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Question

1. How many moles of neon atoms are there in 2.0 x 10^23 atoms of neon?

2. How many carbon atoms are there in 0.50 mol of C?

3. How many hydrogen atoms are there in 4.0 mol of H2O?

Answer 1

Hello, Cotton,

The important thing to remember about the mole is that it is just shorthand for a very large number, 6.023x10²³, also known as Avogadro's Number. The analogy would be a dozen. When someone says "dozen," you know they mean 12. When someone says "mole," consider the context (on face, in ground, or in a lab?) and if in a science setting, it means 6.023x10²³ of something. Usually elements and molecules, but I could say "I took a mole of paperclips from the supply closet" and you'd know I stole 6.023x10²³ paperclips.

In this case you have 2.0 x 10²² atoms of Neon. (It really doesn't matter which element (or paperclip), since this is a count).

Use the conversion factor of 1 mole = 6.023x10²³ atoms. Rearrange it as: 1 mole/(6.023x10²³ atoms) and multiply by 2.0 x 10²² atoms of Neon. The numbers of atoms cancel and moles is left, which is what you are looking for.

2.0 x 10²² atoms of Neon * (1 mole/(6.023x10²³ atoms) = 3.32 x 10^-2 moles of Ne.

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The same logic applies in part two - how many carbon atoms in 0.5 moles of C. Use the same conversion factor as above, but don't invert it:

0.5 moles C * (6.023x10²³ atoms C/(1 mole)) = 3.01x10²³ atoms C

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Use this same approach to solve for the number of atoms of H₂O.

I hope this helps,

Bob

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Extra information:

Avogadro's Number number has a special importance in science. If one wanted to run a reaction in a manner not to waste molecules, then that person would need to know the actual numbers of atoms going into the reaction. Since hiring someone with tweezers to count them out one at a time seemed like a dead end, early researchers discovered that you could take the mass of whatever you wanted to react and calculate the actual number of molecules by using the "molar mass" of that element or compound. The molar mass is that element's atomic weight but expressed in grams instead of AMU (atomic mass units). Copper has an AMU of 63.546, so if you measured out 63.546 grams of copper, you'd have 6.023x10²³ atoms of copper. The same applies with compounds. Determine the molar mass of a compound, such as H₂O by adding the atomic weights of each element every time they appear. Water has 18 for the oxygen and 2x1 for the two hydrogens, for a total of 18, which is expressed as 18 grams/mole. It takes 18 grams of water to have 6.023x10²³ molecules of H₂O.

It is useful to note that moles can mean anything, not just elements and compounds. I could well announce that I took 1 mole of paperclips from the supply closet. That would be 6.023x10²³paperclips. Don't ask how I didn't get caught. The term moles can be confusing. When you hear the word, you must take it in context with what is being discussed (face, lawn, or experimental work). In a science setting, they likely mean Avogadro's number. It is a common unit, so memorize it.