An unknown metal is found to have a density of 7.8748 g/cm3
and t...

Question

An unknown metal is found to have a density of 7.8748 g/cm3
and to crystallize in a body-centered cubic lattice. The edge of the
unit cell is 0.28664 nm. Calculate the atomic mass of the metal.

Accepted Answer

everyone in this example, we need to calculate the atomic mass of an unknown metal that has a body centered cubic lattice with a density of 6.11 g per cubic centimeter. We're told that the edge length of the unit cell is 0.30 point or 0. 48 nanometers. So we're going to first begin by taking our edge length and converting it from nanometers to centimeters. So we are given an edge length of 0.34 eight nanometers. We're going to convert from nanometers two centimeters by recalling that our prefix nano tells us that we have for one centimeter 10 to the seventh power nanometers. And so this is going to give us our new edge length in centimeters equal to 3.48 times 10 To the negative 8th power cm We want to find the volume of our lattice. So we're going to find our volume by taking our edge length which we represent by L to the third power since this is a cubic lattice. And so we would take since we know our edge length is in centimeters as 3.48 times 10 to the negative eighth power centimeters. We're going to place this to the third power to get our volume of our cubic lattice so that we get a volume equal to 2.83 times to the negative 23rd power cubic centimeters per unit cell as our volume. Now according to the prompt were given a density of this value here that I just circled. So because we recall that our formula for density is equal to mass divided by volume. And we need to calculate for atomic mass. We want to solve for em first. So we would say that our mass is going to equal our density from the prompt as 6.11 g per cubic centimeter. Multiplied by our volume, which we just calculated as 2.83 times 10 to the negative 23rd power cubic centimeters per unit cell. And so multiplying these two would give us our mass of our cubic cell equal to 1.73 times 10 to the negative 22nd power grams per unit cell. Now what we wanna do is recall that atomic mass also known as molar masses in units of grams per mole. So we need to get molds into our units here. Right now. We just have grams per unit cell. So this says Graham's Permal. So we want to go ahead and utilize avocados number as a conversion factor to find our molar mass. So we're going to take our mass that we found for unit cell being 1. times 10 to the negative 22nd powder power grams per unit cell. And we're going to multiply by our first conversion factor to go from our one unit cell which we recall can hold two atoms per cell. And then to get moles into our units. We're going to multiply bar second conversion factor where we're going to utilize avocados number, which we recall is 6.22 times 10 to the 23rd power atoms. And this is for one mole of our unknown metal. So now canceling out our units, we can get rid of unit cell here and we can get rid of atoms leaving us with grams per mole as our molar mass for unknown medal. And what we're going to get is a value for molar mass equal to five .20 times 10 to the first power g per mole, Which we can also say is equal to 52 zero g per mole as our final answer. So this would be our final answer here for our molar mass of our unknown metal. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

An unknown metal is found to have a density of 7.8748 g/cm3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is 0.28664 nm. Calculate the atomic mass of the metal.

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