CO2 gas in a temp-controlled, pressure-controlled container

In summary, the problem involves placing 20 g of dry ice in a 2.0*10^4 cm^3 container, pumping out all the air, and sealing the container. The container is then warmed to 0 deg C, and the resulting CO2 gas undergoes an isothermal compression until the pressure is 3.4 atm, followed by an isobaric compression until the volume is 2000 cm^3. The final temperature of the gas is unknown, but can be calculated using the ideal gas law and the molar mass of CO2.
  • #1
mcnivvitz
7
0
The problem:
20 g of dry ice (solid CO2) is placed in a 2.0*10^4 cm^3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0 deg C, a temperature at which CO2 is a gas.

a) What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.4 atm, immediately followed by an isobaric compression until the volume is 2000 cm^3.

b) What is the final temperature of the gas?

My thoughts:
Something to do with latent heat of vaporization. For carbon dioxide, this constant is 574 kJ/kg. 20 g = .2kg of CO2. No idea how this translates into pressure. Where do I go from here? Can anyone give me some relavent equations?

Thanks
 
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  • #2
P = nRT / V
Molar mass of CO is 28.010 g mol^-1.
Therefore number of moles in 20 g is 20 g/28.010 g mol^-1 = 0.71 mol.

P = ((.71)(8.314472e15)(-273.15)) / (2.0*10^4 cm^3)

P = -8.062398*10^19 m^3

Is this correct? What do I do now?
 
  • #3
Err, I put the wrong units and gas constant. Here:

((.71 mol)(8.3145 J/mol K)(-273.15 degrees K)) / (2.0*10^4 cm^3) = P = -80624251.5 kg K / s2

That's not right either. Sigh.
 
  • #4
Did the calculation wrong. Now I've got

((.71 mol)(8.3145 J/(mol*kelvin))(-273.15 degrees kelvin)) / (2.0*10^4 cm^3) = -0.795699496 atm

Not the right answer for pressure. But at least the proper units.
 
  • #5
for your question. I can provide a response to the given scenario.

First, let's start by understanding the conditions of the system. We have a 2.0*10^4 cm^3 container (volume) with 20 g of solid CO2 inside. The container is sealed and the temperature is controlled at 0 deg C. This means that the CO2 will remain in a solid state due to its sublimation point being at -78.5 deg C. However, as the temperature increases to 0 deg C, the solid CO2 will start to sublimate and turn into a gas.

a) To determine the gas pressure, we can use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since we are dealing with a closed system, the number of moles (n) remains constant. We can rearrange the equation to solve for P: P = nRT/V. We know the volume (2.0*10^4 cm^3), the temperature (0 deg C or 273 K), and the gas constant (0.082 L*atm/mol*K). We just need to find the number of moles of CO2 present in the container. To do this, we can use the molar mass of CO2 (44.01 g/mol) and the mass of CO2 present (20 g) to calculate the number of moles (n = 20 g / 44.01 g/mol = 0.454 mol). Plugging these values into the equation, we get: P = (0.454 mol)(0.082 L*atm/mol*K)(273 K) / 2.0*10^4 cm^3 = 0.016 atm. So, the initial gas pressure in the container is 0.016 atm.

After the isothermal compression, the pressure is increased to 3.4 atm. This means that the final volume of the gas will be: V = (0.454 mol)(0.082 L*atm/mol*K)(273 K) / 3.4 atm = 7.2*10^3 cm^3. Now, for the isobaric compression, we know that the pressure remains constant at 3.4 atm and the volume decreases
 

1. What is CO2 gas and why is it important?

CO2 gas, or carbon dioxide gas, is a colorless and odorless gas that is naturally present in the Earth's atmosphere. It is essential for all living organisms as it is used in photosynthesis to produce oxygen. It is also a greenhouse gas, which helps regulate the Earth's temperature.

2. How is CO2 gas stored in a temperature-controlled, pressure-controlled container?

In order to store CO2 gas in a temperature-controlled, pressure-controlled container, the gas must be compressed and cooled to a liquid state. This liquid CO2 is then stored in a tank, which is equipped with temperature and pressure regulators to maintain the desired conditions.

3. What are the benefits of storing CO2 gas in a temperature-controlled, pressure-controlled container?

Storing CO2 gas in a temperature-controlled, pressure-controlled container allows for safe and efficient transportation and storage of the gas. It also ensures that the gas remains in its liquid state, which takes up less space and makes it easier to handle. Additionally, this method helps to prevent the release of excess CO2 into the atmosphere.

4. How is CO2 gas used in various industries and applications?

CO2 gas has a wide range of uses in various industries and applications. It is commonly used in food and beverage production, such as carbonating drinks and preserving food. It is also used in fire extinguishers, as a refrigerant, and in the oil and gas industry for enhanced oil recovery.

5. What are the potential risks associated with CO2 gas in a temperature-controlled, pressure-controlled container?

While CO2 gas is generally considered safe, there are some potential risks associated with storing it in a temperature-controlled, pressure-controlled container. These include the risk of leaks or explosions if the container is not properly maintained, as well as the risk of suffocation if there is a buildup of CO2 gas in an enclosed space. Proper safety protocols and regular maintenance can help mitigate these risks.

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