How many atoms are in 2g of oxygen gas?

[tomchoisc]

Homework Statement

Calculate the total number of atoms in 2g of oxygen gas

Homework Equations

molar mass
no of mole

The Attempt at a Solution

I try to solve that by following steps but i don't know correct or not. in fact, i am so confused with mole

no of mole: 2 / 16x2 mol =0.0625mol
Number of oxygen: 0.0625 x 6.02x10^23 =7.525x10^22 atoms

is that correct?
but i am still confused with molar mass or no of mole,even number of atoms

 

[Borek]

Something is wrong - even if the final answer (7.5x10²³) is correct, it is not result of the multiplication you have listed. Thus even if it is obvious that you are partially correct and partially wrong, it is hard to tell what you got right and what incorrectly.

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[Char. Limit]

But his final answer was 7.5x10²²...

And it isn't correct anyway. You found the total number of oxygen molecules.

 

[Borek]

23 in my post was a typo, I meant 22. And 7.5x10²² is a correct number of atoms in 2 grams of oxygen, no matter if it is atomic, diatomic or triatomic. Number of diatomic molecules is twice lower.

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[Char. Limit]

It does matter if it is monatomic, diatomic, or triatomic. Since he found the number of moles for diatomic oxygen, he found the number of molecules of dioxygen. His first post says he used \frac{2 g}{(16*2) g/mol}.

 

[Borek]

No, it doesn't matter what kind of molecules we are talking about, as long as it is mass of the substance that is given and we are interested in number of atoms. 2 grams of oxygen always contain the same number of oxygen atoms. Number of molecules changes, but number of atoms is identical. Think about it this way - mass of an atom is always identical, so if you have 2 grams of oxygen, number of atoms must be always identical.

And as I wrote earlier, it is hard to say what s/he found, as the answer given is not the result of calculations performed. So the number listed as answer is number of atoms (check it before stating it is not), while the expression used gives number of moles of diatomic molecules.

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methods

 

[Yanick]

This is how I was taught and I always do it this way and pretty much never make a mistake except when I have a brain fart and screw up some of the simple math.

The atomic mass of monatomic Oxygen ~ 16 but since oxygen gas is diatomic the atomic mass = 32. Since atomic mass = molar mass, 1 mol of O₂=32g

So you set up your conversion factors using dimensional analysis (learn this technique if you don't know it already, practice with it and your life will be a lot easier in any science class);

(2g/1) * (1 mol/32g) * (6.02e²³ molecules/1 mol)

I use the 1 in the first term just as a place holder because I can be slow in the head at times and make stupid math errors. The grams will cancel, as will the mols and the units you are left with are molecules of Oxygen. Doing the math gets you

.376e²³ = 3.8e²²

But that tells you how many O=O MOLECULES there are and the question is asking how many ATOMS you need. So just multiply by 2 and you get 7.6e²².

Moles are easy to understand if you think of them in everyday terms. So a mol is just a specific number of things (anything), like a dozen, except where a dozen right away makes you think 12 a mol makes you think Avogadro's Number. You can have a mol of donuts or a mol of oxygens or a mol of cars or people, you get the idea. So if you get stuck just break it down to everyday life. If you have 1 dozen cars, that dozen cars will have 4 dozen tires (4 tires per car, or 4x12=48 tires), 2 dozen headlights (2 per car, 2x12=24) etc. If you have a mol of cars you have 4 mols of tires (4 * Avogadro's #), 2 mols of headlights (2 * Av's #) and so on.

So if you have something like Calcium Chloride (CaCl₂). Then 1 dozen molecules of calcium chloride will have 1 dozen calcium ions (1 * 12=12) and 2 dozen chloride ions (2 * 12 = 24), because just as there are 4 tires per car or 2 headlights per car there are 2 chloride ions per calcium chloride molecule. 1 mol of calcium chloride will have 1 mol of calcium (1 * Av's Number) and 2 mols of chloride (2 * Av's #). 5 mols of it = 5 mols of calcium (5 * Av's #) and 10 mols of chloride (10 * Av's #). Hope this helps, I know that I helped quite a few people get a handle on this concept by explaining it this way.