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

Jun 13, 2017

$3.93 \text{g"/"L}$

#### Explanation:

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

$\rho = \frac{M P}{R T}$

where

• $\rho$ (the lowercase Greek letter rho) is the density, in $\text{g"/"L}$,

• $M$ is the molar mass of the gas (for ${\text{CO}}_{2}$, this is $44.01 \text{g"/"mol}$),

• $P$ is the pressure exerted by the gas ($4.00$ $\text{atm}$),

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"·"atm")/("mol"·"K}\right)$, and

• $T$ is the absolute temperature of the gas ($546$ $\text{K}$).

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.