Answer:
[tex]\boxed {\boxed {\sf 63.57 \ mol }}[/tex]
Explanation:
We are asked to find how many moles of gas are in a sample.
At standard temperature and pressure (STP), any gas has a molar mass of 22.4 liters per mole. This means 1 mole of every gas at STP has a volume of 22.4 liters.
We will convert using dimensional analysis. Set up a conversion factor using the molar mass.
[tex]\frac {22.4 \ L }{1 \ mol }[/tex]
We are converting 1424 liters of gas to moles, so we multiply the conversion factor by this value.
[tex]1424 \ L *\frac {22.4 \ L }{1 \ mol }[/tex]
Flip the ratio so the units of liters cancel.
[tex]1424 \ L *\frac {1 \ mol }{22.4 \ L }[/tex]
[tex]1424 *\frac {1 \ mol }{22.4 }[/tex]
[tex]\frac {1 424}{22.4 } \ mol[/tex]
[tex]63.5714286 \ mol[/tex]
The original value of volume (1424 L) has 4 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 1 in the thousandth place tells us to leave the 7 in the hundredth place.
[tex]63.57 \ mol[/tex]
There are approximately 63.57 moles of gas in a sample of 1424 liters.
