Question

What is the density of carbon dioxide gas at the temperature 400k and 0.0821 atmospheric pressure?

Answer 1

Step 1: Ideal gas equation :

• To understand the behavior of gases, the ideal gas law is used.
• The ideal gas equation is $\mathrm{PV}=\mathrm{nRT}$………. (i)
• Here, P = Pressure, V = Volume, n = No. of moles , R = Universal gas constant $(0.0821\mathrm{L}\mathrm{atm}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1})$, T = Temperature
• It can also be written as $\mathrm{PM}=\mathrm{dRT}$……….(ii)
• Here, M = Molar mass of the gas and d = Density

Step 2: Given Information

• Carbon dioxide: It exists in the earth's atmosphere as a gas and its chemical formula is ${\mathrm{CO}}_2$.
• The molar mass of carbon dioxide gas is $44\mathrm{g}{\mathrm{mol}}^{-1}$.
• The temperature is $400\mathrm{K}$ and the pressure is $0.0821\mathrm{atm}$.

Step 3: Calculation for density:

• Substituting the given values in equation (ii)

$$\begin{gathered} 0.0821\mathrm{atm}\times 44\mathrm{g}{\mathrm{mol}}^{-1}=\mathrm{d}\times 0.0821\mathrm{L}\left(\mathrm{atm}\right){\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\times 400\mathrm{K} \\ \mathrm{d}=\frac{0.0821\mathrm{atm}\times 44\mathrm{g}{\mathrm{mol}}^{-1}}{0.0821\mathrm{L}\left(\mathrm{atm}\right){\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\times 400\mathrm{K}} \\ \mathrm{d}=0.11\mathrm{g}{\mathrm{L}}^{-1} \end{gathered}$$

Hence, the density of ${\mathrm{CO}}_2$ gas at $400\mathrm{K}$ and $0.0821\mathrm{atm}$ is $0.11\mathrm{g}{\mathrm{L}}^{-1}$