## Chapter 5

## Q. 5.8

## Q. 5.8

Calculate the density of carbon dioxide (CO_{2}) in grams per liter (g/L) at 0.990 atm and 55°C.

Strategy We need Equation (5.11) d=\frac{m}{V}=\frac{P.M}{RT}

to calculate gas density. Is sufficient information provided in the problem? What temperature unit should be used?

## Step-by-Step

## Verified Solution

To use Equation (5.11), we convert temperature to kelvins (T = 273 + 55 = 328 K) and use 44.01 g for the molar mass of CO_{2}; that is,

d=\frac{P.M}{RT}=\frac{(0.990 atm)(44.01 g/mol)}{(0.0821 L . atm/K . mol)(328 K)}=1.62 g/L

Alternatively, we can solve for the density by writing

density \frac{mass}{volume}Assuming that we have 1 mole of CO_{2}, the mass is 44.01 g. The volume of the gas can be obtained from the ideal gas equation

V=\frac{nRT}{P}=\frac{(1 mol)(0.0821 L . atm/K . mol)(328K)}{0.990 atm}

=27.2 L

Therefore, the density of CO_{2} is given by

\frac{44.01 g}{27.2 L}=1.62 g/LComment In units of grams per milliliter, the gas density is 1.62 \times 10^{-3} g/mL, which is a very small number. In comparison, the density of water is 1.0 g/mL and that of gold is 19.3 g/cm^{3}.