Final answer:
The mass of vanadium(V) oxide containing one million vanadium atoms is approximately 3.02 × 10^-16 grams, calculated using the molar mass and Avogadro's number.
Step-by-step explanation:
To calculate the mass of vanadium(V) oxide that contains one million vanadium atoms, we first need to know the formula for vanadium(V) oxide, which is V2O5. The molar mass of V2O5 is calculated by summing the atomic masses of 2 vanadium atoms and 5 oxygen atoms. Using the provided information, the atomic mass of vanadium (V) is 50.9415 g/mol, and the standard atomic mass of oxygen (O) is approximately 16 g/mol. Therefore, the molar mass of V2O5 is (2 × 50.9415) + (5 × 16) = 181.883 g/mol.
Next, since 1 mole of V2O5 contains Avogadro's number of vanadium atoms (approximately 6.022 × 1023 vanadium atoms), to find the number of moles that contains one million vanadium atoms, divide 1,000,000 by Avogadro's number:
Moles of vanadium = 1,000,000 vanadium atoms × (1 mole / 6.022 × 1023 vanadium atoms) = 1.66 × 10-18 moles of V2O5
Finally, to get the mass of V2O5 containing one million vanadium atoms, multiply the moles of V2O5 by its molar mass:
Mass of V2O5 = 1.66 × 10-18 moles × 181.883 g/mol = 3.02 × 10-16 g
Therefore, the mass of vanadium(V) oxide containing one million vanadium atoms is approximately 3.02 × 10-16 grams.