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Chapter 5

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?

 

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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/L

Comment 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}.