Hw Help E3

[Luke Schwuchow 14A]

Hello! I was just working on problem E3 "In a nanotechnology lab you might have the capability to manipulate individual atoms. The atoms on the left are gallium atoms (molar mass 70g.mol), and those on the right are atoms of astatine (molar mass 210g.mol). How many astatine atoms would the pan on the right have to contain for the masses on the two pans to be equal?" I was wondering if someone could explain why the correct answer is 3 and not 1? Since astatine has a molar mass that is 3 times as much as gallium, why wouldn't you only need 1 astatine and 3 gallium?

[Tomas Burgess 3F]

Hi, if you look at the diagram, it shows that there are 9 atoms of Gallium on the left side. As you said, the molar mass of Astatine is 3x the molar mass of Gallium, so you would need 3 Astatine atoms to balance the masses.

[405745446]

For this problem, I first counted the amount of gallium atoms that are in the diagram (which is 9). Next I converted the molar mass of both gallium and astatine into grams:
1mol *70g/1mol =70g per gallium atom
1mol* 210g/1mol = 210g per astatine atom
Then I multiplied the amount of gallium atoms times the mass of 1 gallium atom:
9*70g =630g
Lastly, I divided the total mass of the 9 gallium atoms by the mass of 1 astatine atom to figure out how many astatine atoms it'll take to balance the scale :
630g / 210g = 3 atoms of astatine.
The answer is 3 and not one because the total mass of the gallium is 630g because there are 9 atoms. 9*70g is 630g and the mass of one astatine is 210g, so you need 3 astatine atoms to get 630g which balances the scale.

[Mia Orr 3B]

I was confused about this problem too, but you just need to look at the diagram to see that there are 9 atoms of gallium on the left side. You are correct in that the molar mass of astanine is three times the molar mass of gallium, so in order to make the two masses equal you only need 3 atoms of astanine.

[Madison Kiggins 1E]

Hi, I was a bit confused on this question at first as well, but then I realized that you need to utilize the diagram. Since the diagram shows that there are 9 atoms of gallium on the left side, you will want to multiply the molar mass of gallium by 9, then divide that number by the molar mass of astatine to find the number of astatine atoms needed to make the two sides equal in terms of mass. This should give an answer of three astatine atoms. This makes sense since, like you mentioned, the molar mass of astatine is three times that of gallium, so you would only need 3 astatine atoms to be equal to 9 gallium atoms in terms of mass.