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Bingel [31]
3 years ago
15

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 contai

ner 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?
Chemistry
1 answer:
marta [7]3 years ago
4 0

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 \rm CO_2:

M\!\left(\mathrm{CO_2}\right) = 12.011 + 2\times 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 = \dfrac{m}{M} = \dfrac{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 = \frac{n \cdot R \cdot T}{V}.

Look up the ideal gas constant in the appropriate units.

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

Evaluate the expression for P:

\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}.

Apply dimensional analysis to verify the unit of pressure.

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