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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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Answer:

Approximately 6.81 × 10⁵ Pa.

Assumption: carbon dioxide behaves like an ideal gas.

Step-by-step 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
\rm CO_2:


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

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


n = (m)/(M) = (41.1)/(44.009) \approx 0.933900\; \rm mol.

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


P \cdot V = n \cdot R \cdot T,

where


  • P is the pressure inside the container.

  • V is the volume of the container.

  • n is the number of moles of particles (molecules, or atoms in case of noble gases) in the gas.

  • R is the ideal gas constant.

  • T is the absolute temperature of the gas.

Rearrange the equation to find an expression for
P, the pressure inside the container.


\displaystyle P = (n \cdot R \cdot T)/(V).

Look up the ideal gas constant in the appropriate units.


R = 8.314 * 10^3\; \rm L \cdot Pa \cdot K^(-1) \cdot mol^(-1).

Evaluate the expression for
P:


\begin{aligned} P &=\rm (0.933900\; mol * 8.314 * 10^3 \; L \cdot Pa \cdot K^(-1) \cdot mol^(-1) * 298\; K)/(3.4\; L) \cr &\approx \rm 6.81* 10^5\; Pa \end{aligned}.

Apply dimensional analysis to verify the unit of pressure.

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