Question #3f076

2 Answers

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)

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")