DAT Bootcamp GC Test #9 Question #2

[dentaltab4life]

I was particularly confused with this question due to the fact that the answer I got when solving the problem was not one of the available choices. Why, after finding that the number of total Al2O3 atoms is ~6.02*10^21, do we multiply that number by 3 to get the number of O atoms in the molecule? This seems illogical to me considering that the answer we get from this ends up saying that we have 1.8*10^22 oxygen atoms, which is somehow more than the number of atoms in the entire molecule. From my understanding it would make more sense to divide the total number of atoms (6.02*10^21) by the number of atoms in the molecule (5) and then multiply this number by the number of oxygen atoms in the molecule (3). This tells us that the number of atoms of oxygen present in 1g of Al2O3 is 3.612*10^21. This answer makes more sense considering that it is a fraction of the total number of molecules present (6.02*10^21). Can someone please explain why my reasoning is wrong and why DAT Bootcamp's answer is correct?

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[8_man]

Each molecule of Al2O3 contains 3 oxygen atoms. So, if you have 5 molecules of Al2O3 and you count up all the O's, you'll have 15 oxygen atoms–which is the same thing as multiplying the # of molecules of Al2O3 by 3.

What you're doing, by dividing by 5 atoms and multiplying by 3 oxygen atoms, is something used to determine % composition of a compound (this is something I'd expect to use in a partial pressure question). This is incorrect to use in this situation, and it is irrelevant to what the question is asking.

Hope that helps!

 

[dentaltab4life]

Each molecule of Al2O3 contains 3 oxygen atoms. So, if you have 5 molecules of Al2O3 and you count up all the O's, you'll have 15 oxygen atoms–which is the same thing as multiplying the # of molecules of Al2O3 by 3.

I was stating that there are 5 atoms in the molecule Al2O3, 2 Al's and 3 O's. Based on the math we find that there are 6.02*10^21 total atoms in 1 g of Al2O3. Why would we multiply this number by 3 to find the number of oxygen atoms? Through my interpretation that would result in an incorrect answer. Instead it made more sense to me to divide 6.02*10^21 by the number of atoms in the molecular formula Al2O3, which as I stated was 5. After finding how many atoms are in one of the atoms in the molecule of Al2O3, I then multiplied that particular number by 3 to find the total number of oxygen atoms in the 1g of Al2O3.

 

[8_man]

Hey sorry! Just updated my answer to reply to the second part of your question. Let me know if that makes sense.

 

[dentaltab4life]

Interesting. I still don't completely understand the reasoning behind the answer. But I guess I'll have to accept it as is. Thank you for your help!

 

[8_man]

I was stating that there are 5 atoms in the molecule Al2O3, 2 Al's and 3 O's. Based on the math we find that there are 6.02*10^21 total atoms in 1 g of Al2O3.

The value we found (6.02*10^21) was for molecules of Al2O3 in a 1g sample, not for the individual atoms that make up Al2O3.

Don't sweat it if you don't get it right away. But once you understand this, everything will make sense.

 

[dentaltab4life]

The value we found (6.02*10^21) was for molecules of Al2O3 in a 1g sample, not the individual atoms that make up Al2O3.

That actually clears things up for me. 6.02*10^21 is the number of molecules Al2O3. This is composed of 3 O's and 2 Al's. That is why you multiply by 3 to find the number of Oxygens by themselves. Thanks! I think I was trying to over-analyze it.

 

[8_man]

That actually clears things up for me. 6.02*10^21 is the number of molecules Al2O3. This is composed of 3 O's and 2 Al's. That is why you multiply by 3 to find the number of Oxygens by themselves. Thanks! I think I was trying to over-analyze it.

Glad it makes sense now. As some parting advice, I recommend that you become really proficient at unit analysis. Once you make it a habit to follow your units, gen chem will be a breeze. I made an example of what it'd look like, step by step, for this problem. Overall, all the unwanted units will cancel out and you're only left with what the question is asking for (atoms of oxygen).