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On problem E3, if a mole of gallium weighs 70.0 g and a mole of astatine weighs 210.0 g wouldn’t you need 3 times as many atoms of astatine as gallium for them to have the same mass? In the problem, it asks how many atoms of astatine would need to be added to the nine already present to equal the mass of 9 gallium atoms. It appears to me that you would need 3 times as many atoms of astatine to have the equivalent mass, however the solution manual states only 3 additional atoms of astatine are needed to have the same weight as the 9 atoms of gallium. Could someone explain to me why only 3 atoms are needed and not 3 times as many atoms? What’s part of my logical thinking in translation to my math is wrong?
For that question, I think since 1 mol of astatine has 3 times the mass of 1 mole of gallium, then only 3 astatine atoms would have to be added on the right for them to have the same mass. If you had 3 times the amount of gallium atoms, then the mass on the right would be 9 times as much mass as the left. That's why if 9 atoms of gallium are on the left, then only 3 atoms of astatine are needed (since it has three times the mass). Correct me if I'm wrong, but I believe that's the reason why. If you had more astatine atoms than gallium atoms, the right side would have too much mass.
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