Question

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?

Answer 1

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.