Dating methods: calculating atomic ratio?

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Discussion Overview

The discussion revolves around calculating the atomic ratio of Rb-87 to Sr-86 in a rock sample, focusing on the application of isotopic abundances and atomic weights. Participants explore the necessary steps and formulas involved in this calculation, addressing both theoretical and practical aspects of the problem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Martine seeks assistance in calculating the atomic Rb-87/Sr-86 ratio using given values for Rb and Sr concentrations, atomic weights, and isotopic abundances.
  • Some participants suggest breaking down the problem into smaller steps, questioning whether the formula provided is applicable to the problem at hand.
  • There is a discussion about the difference between mass ratios and atom ratios, with a focus on the need to convert mass to moles for accurate calculations.
  • Martine expresses confusion over how to apply the provided data and formulas, indicating a lack of prior chemistry knowledge.
  • One participant explains the mole concept and provides a general formula for calculating moles based on mass and molecular weight, aiming to clarify the process for Martine.
  • Martine acknowledges understanding the mole concept but still feels challenged by the material due to a lack of foundational knowledge in chemistry.

Areas of Agreement / Disagreement

Participants generally agree on the need to calculate the atomic ratio correctly and the importance of understanding the mole concept. However, there is no consensus on the specific steps Martine should take to arrive at the solution, and some participants express differing views on the appropriateness of the initial formula provided.

Contextual Notes

Martine's struggle with the problem appears to stem from a lack of foundational chemistry knowledge, which may affect her ability to apply the concepts discussed. The discussion highlights the importance of understanding isotopic abundances and the conversion between mass and moles in such calculations.

Who May Find This Useful

This discussion may be useful for students encountering similar challenges in introductory chemistry courses, particularly those related to isotopic dating methods and the application of atomic ratios in geochemical contexts.

martine
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Please help me with this calculation. I read that chapter in my book three times now and still don't know what actually do to

calculate the atomic Rb-87/Sr-86 ratio of a rock sample containing Rb=125 microg/g and Sr=275 microg/g.
Atomic weights: Rb=85.46, Sr=87.62
isotopic abundancy: Rb-87=27.83%, Sr-86=9.90%

I found the following formula:
Sr-87/Sr-86 = (Sr-87/Sr-86) small 0 + Rb-87/Sr-86 (e^labda*t -1)

Well, what do I do with this formula and how do I put all the given data into it?

Thousand thanks!

Martine
 
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Originally posted by martine
Please help me with this calculation. I read that chapter in my book three times now and still don't know what actually do to

calculate the atomic Rb-87/Sr-86 ratio of a rock sample containing Rb=125 microg/g and Sr=275 microg/g.

What can you do with the information given up to this point?
Atomic weights: Rb=85.46, Sr=87.62

What can you do with the first result plus this added information?
isotopic abundancy: Rb-87=27.83%, Sr-86=9.90%

What does this information allow you to do with the second step result? (Check your text for a specific statement whether the isotope abundances are given in weight percent or atom percent.)
I found the following formula:
Sr-87/Sr-86 = (Sr-87/Sr-86) small 0 + Rb-87/Sr-86 (e^labda*t -1)

This is the formula for calculating ages --- do you think it applies to the problem statement you've posted?
 
Bystander, you just asked him the same questions he is asking the board. If he knew the answers to those questions, do you really think he would be asking for help?
 
The request for help is phrased to indicate the usual beginner's problem of attempting to solve a problem in a single leap rather than taking it a step at a time. You don't like it now, when homework is "fish in a barrel" type stuff, wait 'til you get to the real world.
 
It's the other way around. Questions asked in school are usualy much harder than anything you will ever experience in the real world.
 
OK, I understand now that the formule has nothing to do with the problem. I guess I have to calculate the weight based on the abundancy.

Rb:
85.46 = 100%
x = 27.83%

x times the sample amount in rock.

same for Sr

then calculating the ration by dividing the higher through the lower value. Though, this is not totally correct if the answer given in the book is right (should be 1.31) as I only receive 1.24

Is this result right or do I have to calculate in other values, moles, whatever?

Thanks.
 
Originally posted by martine
OK, I understand now that the formule has nothing to do with the problem.

Check.
I guess

This is NOT a guessing game.
I have to calculate the weight based on the abundancy.

Yes.
Rb:
85.46 = 100%
x = 27.83%

x times the sample amount in rock.

same for Sr

then calculating the ration by dividing the higher through the lower value.

Okay to here --- you do seem to be guessing rather than thinking the problem through.

What have you got at this point? A MASS ratio --- the question asks for an atom ratio. The ratio of the numbers of each type of atom, or the ratio of the number of moles of each type of atom.
Though, this is not totally correct if the answer given in the book is right (should be 1.31) as I only receive 1.24

Is this result right or do I have to calculate in other values, moles, whatever?

Thanks.

The answer in the book is correct.
 
Well, I really do not know what I have to do to solve that question. You wrote:

----
The ratio of the numbers of each type of atom, or the ratio of the number of moles of each type of atom.
-----
*sigh*

the molar mass of
Rb = 85.4678 g/mol
Sr = 87.62 g/mol

but now? I'm really unsure as to what I have to do now. I'm getting more and more figures and really don't know how to use them decently :(
 
Originally posted by martine
Well, I really do not know what I have to do to solve that question. You wrote:----
The ratio of the numbers of each type of atom, or the ratio of the number of moles of each type of atom.
-----
the molar mass of
Rb = 85.4678 g/mol
Sr = 87.62 g/mol

but now? I'm really unsure as to what I have to do now. I'm getting more and more figures and really don't know how to use them decently :(

Oh, boy --- it will be useful if you state what level course this is; "Rb-Sr dating" suggests one thing, and the struggle you're having suggests another --- tailoring hints to an appropriate level gets a little bit tough.

That said, if you are handed a mass of a compound, or element, or species, such as Rb or Sr, and the molecular or elemental atomic or molecular weight (relative atomic mass), do you know how to calculate the number of moles? Has this been covered in the course, or in previous courses you've taken?
 
  • #10
well, as embarrasing as it is: this actually is introductory university level. Unfortunately i didn't have any chemistry at school apart from 6 months and as I'm studying in a different country then where I attended school I'm probably the only one having problems: chemistry was mandatory at school for my fellow students but not for me *grr*. And as I live about 90 minutes away from university I mostly stay at home as it's too expensive to commute every day. Not a problem with all the other courses. With a bit of luck I'll have a student chamber near my university within 1-2 years *sigh*

Martine
 
  • #11
"Embarassing?" Naa --- everybody has to start somewhere. Now that the background is clear, let's see what we can do about getting you up to speed on this.

First "guess:" "the mole concept" is a mystery to you; "mole" of atoms or of molecules is a number, just like a dozen eggs or a dozen doughnuts; "mole" of a substance (elemental or molecular) is the gram formula mass of that substance, molecular(atomic) weight times one gram. With me so far?

We'll call the substance you're interested in "S" and let it represent Sr, Rb, DNA, whatever you want --- this is a general principle --- you can apply it to anything. Then, the mass of the substance, "M," is equal to the product of the number of moles of the substance, "n," times the molecular weight (or atomic weight if an element) of the substance, "MW."

MS = nS MWS

This can be rearranged to emphasize whichever quantity interests you:

n = M/MW , MW = M/n .

Does this work for you so far?
 
  • #12
Yes, I understand that :)

ah well, it's not that I don't understand anything at all. When studying a chapter where no previous knowledge is needed are nto much of a problem, like isotope fractionation or geochemical cycles. Finally, got myself a chemistry school book and hope there's still enough time to understand the important concepts I'd missed.

Martine
 

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