The metal vanadium crystallizes in a body-centered cubic lattice.If the density of vanadium is 6.11 g/cm³,what is the unit cell volume? A) 5.44 × 10⁵ pm³ B) 1.99 × 10⁵ pm³ C) 2.77 × 10⁷ pm³ D) 1.38 × 10⁷ pm³ E) 3.98 × 10⁵ pm³

Question

Quizplus · Accepted Answer

First, we need to determine the atomic weight of vanadium (V) which is 50.94 g/mol.

To find the unit cell volume, we can use the formula:

density = (mass of 1 unit cell * Avogadro's number) / (volume of 1 unit cell * atomic weight)

We are looking for the volume of 1 unit cell, so we can rearrange the formula as:

volume of 1 unit cell = (mass of 1 unit cell * Avogadro's number) / (density * atomic weight)

The mass of 1 unit cell can be found by multiplying the atomic weight by the mass of one atom in grams and dividing by Avogadro's number:

mass of 1 unit cell = (50.94 g/mol * 1 atom/6.022 x 10^23 atoms/mol) = 8.461 x 10^-23 g

Plugging in the given values for density and atomic weight:

volume of 1 unit cell = (8.461 x 10^-23 g * 6.022 x 10^23) / (6.11 g/cm^3 * 50.94 g/mol)

Simplifying the expression:

volume of 1 unit cell = 2.767 x 10^-23 cm^3

Converting to picometers:

volume of 1 unit cell = 2.767 x 10^-13 pm^3

The closest answer choice is C, 2.77 × 10^17 pm^3.

The Metal Vanadium Crystallizes in a Body-Centered Cubic Lattice