How to get the atomic weight of O 16g/mole to amu?

[HCverma]

Homework Statement

How to get the atomic weight of O atom 16g/mole to amu?

Homework Equations

The Attempt at a Solution

As I know, 1 mole of O atoms = 16g
6.023 x 10^23 O atoms = 16g
So, 1 O atom = 16 x 1/6.023 x 10^23
1 atom of O = 16 amu [1 amu = 1/ Avogadro's number]
But I am confused about the units here. How is it possible 16g to 16 amu?

 

[nomadreid]

First, your use of "=" is a bit loose. For example, a mole of oxygen atoms does not "equal" 16 grams, a mole of oxygen atoms "weighs" 16 grams. The same for the other entries.
That technicality aside, your solution is correct, but if you write down your units a bit more carefully, the confusion should go away.
That is, your equation is
16 amu / oxygen atom = 16 grams / mole of oxygen atoms.
Let me be lazy and write N for Avogadro's Number
Then you can either multiply the left hand side times N/N, and since N*amu = gram, and N* atom = mole of atoms, then
16 grams / mole of oxygen atoms = 16 grams / mole of oxygen atoms.
Equivalently, multiply the right-hand side of
16 amu / oxygen atom = 16 grams / mole of oxygen atoms
times ((1/N)/(1/N)) to get
16 amu / oxygen atom =16 amu / oxygen atom
A third way, still equivalent to the other two, is to convert the mole to atoms, and divide.
Hopefully this clears things up. If not, ask some more, being more precise about your confusion.

 

[HCverma]

Then you can either multiply the left hand side times N/N, and since N*amu = gram, and N* atom = mole of atoms, then
16 grams / mole of oxygen atoms = 16 grams / mole of oxygen atoms.
Equivalently, multiply the right-hand side of
16 amu / oxygen atom = 16 grams / mole of oxygen atoms
times ((1/N)/(1/N)) to get
16 amu / oxygen atom =16 amu / oxygen atom
A third way, still equivalent to the other two, is to convert the mole to atoms, and divide.
Hopefully this clears things up. If not, ask some more, being more precise about your confusion.

Still, I don't understand the steps above. Could you get it a little bit easier, please?

 

[nomadreid]

OK, in the absence of your responding to my request to indicate what the precise difficulty is, I will start from the assumption that you do not understand the "equation" 1 atom of O = 16 amu . Perhaps one of your main problems is that you have an error when you write
"1 amu = 1/ Avogadro's number"
This is incorrect! 1 amu = 1 gram/Avogadro's Number, approximately 1.6 x 10^-24 grams.
With this in mind, I replay the last option.
Write your equation more carefully (replacing "=" by "has the mass")
The mass per 1 atom of O = 16 grams/mole = 16 amu = 16*(1.6 x 10^-24 grams) = 2.56 x 10^-23
Convert "mole" to Avogadro's Number, and make explicit that the units involved in the mole are oxygen atoms, and you have
16 grams/(6 x 10^-23 oxygen atoms) = 2.56 x 10^-23 grams/ Oxygen atom
which works out.
Does this help?

 

[HCverma]

OK, in the absence of your responding to my request to indicate what the precise difficulty is, I will start from the assumption that you do not understand the "equation" 1 atom of O = 16 amu . Perhaps one of your main problems is that you have an error when you write
"1 amu = 1/ Avogadro's number"
This is incorrect! 1 amu = 1 gram/Avogadro's Number, approximately 1.6 x 10^-24 grams.
With this in mind, I replay the last option.
Write your equation more carefully (replacing "=" by "has the mass")
The mass per 1 atom of O = 16 grams/mole = 16 amu = 16*(1.6 x 10^-24 grams) = 2.56 x 10^-23
Convert "mole" to Avogadro's Number, and make explicit that the units involved in the mole are oxygen atoms, and you have
16 grams/(6 x 10^-23 oxygen atoms) = 2.56 x 10^-23 grams/ Oxygen atom
which works out.
Does this help?

Yes, Still I don't understand steps of how to get the mass of O atom 16g/mole to 16 amu?

 

[nomadreid]

Please let me know which of the steps I put in my last post you do not understand.

 

[HCverma]

16 amu / oxygen atom = 16 grams / mole of oxygen atoms.
Let me be lazy and write N for Avogadro's Number
Then you can either multiply the left hand side times N/N, and since N*amu = gram, and N* atom = mole of atoms, then
16 grams / mole of oxygen atoms = 16 grams / mole of oxygen atoms.
Equivalently, multiply the right-hand side of
16 amu / oxygen atom = 16 grams / mole of oxygen atoms
times ((1/N)/(1/N)) to get
16 amu / oxygen atom =16 amu / oxygen atom
[/QUOTE]
I don't understand the steps above.

 

[Dale]

I don't understand the steps above.

Which specific step? We can’t help you if you can’t tell us what is the problem.

 

[HCverma]

Which specific step? We can’t help you if you can’t tell us what is the problem.

In the thread #2

 

[Borek]

You were asked several times to explain which which part of the whole post containing multiple steps is a problem. Just by repeating "I don't understand" and not explaining which part stops you from following the line of reasoning won't get us far.

 

[Dale]

I am sorry @HCverma. We cannot help you if you refuse to clarify.

This thread is closed, so that the homework helpers can focus their efforts on people willing to do the necessary work.