How do you calculate the density of carbon dioxide at 546 K and 4.00 atmospheres pressure?

1 Answer
Jun 13, 2017

Answer:

#3.93"g"/"L"#

Explanation:

The equation for the density of a gas is given by the equation

#rho = (MP)/(RT)#

where

  • #rho# (the lowercase Greek letter rho) is the density, in #"g"/"L"#,

  • #M# is the molar mass of the gas (for #"CO"_2#, this is #44.01"g"/"mol"#),

  • #P# is the pressure exerted by the gas (#4.00# #"atm"#),

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

  • #T# is the absolute temperature of the gas (#546# #"K"#).

Plugging in known values, we have

#rho = ((44.01"g"/cancel("mol"))(4.00cancel("atm")))/((0.082057 ("L"·cancel("atm"))/(cancel("mol")·cancel("K")))(546cancel("K"))) = color(red)(3.93"g"/"L"#

The density of the gas is thus #3.93# grams per liter.