# Atomic Ratio and Ratio of Mole Fractions

• Chemistry
In summary: NCO:XCO2 = XCO + NCOIn summary, the author suggests that we can relate the ratio of oxygen atoms:carbon atoms to the mile fractions by the following.

## Homework Statement

Hi folks!

This is just a conceptual question that has arisen during some reading. At one point the author states that for the reaction:

$CO_2 \leftrightharpoons X_{CO}CO + X_{CO_2}CO_2 + X_{O_2}O_2$

where X is the mole fraction of each component at equilibrium, that we can relate the ratio of oxygen atoms:carbon atoms to the mile fractions by the following.

$$\frac{\text{No. carbon atoms}}{\text{No. oxygen atoms}}=\frac{1}{2}=\frac{X_{CO}+X_{CO_2}}{X_{CO}+X_{CO_2}+X_{O_2}}$$Now I can see that what they have essentially written is

$$\frac{\text{No. oxygen atoms}}{\text{No. carbon atoms}} = \frac{\text{mole fractions of everything with carbon in it}}{\Sum\text{mole fractions of everything with oxygen in it}}$$

Now intuitively this makes sense to me and I can dig it! BUT, I would like to make the math work to prove it to myself, but I cannot seem to figure it out

## The Attempt at a Solution

This is what I did to try to "prove" it. Since Xi = Ni / NT where NT is the total number of moles in the mixture at equilibrium, I can write

$$\frac{X_{CO}+X_{CO_2}}{X_{CO}+X_{CO_2}+X_{O_2}} = \frac{N_{CO}/N_T+N_{CO_2}/N_T}{N_{CO}/N_T+N_{CO_2}/N_T+N_{O_2}/N_T} = \frac{N_{CO}+N_{CO_2}}{N_{CO}+N_{CO_2}+N_{O_2}}$$I am just not sure where to go from here? I thought about writing each Ni as something like: NCO = (NC + NO), but did not get too far.

Any thoughts?

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$$\frac{\text{No. oxygen atoms}}{\text{No. carbon atoms}}=\frac{1}{2}$$

And not

$$\frac{\text{No. oxygen atoms}}{\text{No. carbon atoms}}=\frac{2}{1}$$?

After all that's the ratio in CO2 which is present initially.

I will try to get back to the problem, have to do something else at the moment. Seems like your approach should lead to the correct conclusion.

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How many atoms of everything in 1 mole of CO2?

And you probably need to use stoichiometry of the reaction:

2CO2 <-> 2CO + O2

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Borek said:
And not

$$\frac{\text{No. oxygen atoms}}{\text{No. carbon atoms}}=\frac{2}{1}$$?

After all that's the ratio in CO2 which is present initially.

I will try to get back to the problem, have to do something else at the moment. Seems like your approach should lead to the correct conclusion.

--

Yes Borek; my mistake. I have edited to reflect the correct problem.

Borek said:
How many atoms of everything in 1 mole of CO2?

And you probably need to use stoichiometry of the reaction:

2CO2 <-> 2CO + O2

--

So if me let ai be the number of atoms in the ith species and NAis Avagadros number, we have for 1 mole of CO2:

$$a_{\text{1mol}_{CO_2}} = \text{1mol}_C*N_A\frac{\text{atoms}} + 2*\text{1mol}_O*N_A\frac{\text{atoms}}{\text{mol}} = 3N_A \, \text{atoms}$$

I am can presumably do this for all remaining species and find that the ration is indeed 1/2. Now that I think about it, if I really wanted to *prove* it in general I should have let the subscripts be dummy variables as well as the species names...but that is for another time. When I get the time I will do this on paper since I am still not sure where I would use the stoichiometry of the rxn.

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I am still not sure where I would use the stoichiometry of the rxn.

For example - to combine amounts of CO and O2 present. If you assume initially there was CO2 only, you can also calculate XCO2 knowing XCO (or XO2)

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## 1. What is atomic ratio?

Atomic ratio is the ratio of the number of atoms of one element to the number of atoms of another element in a compound or molecule.

## 2. How is atomic ratio calculated?

Atomic ratio is calculated by dividing the number of atoms of one element by the number of atoms of another element in a compound or molecule.

## 3. What is the significance of atomic ratio?

Atomic ratio is important because it helps determine the chemical formula of a compound and provides information about the composition of a substance.

## 4. What is the ratio of mole fractions?

The ratio of mole fractions is a measure of the relative amounts of different substances present in a mixture. It is the ratio of the number of moles of one substance to the total number of moles in the mixture.

## 5. How is the ratio of mole fractions related to atomic ratio?

The ratio of mole fractions is related to atomic ratio because it takes into account the relative number of atoms in a compound or molecule, while the ratio of mole fractions considers the relative number of moles of each substance in a mixture.

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