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  1. Does 1 C atom mean 1 single C atom out of Avogadro's number of C atoms = 1 single C atom out of 6.023 X 10^23 numbers of C atoms?
  2. Does 1 mole of C atoms mean Avogadro's number of C atoms = 6.023 X 10^23 numbers of C atoms?

I am confused. Could you clarify it, please?

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    $\begingroup$ Clarify what? 2) is exactly what the definition says and no idea what 1) is supposed to be, 1 atom is one atom, that's it. $\endgroup$ – Mithoron Apr 15 '18 at 17:03
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    $\begingroup$ What is the difference between 1 grain of sand and 1 tonne of grains of sand? Does the former mean 1 grain of sand out of 10^9 numbers of grains of sand? $\endgroup$ – user253751 Apr 15 '18 at 22:58
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What is the difference between one egg and one dozen eggs? A dozen is simply a certain count, in this case 12, that is rendered as one unit for our convenience. Avogadro's number s just the same thing as a dozen, except we made the unit count larger than 12 in order to match it up with our conventionally used units.

Your assumptions about a "mole" are thus correct.

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    $\begingroup$ This sounds more like a badly-worded notation question to me. $\endgroup$ – Joshua Apr 15 '18 at 19:41
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1 C atom is just one particle of the unique element Carbon. There is virtually no way to isolate or work with a single atom of anything.

1 mole of C is a quantity, like a dozen or a gross. We use dozens for food sale, like eggs, and a gross for small items like pencils. The power of the quantity a 'mole' comes from the mass of a mole in grams. When you have 6.02 x 10^23 particles, you have the formula mass in grams.

1 dozen eggs will weigh differently than 1 dozen bicycles.

Likewise, i mole of any substance will have a mass equal to the species atomic mass, or formula mass.

So, 1 mole of Carbon will have a mass of about 12.01 g (the number written will depend on the periodic table). 1 Mole of water will have a mass of 18 g (approx)

This is why the mole is such a useful quantity.

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