Question

How to find the mol contained in a sample of 5.84 x 10^23 atoms of a specific element?

I have a question "How many mol are contained in a sample of 5.84 x `10^32` atoms of tin (Sn)?" that I don't know how to answer. I would really like an explanation and how to, So I can work out any further questions relating to this. Thank you.

Answer 1

`"Moles"="Mass"/"Molar mass"`

Explanation:

You know that `1*mol` specifies `6.022xx10^23*mol^-1`...

And so we take the following quotient to get the molar quantity:

`"Moles of tin"=(5.84xx10^23*"tin atoms")/(6.022xx10^23*"tin atoms"*mol^-1)=??*mol`

Why do I include the units? Because then I get an answer with the appropriate dimensions, if I have followed the right order of operation in my calculation...here I get an answer in moles as required....

And what is the mass of this quantity?

I think there is a typo in your original question...

Answer 2

`9.70xx10^8 " mol" " Sn"`

Explanation:

To convert from atoms to moles of an element/molecule, you must divide by Avogadro's number (`6.023xx10^23 " atoms"`)

`5.84xx10^32 cancel" atoms Sn" * ( 1 " mol Sn")/(6.022xx10^23 cancel " atoms Sn")`

`= color(green)(9.70xx10^8 " mol" " Sn")`

Anytime you are converting from one unit to another, you must cancel out your initial units so that the remaining units are whatever units the question is asking for. So let's consider that the question initially gave you moles of a tin sample and asked you to determine how many atoms were in that sample, you then have to multiply by Avogadro's number to get the unit of atoms.

Answer 3

`"0.970 mol Sn"` are present in `5.84xx10^23` `"atoms Sn"`.

Explanation:

1 mole of anything is `6.022xx10^23` anythings, including atoms. To determine mol atoms in the given number of atoms, divide the given number of atoms by `(6.022xx10^23" atoms")/"mol"`. I prefer to divide by multiplying by the reciprocal `("1 mol")/(6.022xx10^23"atoms")`.

`5.84xx10^23color(red)cancel(color(black)("atoms Sn"))xx(1"mol Sn")/(6.022xx10^23color(red)cancel(color(black)("atoms Sn")))="0.970 mol Sn"` (rounded to three significant figures)