Calculate the mass of vanadium(V) oxide (V2O5) that contains a trillion (1.00*10^12) vanadium atoms.
The Correct Answer and Explanation is:
Answer:
The mass of vanadium(V) oxide (V₂O₅) that contains 1.00 × 10¹² vanadium atoms is approximately:
0.0810 mg
Explanation
To determine the mass of vanadium(V) oxide (V₂O₅) that contains 1.00 × 10¹² vanadium atoms, we follow a step-by-step stoichiometric approach based on atomic and molar relationships.
Step 1: Determine the number of moles of vanadium atoms
The number of atoms in a mole (Avogadro’s number) is: 6.022×1023 atoms/mol6.022 \times 10^{23} \text{ atoms/mol}
So the number of moles of vanadium atoms is: 1.00×1012 atoms6.022×1023 atoms/mol=1.661×10−12 mol\frac{1.00 \times 10^{12} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 1.661 \times 10^{-12} \text{ mol}
Step 2: Determine moles of V₂O₅ needed
Each molecule of vanadium(V) oxide (V₂O₅) contains 2 vanadium atoms.
So, the number of moles of V₂O₅ required is: 1.661×10−122=8.307×10−13 mol\frac{1.661 \times 10^{-12}}{2} = 8.307 \times 10^{-13} \text{ mol}
Step 3: Calculate the molar mass of V₂O₅
- Vanadium (V) = 50.94 g/mol × 2 = 101.88 g/mol
- Oxygen (O) = 16.00 g/mol × 5 = 80.00 g/mol
- Molar mass of V₂O₅ = 101.88 + 80.00 = 181.88 g/mol
Step 4: Calculate the mass
Mass=moles×molar mass=(8.307×10−13)×181.88\text{Mass} = \text{moles} \times \text{molar mass} = (8.307 \times 10^{-13}) \times 181.88 Mass=1.511×10−10 g=0.0000001511 g=0.0810 mg\text{Mass} = 1.511 \times 10^{-10} \text{ g} = 0.0000001511 \text{ g} = \boxed{0.0810 \text{ mg}}
This very small mass highlights how many atoms are packed in even minuscule amounts of chemical compounds. This calculation is important in nanotechnology, analytical chemistry, and fields where trace quantities of materials are used or measured.
