(a) The unified atomic mass unit (u) is used to represent the extremely small mass of atoms. How many grams are equivalent to 1 u?

Video transcript

Hi everyone. This problem reads. Imagine if the atomic mass unit is now defined as 1/4 of the mass of a oxygen 16 adam atomic mass of oxygen 16 equals 15.995 g per mole. Using this new definition. How many grams are equal to one atomic mass unit. Okay, so this is what we want to solve here. And we know that we are starting with 15.995 g per mole of oxygen 16. So let's go ahead and write out what we're starting with. Alright, so we have 15. g Permal of oxygen 16. And our goal is we want to use this new definition to figure out how many grams are equal to one atomic mass unit. Alright, so Now we know we have units of g per mole. And we want to go from g per mole, 2g per atom by going from grams per mole. two g per atom will be able to figure out our atomic mass unit. So let's start here. Alright, so we have grams per mole. We want to go to grams per atom. So that means we want our molds to cancel out. Okay. And one thing we're going to need to remember is avocados number and avocados number tells us that there are 6.02, 2 times 10 to the 23 entities per one. More of entities. Okay. And entities can mean a variety of things and those things include atoms, ions, molecules, particles and formula units. So we know that we want to go from 15. g of oxygen. 16 two g per mole of oxygen 16 2 atoms. Okay, so our entity here is Adam. So what that means is in one mole there is 6.022 times 10 to the 23 Atoms. Alright, so let's go ahead and write that out. And one more. There is 6.22 times 10 to the 23 atoms. Because Adams is our entity. Alright, so here grams of oxygen 16. Excuse me, moles of oxygen 16 cancel. And we're left with the units of grams per atom, which is what we wanted. So let's go ahead and do this calculation. We're going to take 15.995 and divide it by 6. times 10 to the 23 atoms. And we get an answer of 2. times 10 to the negative g per atom. So now that we know how many grams per atom we have. We want to go from grams per atom. Two atomic mass unit. And in the problem we're told that the new definition is now defined as 1/4 of the mass of oxygen 16 atom. So that means one atomic mass unit is going to equal 1/4 times the mass. We just calculated which is the grams per atom. So we're going to take that and multiply it by 2. times 10 To the negative Adams. Excuse me, grams. Okay. And well, that's g per atoms. Okay, so we'll just write that out. So once we do this calculation we get 4.150 times To the -25 g. So this is the using the new definition. This is how many grams are equal to one atomic mass unit. Okay, so that is the answer to this problem. One atomic mass unit is equal to 4.150 times 10 to the negative 25 g. That's it for this problem. I hope this was helpful.