Atomic Mass of Element X: Solving with John Dalton Ratios

[dshipp17]

I believe that this question may be solved by the John Dalton ratios, but, I'm confused: While traveling to a distant universe, you discover the hypothetical element “X.”You obtain a representative sample of the element and discover that it is made up of two isotopes,X-23 and X-25. To help your science team calculate the atomic mass of the substance, you send the following drawing of your sample with your report. In the report, you also inform the science team that the gold atoms are X-23, which have an isotopic mass of 23.02 amu, and the green atoms are X-25,which have an isotopic mass of 25.147 amu. What is the atomic mass of element X?

Would you help me solve this problem? Is there an equation that I can use? I tried the finding x thing, by saying one isotope is x and the other isotope is 1-x, but, there isn't enough information or seemingly too many unknowns.

 

[Borek]

Not enough information to answer the problem in the text, but perhaps there is an additional information on the respective abundances of both isotopes on the drawing?

 

[dshipp17]

Not enough information to answer the problem in the text, but perhaps there is an additional information on the respective abundances of both isotopes on the drawing?

Seemingly, the drawing does not offer much more information, but, I'll describe the drawing for you; X-23 is represented by gold balls and there are 5 of these gold balls; X-25 is represented by green balls and are 15 of these green balls; textbook is by Darrell, Ninth Edition

 

[Borek]

5:15, sounds like a ratio.

 

[dshipp17]

5:15, sounds like a ratio.

Yes, but, I'm still stuck; how do I begin?

 

[Borek]

Atomic mass is a weighted average of the masses of isotopes.

 

[dshipp17]

Atomic mass is a weighted average of the masses of isotopes.

That's true, but, I'm still stuck; the weighted average only helps you determine the atomic mass; can you be more specific with say, an equation might use?

 

[Borek]

the weighted average only helps you determine the atomic mass;

And that's what you are asked to do, aren't you?

What is the weighted average, how is it applied?

 

[dshipp17]

And that's what you are asked to do, aren't you?

What is the weighted average, how is it applied?

To get the weighted average, you'd need to know the total mass or the mass in the isotopes most abundant state; however, the question is actually asking for the total mass, so, it doesn't appear as if enough information has been provided.

 

[Borek]

No, weighted average doesn't require you to know masses. In other words - "weight" in this context is not necessarily related to the mass, rather to relative amounts of something.

 

[Borek]

Or, to put it even differently: you have 5 atoms of one type and 15 atoms of other type. What is the average mass of an atom?

(And yes, when you get the result, it will be the weighted average.)

 

[dshipp17]

What specifically about weighted average? Right now, there isn't enough information to do a weighted average; weighted average is usually associated with finding atomic masses; however, this question is before or after that, depending on Dalton's formulations.

 

[dshipp17]

Oh, actually, I got it now; as I said in my intro, I took a chemistry class nearly 20 years ago, not just last semester, as with most of the cases on this website; I'm just trying to get refreshed and get through these textbooks in consideration for prep for graduate school and the subject matter GRE; this question is related to that standard deviation stuff that you normally start in analytical chemistry or quantitative analysis; but, can't complain, as this is the level that I need, as I'm reviewing instead of taking a general college level chemistry course for the first time; I had to research how to get a weighted average again. But, I still have to actually get the answer right. Although I'm in this section, I'm not actually completing assigned homework; I'm doing this stuff on my own to see if I want to proceed to graduate school; hence, you wouldn't be giving me the answer to homework problems by being a lot less vague.

 

[Borek]

Perhaps I am missing something, but the question asks you to calculate atomic mass, you say that weighted average is used for calculation of atomic masses - sounds like a simple plug and chug, I don't see where is the problem. I feel like you are trying to make it more complicated than it really is.

And not giving answers, but helping you to solve the problem on your own is how the forum works, it is in the rules.