Plonium crystallizes with a simple cubic structure. It has a dens...

Question

Plonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm3, a radius of 167 pm, and a molar mass of 209 g/mol. Use these data to calculate Avogadro's number (the number of atoms in one mole).

Accepted Answer

Hey everyone in this example we have a hypothetical element with the following radius. Were given the following molar mass and the following density. We need to estimate the value of avocados number. We should recall that avocados number is describing number of entities per mole. We also next want to recall our edge length of a simple cubic unit for a given element. And this is represented by L where it is going to equal two times our radius and this is per adam per unit cell. So for one atom per unit cell, recall that edge length should be in units of centimeters. So we're going to take the radius given to us as kilometers and convert from PICO meters to meters by recalling that are prefixed, PICO tells us we have 10 to the negative 12 power meters For one pick a meter. We're now able to cancel out pedometers and we want to go ahead and convert from meters to centimeters By recalling that for one m we have 10 to the negative second power centimeters. So now we're able to cancel out meters were left with centimeters for our edge length And we want to go ahead and also multiply this by two. Since this was our radius that we were converting two cm and multiplying by two will make this our edge length. So in doing so we should get a value equal to 3.12 times to the negative 8th power cm as our edge length. So our next step is to recognize that were given a value for density but we don't know volume. So we also need to calculate volume and recall that volume is going to be our edge length to the third power. So we would take 3.12 times 10 to the negative eighth power centimeters which we found above as our edge length and cube that So that we have our volume equal to a value of 3.0371. Sorry that's 7 1 Times 10 to the negative 23rd power cm cubed. So now that we have volume, we can go ahead and find avocados number. So beginning with our volume, we would say that we have a volume of For one unit cell 3.0371 times 10 to the negative 23rd power cubic centimeters. We are then going to multiply this by our density given in the prompt which for one cc is a value of 10.7 g were given the molar mass for our hypothetical element Where we have 196 g. And sorry we need to have cubic centimeters in the numerator. So we should have plugged in the density as one cc for 10.7 g. And so that way we would be able to cancel out cubic centimeters. And so now this is where we take our given molar mass from the prompt of 196 g For one mole of our hypothetical element. And now we're able to cancel out gramps. So our last conversion factor is to go from unit cells to atoms. So we would have for one unit cell which we actually want in the denominator so that it can cancel out. So for one atom we should say we have one unit cell and so we would go ahead and cancel out unit cells over here and here, leaving us with Adams per mole as our final units. And so now we can estimate avocados number which should equal a value of about 6.03 Times 10 to the 23rd power atoms per mole. And this would be our final answer here for avocados number. So this is our estimate to complete this example as our final answer. 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.

Plonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm3, a radius of 167 pm, and a molar mass of 209 g/mol. Use these data to calculate Avogadro's number (the number of atoms in one mole).

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