What is the density of 5.0 L of #NO_2# gas at 1.0 atm at 0.0°C?

1 Answer
Nathan L.
Jul 5, 2017

#2.1# #"g/L"#

Explanation:

We're asked to find the density of #"NO"_2# at a certain temperature and pressure.

To do this, we can use the equation

#d = (MP)/(RT)#

where

  • #M# is the molar mass of #"NO"_2#, which is #46.01# #"g/mol"#

  • #P# is the pressure of the gas, in #"atm"#, given as #1.0# #"atm"#

  • #R# is the universal gas constant, equal to #0.082057("L"•"atm")/("mol"•"K")#

  • #T# is the absolute temperature of the gas, in #"K"#

Notice how the given volume measurement is not needed, because the density of a material does't change by increased volume (because quantity will also have increased).

The given temperature converted to Kelvin is

#T = 0.0^"o""C" + 273 = 273# #"K"#

Plugging in known values, we have

#d = ((46.01"g"/(cancel("mol")))(1.0cancel("atm")))/((0.082057("L"•cancel("atm"))/(cancel("mol")•cancel("K")))(273cancel("K"))) = color(red)(2.1# #color(red)("g/L"#

rounded to #2# significant figures.

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