# How many litres of nitrogen gas would result from spilling 3 litres of liquid nitrogen at room temperature?

a) 2049 litres

b) 365 litres

c) 3 litres

d) 800 litres

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• I don't know the density of liquid Nitrogen ...   This question is kind of screwy because the liquid Nitrogen must be at a temp of -150 deg, C (just an est.  ..  don't know it or want to look it up)  so I will use 1,0 g/ml to make a guess.

3000 mL is about 3000 g

3000 / 28  =  107 mol

1 mole at STP occupies 22.4 L

107 X 22.4  =  ~2400 L

of your 4 choices  I would pick a

.. remember my numbers are just estimate so there is a lot of error

if the  real density is about 0.85g/ml  the calculations would be very close to  answer a.

• V = nRT/ P

= 86.53 mol * 293 K * 0.0820 L⋅atm⋅K−1⋅mol−1 / 1 atm

=  2078 L

• room temperature is not STP billrussell42

assuming room T = 20°C = 293K

density Liquid N2 = 808g/L

from the ideal gas law

.. PV = nRT

.. PV = mass / mw RT

.. V = (mass / mw) RT/P

then you should be able to follow

3L.. 808g.. 1 mol .. ..0.08206 Latm/molK * 293.15K

---- x ------ x ----- --- x--- ----- ---- ----- ----- ----- ---- ----- = 2081 L

1... . 1L.. .. 28.02g... .. ... .. .. 1 atm

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that doesn't match any of your choices... so YOU figure out what room temp means and update the calcs

• density as a liquid is 0.808 g/cm³

3 L  = 3000 mL = 3000 cm³

0.808 g/cm³ x 3000 cm³ = 2424 g

N₂ is 28.014 g/mol

2424 g / 28.014 g/mol = 86.53 mol

One mole of any ideal gas at STP has a volume of 22.41L

(old def of STP, 1 atm)

22.41 L/mol x 86.53 mol = 1939 L