[B9766]

The problem presented in the text states:

"How many moles of rubidium (Rb) are there in 3.75 x 10²⁴ rubidium atoms?"

I thought this would be a simple problem and solved by dividing Avagrado's number by the number of atoms given. It made sense to me that if 1 mole = 6.022 x 10²³ atoms, then 3.75 x 10²⁴ atoms would be something like 0.15 moles (6 / 40).

(6.022 x 10²³ atoms) / (3.75 x 10²⁴ atoms) = 1.60587 x 10^-1 moles = 0.161 moles

But the answer given in the book is 6.23 moles. How can that be? I mean, 6.23 is the reciprocal of my answer but why would the answer be the reciprocal?

[sjb]

If there were e.g. 10 houses in a road, how many roads would you expect to need for 50 houses?

[Borek]

I thought this would be a simple problem and solved by dividing Avagrado's number by the number of atoms given.

If you have 60 atoms, how many dozens do you have? 12/60 or 60/12?

[mjc123]

It would help you if you were careful about units. If Avogadro's number is 6.022 X 10²³ atoms/mol, then
(6.022 x 10²³ atoms/mol) / (3.75 x 10²⁴ atoms) = 1.60587 x 10^-1 moles^-1 = 0.161 moles^-1
and you would see at once that you had the expression upside down.
Can't express too strongly the importance of units!

[B9766]

Thank you! I do make stupid mistakes like that. I'm still sorting out equivalents in my mind. Your point is well taken.