Answer:
[tex]\boxed {\boxed {\sf 2.62 \ mol \ N_2}}[/tex]
Explanation:
The relationship between moles and gases is unique. Regardless of the type of gas, there will always be 22.4 liters of gas in 1 mole, as long as it's at STP (standard temperature and pressure).
We can make a ratio using this information.
[tex]\frac {22.4 \ L \ N_2}{ 1 \ mol \ N_2}[/tex]
Multiply by the given number of moles.
[tex]58.6 \ L \ N_2 *\frac {22.4 \ L \ N_2}{ 1 \ mol \ N_2}[/tex]
Flip the fraction so the liters of nitrogen cancel.
[tex]58.6 \ L \ N_2 *\frac {1 \ mol \ N_2}{ 22.4 \ L \ N_2}[/tex]
[tex]58.6 *\frac {1 \ mol \ N_2}{ 22.4 }[/tex]
[tex]\frac {58.6 \ mol \ N_2}{ 22.4 }= 2.61607143 \ mol \ N_2[/tex]
The original measurement of liters has 3 significant figures, so our answer must have the same.
For the number of moles calculated, 3 sig figs is the hundredth place. The 6 in the thousandth place tells us to round the 1 to a 2.
[tex]2.62 \ mol \ N_2[/tex]
58.6 liters of N₂ gas at STP is equal to about 2.62 moles.
