How many oxygen molecules are present in 207 liters of oxygen gas at STP?

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Oct 25, 2017

Answer:

#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)

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Oct 25, 2017

Answer:

#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")#

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