Calculate the mass of vanadium(V) oxide (V2O5) that contains a billion (1.000e9) vanadium atoms. Be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.

1.510 × 10⁻¹³ g

Explanation:

Step 1: Given data

Number of atoms of vanadium: 1.000 × 10⁹ atoms

Step 2: Calculate the molecules of V₂O₅ that contain 1.000 × 10⁹ atoms of V

Each molecule of V₂O₅ has 2 atoms of V.

1.000 × 10⁹ atom V × (1 molecule V₂O₅/2 atom V) = 0.5000 × 10⁹ molecule V₂O₅

Step 3: Calculate the moles corresponding to 0.5000 × 10⁹ molecules of V₂O₅

We will use Avogadro's number: there are 6.022 × 10²³ molecules of V₂O₅ in 1 mole of V₂O₅.

0.5000 × 10⁹ molecule × (1 mol/6.022 × 10²³ molecule) = 8.303 × 10⁻¹⁶ mol

Step 4: Calculate the mass corresponding to 8.303 × 10⁻¹⁶ moles of V₂O₅

The molar mass of V₂O₅ is 181.88 g/mol.

8.303 × 10⁻¹⁶ mol × 181.88 g/mol = 1.510 × 10⁻¹³ g

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