If the atomic weight of an element is x, what is the mass in grams of 3.17 * 1020 atoms of the element?

Video transcript

Hi everyone for this problem it reads how many grams of an element are in 6.12 times 10 to the 19th atoms of this element. Let y be the atomic weight of the element. Okay, So here we want to figure out grams of an element and our starting point is the number of atoms. So let's go ahead and write down our starting point. So we have 6.12 times 10 to the 19th Adams. And our goal is to go from Adams two g. Okay, so because our our entity is Adam's, something we need to recall is the definition for of a God Rose number. Okay, and the definition of abogados number is that there are 6.22 times 10 to the 23 entities per one mole of entities. Okay. And entities can mean a number of things and those are atoms, ions, molecules, particles and formula units. Okay, so with the problem above, we know our entity is atoms and so what that means is according to average joe's number for every one mole Of so for every one mole there is 6.02, 2 times 10 to the 23rd atoms. Okay, because the definition is per one mole and our entity here is atoms. So we want to go from atoms to grams. And so that means we need to first go to moles. Alright, so that we can get rid of the atoms so that the atoms cancel. So when we set this up we'll put the atoms at the bottom so there is for every one mole There is 6.02, 2 times 10 to the 23 atoms. Okay, so now our units of adam's cancel and we're left in moles. So now we need to go from moles to grams. Okay? And in order to do that, we need moller mass. And then the problem they tell us to let y be the atomic weight of the element. So that means for every one mole of our element, the atomic weight is why grams. Okay, so now our units of moles cancel and we're left with grams, which is the unit that we want. The um we want the grams of the element. Okay, so we'll go ahead and solve. So we'll take 6.12 times 10 to the 19th and divide it by 6.22 times 10 to the 23. And we get an answer of 1.2 times 10 to the negative. Four y grams. Okay, so this is going to be our final answer. This is the grams of an element. That this is How many grams of an element are in 6.1? Two times 10 to the 19th atoms. Okay, so that is it for this problem? I hope this was helpful