half life

[inaccensa]

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I did the problem and got it wrong, I was thinking there is 100 gm of sample, 1.5 gms of X was detected, ie 98.5 was used up. Anyhow, I got it wrong because by mass meant the mass of meteorite and not the total mass of X and Y right?

half life of substance X is 45 years and it decomposes to Y. There is 1.5% X and 13.5% Y by mass in a sample of meteorite where Y is not normally found.What is the age of meteorite?

Actual solution follows as total mass X+Y = 1.5+13.5 = 15..you start with 15 units of X and 15/2, 7.5/2, 3.75/2, 1.87...its a little more than 3 half lives, so 45*3=135 + a little more.

 

[indianjatt]

I'm also slightly confused. If you have a substance X and it decomposes to Y, then you have lost that much. In this case you have 1.5% left of X, which is your sample..... So I would have thought it went through ~6 half lives, but apparently not.

 

[inaccensa]

I'm also slightly confused. If you have a substance X and it decomposes to Y, then you have lost that much. In this case you have 1.5% left of X, which is your sample..... So I would have thought it went through ~6 half lives, but apparently not.

Yeah, when I read the q, I couldnt figure why there was only 13.5% Y, if 98.5% X was used up. I did the same thing as you said, six half lives, but that is wrong, since X and Y comprise only a fraction of the total mass of meteorite.

 

[paul411]

Anyhow, I got it wrong because by mass meant the mass of meteorite and not the total mass of X and Y right?

Yes:

half life of substance X is 45 years and it decomposes to Y. There is 1.5% X and 13.5% Y by mass in a sample of meteorite where Y is not normally found.What is the age of meteorite?

When you see "there is 1.5% of X by mass in a sample", it means that if the sample is 100g, there is 1.5g of X in there.

Actual solution follows as total mass X+Y = 1.5+13.5 = 15..you start with 15 units of X and 15/2, 7.5/2, 3.75/2, 1.87...its a little more than 3 half lives, so 45*3=135 + a little more.

Conservation of mass applies here. Let's assume we are using a 100g sample of the meteorite. At the present time we have: 1.5g of X and 13.5g of Y in this meteorite sample. We know that X decays into Y. Initially, we had: 0g of Y, so how much X did we have? Since mass cannot be destroyed (in a closed system), we had 15g of X (1.5 + 13.5) to begin with. You had the rest of the solution correct up there.

I hope this helps. If something is not clear, let me know so I can try and better explain what I just said.

 

[inaccensa]

Yes:


When you see "there is 1.5% of X by mass in a sample", it means that if the sample is 100g, there is 1.5g of X in there.



Conservation of mass applies here. Let's assume we are using a 100g sample of the meteorite. At the present time we have: 1.5g of X and 13.5g of Y in this meteorite sample. We know that X decays into Y. Initially, we had: 0g of Y, so how much X did we have? Since mass cannot be destroyed (in a closed system), we had 15g of X (1.5 + 13.5) to begin with. You had the rest of the solution correct up there.

I hope this helps. If something is not clear, let me know so I can try and better explain what I just said.

Got it... the light should have gone on when I read the q..😱

 

[isc2110]

Yes:


When you see "there is 1.5% of X by mass in a sample", it means that if the sample is 100g, there is 1.5g of X in there.



Conservation of mass applies here. Let's assume we are using a 100g sample of the meteorite. At the present time we have: 1.5g of X and 13.5g of Y in this meteorite sample. We know that X decays into Y. Initially, we had: 0g of Y, so how much X did we have? Since mass cannot be destroyed (in a closed system), we had 15g of X (1.5 + 13.5) to begin with. You had the rest of the solution correct up there.

I hope this helps. If something is not clear, let me know so I can try and better explain what I just said.

How do you know you can just add the mass of Y to the mass of X? What if X-->Y via alpha decay? Then you'd be less with less mass of Y than you had of X, because some of that mass is being lost as an alpha particle.

 

[amy_k]

If the actual wording is "substance X decomposes to Y" and nothing else is mentioned about the decomposition just that it is straight X->Y then we can just assume conservation of mass and initial mass of X was 15g for every 100g of the meteorite. Even in an alpha decay we still dont consider the mass "lost" as we write a balanced chemical equation showing an alpha particle product, and since nothing like that is mentioned in the question I'd keep it simple 🙂

 

[chemist16]

If the actual wording is "substance X decomposes to Y" and nothing else is mentioned about the decomposition just that it is straight X->Y then we can just assume conservation of mass and initial mass of X was 15g for every 100g of the meteorite. Even in an alpha decay we still dont consider the mass "lost" as we write a balanced chemical equation showing an alpha particle product, and since nothing like that is mentioned in the question I'd keep it simple 🙂

No, you can't just "assume" just because it doesn't specify the decay process. The alpha decay concern is a real one and the point isn't that you consider the mass as "lost," but you're missing part of the mass when you say X+Y equals original mass. It's more correct to say X+Y+alpha particle equals original mass. However, there's no need for concern here. If X and Y were light nuclei, then the loss of an alpha particle would introduce a significant error into your calculation. However, alpha decay can only occur in elements heavier than Ni and really only occur in nature in elements much heavier than Ni (think uranium). At that point, the loss of a single alpha particle is negligible (on the order of ~1% error in your result).

 

[amy_k]

Agreed, i am not arguing that, we could go on about the specifics and details of the process, but regardless, these statements are way overcomplicating what is a simple MCAT conservation of mass question and the correct answer is calculated as @paul411 mentioned. There are are a lot of these MCAT practice questions that could be debated on and on and have been in this forum but at the end of the day the students need to pass the MCAT rather than prove all the question writers wrong.

 

[chemist16]

Yeah, but my point isn't to prove the question writers wrong. What I'm saying is that you should know why you can make the approximation that X+Y equals initial mass even if alpha decay occurs. It's basically reasoning out why you can make certain assumptions without simply making the assumption for the sake of simplicity.