Iron crystallizes in a body-centered cubic unit cell with an
edge length of 287 pm. Iron metal has a density of 7.86 gcm3
and a molar mass of 55.85 g. Calculate a value for Avogadro's
number.

Question

Iron crystallizes in a body-centered cubic unit cell with an 
edge length of 287 pm. Iron metal has a density of 7.86 g>cm3 
and a molar mass of 55.85 g. Calculate a value for Avogadro's 
number.

Accepted Answer

though in this problem we're told the edge length of the body, center cubic unit cell. Uh, vanadium is 303 PICO meters. The density and mass, vanadium is 6.11 g per cubic centimeter and 50.94 g per mole respectfully were asked to estimate the value for avocados number. So recall that I've got his number is 6.02, 2 Times 10 to the 23rd particles per mole. In this case we have vanadium. So this would be six point oh 22 times 10 to 23rd Adam's pro bowl. So this is what we're trying to find the number of atoms per mole. Given that we have a cube, we could find its volume by taking the edge length and keeping it once we know the volume, we can make use of the density to convert from volume to mass. And once we know mass we can use the more mass to convert from master moles and moles are the units that we need in the denominator to calculate our estimated value of avocados number. So let's begin with finding the volume. The volume then is equal to the edge length cubed. We're told the edge length is 303 people meters. And we want to convert our units from cubic kilometers two cubic centimeters. We have one times 10 to the 12 people meters. Everyone meet her. And we need to queue both of those to get our units to cancel. And one m is equivalent to 100 cm when they hear both of those. So that our units on top and bottom cancel. This works out to 2.78 Times 10 to the 23rd cubic centimeters. Now that we know our volume. We can make use of the density and the molar mass to get to our units of moles. You have 2.78 Times 10 -23. Keep examiners making use of the density. We have 6.11 g per cubic centimeters. We set it up so our units of cubic centimeters cancels on top and bottom. We then make use of the molar mass. We have 50.94 g. Very more grams goes in the denominator so it cancels with grams in the numerator. And this works out to 3.34 24. No, we have the value that needs to go into the denominator of our estimated value for avocados number. You're told in the problem that we have a body centered cubic unit cell. So for the body center cubic unit cell recall, we have Adams at each of the four corners of the cubic unit cell. And since the body center cubic unit cell, we also have one in the center. Each of these atoms at the corners are shared with eight other neighboring unit cells. So that means we have 1/8 of an atom. So we have eight corners Since 1/8 of an atom We have one Adam with the corners And we have one Adam at the center. so we have a total of two atoms, the car to atoms and divided by are moles that we found Just 3.3, 4 times 10 -24 moles. This works out to 5.99, 10% to 23 Adams caramel and so our estimated value avocados number is 5.99, 10, 10 to 23rd Adams per mole, which is fairly close to our known value of six point oh 22 times 10, 23rd Adams per mole. I hope this video always helpful. Thanks Goodbye.

Iron crystallizes in a body-centered cubic unit cell with an edge length of 287 pm. Iron metal has a density of 7.86 g>cm3 and a molar mass of 55.85 g. Calculate a value for Avogadro's number.

Verified Solution

Key Concepts

Body-Centered Cubic (BCC) Structure

Density and Molar Mass Relationship

Avogadro's Number