Question

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

Answer 1

`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.