.306×10−19 mol\text{mol V₂O₅} = \frac{1.661 \times 10^{-18}}{2} = 8.306 \times 10^{-19} \text{ mol}
Step 3: Molar Mass of V₂O₅
- Atomic mass of V = 50.94 g/mol
- Atomic mass of O = 16.00 g/mol
So, molar mass of V₂O₅: (2×50.94)+(5×16.00)=101.88+80.00=181.88 g/mol(2 \times 50.94) + (5 \times 16.00) = 101.88 + 80.00 = 181.88 \text{ g/mol}
Step 4: Calculate Mass
mass=mol V₂O₅×molar mass=(8.306×10−19)×181.88=2.517×10−17 g\text{mass} = \text{mol V₂O₅} \times \text{molar mass} = (8.306 \times 10^{-19}) \times 181.88 = 2.517 \times 10^{-17} \text{ g}
Final Answer:
2.517 × 10⁻¹⁷ g of V₂O₅ contains 1.000 × 10⁶ vanadium atoms.
