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

Md Ariful Islam

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Md Ariful Islam

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The equation for the 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.

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