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

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.