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Topic: Help Understanding Atomic Mass Ratio Problem  (Read 2225 times)

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Offline logan3

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Help Understanding Atomic Mass Ratio Problem
« on: July 02, 2014, 04:01:13 AM »
The problem says:

"The ratio of atoms of Y to atom of X in a certain compound is 2:3. The mass of X in a certain sample is 2.50 g, and the mass of Y in the sample is 3.40 g. What is the ratio of their atomic masses?"

The answer given is as follows:

"Let N = number of atoms of Y; then 1.5N = number of atoms of X. Ay and Ax represent their atomic masses.

So

[tеx]\frac{NA_{y}}{1.5NA_{x}} = \frac{3.40g}{2.50g}[/tеx]

The Ns cancel, and the ratio of the atomic masses is Ay/Ax = 2/1"

I think I understand the reasoning, which is that the number of atoms multiplied by their atomic mass should equal the sample's mass. For example, N * Ay = 3.40 g, and 1.5 * N * Ax = 2.50 g; and the compound would equal  (N * Ay) + (1.5 * N * Ax) =  3.40 g + 2.50 g. But I guess I'm not understanding the final ratio of 2/1. The closest I can get is to take the equation

N(Ay)/1.5N(Ax) = 3.40 g / 2.50 g

cancel the Ns, and multiple by 1.5 to give:

Ay/Ax = 3.40 g *(1.5) / 2.50 g

But that equals 5.1 g/ 2.50 g, which is not the integer ratio of 2/1.

Offline Hunter2

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Re: Help Understanding Atomic Mass Ratio Problem
« Reply #1 on: July 02, 2014, 06:34:40 AM »
You use n = m/M

You have X3Y2 => 3 X + 2 Y

You take M = m/n   M(X) = 2,5 g/3 mol = 0,833333 g/mol and M(Y) = 3,4 g/2 mol = 1,7 g/mol

Ratio is 1,7/0,833333333333 =  2,04/1 ~ 2/1

Offline logan3

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Re: Help Understanding Atomic Mass Ratio Problem
« Reply #2 on: July 02, 2014, 01:17:10 PM »
We haven't been introduced to moles or molar mass yet. How do I understand this problem without referencing those concepts and units?

Also, I see that you did some rounding in the end, was that for significant figures? If so, maybe in the final sentence I posed "5.1 g / 2.50 g" = 2.04 / 1 was rounded to 2 / 1. But in my example I counted the s.f. and found that it was three s.f., not two, so why would it be rounded as such?

Offline Hunter2

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Re: Help Understanding Atomic Mass Ratio Problem
« Reply #3 on: July 02, 2014, 01:28:37 PM »
Quote
What is the ratio of their atomic masses?"

Strange why this question then, if not introduced.

Offline logan3

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Re: Help Understanding Atomic Mass Ratio Problem
« Reply #4 on: July 02, 2014, 03:55:43 PM »
They'll be introduced in four chapters. Right now we're going over the law of definite and multiple proportions, atomic masses, isotopes and the basic atomic structure.

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