Question

Question #3f076

Answer 1

`5.56 xx 10^24 color(white)"x"`molecules`color(white)"x" O_2`

Explanation:

At STP conditions for ideal gases, we use the conversion factor

`1 color(white)"x" mol ~~ 22.4 color(white)"x" L`

Given `207L` of oxygen (or any ideal gas for that matter) at STP

`207 color(white)"x" cancel(L color(white)"x" O_2) xx (1 color(white)"x" mol color(white)"x" O_2)/(22.4 color(white)"x" cancel(L color(white)"x" O_2))=9.24 color(white)"x" mol color(white)"x" O_2`

Then we convert from `mol` to number of molecules `(mlc)` using Avogadro's number:

`9.24 color(white)"x" cancel(mol color(white)"x" O_2)xx(6.02xx10^23 color(white)"x" mlc color(white)"x" O_2)/(1 color(white)"x" cancel(mol color(white)"x" O_2)) = 5.56 xx 10^24 color(white)"x" mlc color(white)"x" O_2`

(make sure to use unrounded intermediate answers and round to correct number of significant figures at the end)

Answer 2

`5.56` x `10^24` `"molecules"`

Explanation:

1 mole of any ideal gas at STP occupies volume = `22.414dm^3`

Thus, at STP, 207 liters of oxygen contains

`"1 mol"/"22.414 L" xx "207 L" = "9.24 moles"`

`"Molecules of oxygen = Number of moles"` `xx` `"Avogadro's number"` (`N_A`)

`= "9.24 mols" xx 6.02 xx 10^23 "mol"^(-1)`

`= ul(5.56 xx 10^24 "molecules")`