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A 41.1 g sample of solid CO2 (dry ice) is added to a container at a temperature of 100 K with a volume of 3.4 L.A. If the container is evacuated (all of the gas removed), sealed, and then allowed to warm to room temperature T = 298 K so that all of the solid CO2 is converted to a gas, what is the pressure inside the container?

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jacob193

Answer:

Approximately 6.81 × 10⁵ Pa.

Assumption: carbon dioxide behaves like an ideal gas.

Explanation:

Look up the relative atomic mass of carbon and oxygen on a modern periodic table:

  • C: 12.011;
  • O: 15.999.

Calculate the molar mass of carbon dioxide [tex]\rm CO_2[/tex]:

[tex]M\!\left(\mathrm{CO_2}\right) = 12.011 + 2\times 15.999 = 44.009\; \rm g \cdot mol^{-1}[/tex].

Find the number of moles of molecules in that [tex]41.1\;\rm g[/tex] sample of [tex]\rm CO_2[/tex]:

[tex]n = \dfrac{m}{M} = \dfrac{41.1}{44.009} \approx 0.933900\; \rm mol[/tex].

If carbon dioxide behaves like an ideal gas, it should satisfy the ideal gas equation when it is inside a container:

[tex]P \cdot V = n \cdot R \cdot T[/tex],

where

  • [tex]P[/tex] is the pressure inside the container.
  • [tex]V[/tex] is the volume of the container.
  • [tex]n[/tex] is the number of moles of particles (molecules, or atoms in case of noble gases) in the gas.
  • [tex]R[/tex] is the ideal gas constant.
  • [tex]T[/tex] is the absolute temperature of the gas.

Rearrange the equation to find an expression for [tex]P[/tex], the pressure inside the container.

[tex]\displaystyle P = \frac{n \cdot R \cdot T}{V}[/tex].

Look up the ideal gas constant in the appropriate units.

[tex]R = 8.314 \times 10^3\; \rm L \cdot Pa \cdot K^{-1} \cdot mol^{-1}[/tex].

Evaluate the expression for [tex]P[/tex]:

[tex]\begin{aligned} P &=\rm \frac{0.933900\; mol \times 8.314 \times 10^3 \; L \cdot Pa \cdot K^{-1} \cdot mol^{-1} \times 298\; K}{3.4\; L} \cr &\approx \rm 6.81\times 10^5\; Pa \end{aligned}[/tex].

Apply dimensional analysis to verify the unit of pressure.