What is the total pressure and partial pressure of gases in a closed system?

In summary, two cylinders at 27° C with different volumes and pressures are connected by a closed stopcock system. One cylinder contains hydrogen and the other contains helium. Using the ideal gas law and Dalton's partial pressure equation, the number of moles of each gas can be calculated. When the valve is opened, the total pressure will be a combination of the individual pressures of the two gases. The partial pressure of each gas can also be determined at 27° C when the valve is opened. The volume of the tube connecting the two cylinders can be neglected.
  • #1
elitespart
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1. Assume that two cylinders at 27° C are connected by a closed stopcock(valve) system. The right-hand cylinder contains 2.4L of hydrogen at 0.600 atm; the left cylinder is larger and contains 6.8 L of helium at 1.40 atm.
a) How many moles of each gas are present?
b) What is the total pressure when the valve is open?
c) Determine the partial pressure of these two gases at 27° C when the stopcock is opened.




2. Homework Equations : PV=nRT and Dalton's partial pressure equation.



3. I got the moles of each gas for part a. For b and c, do I just add up the the individual volumes to get the total volume when the valve is opened? For some reason I'm just thinking that there is a tube connecting the two cylinders which would add additional volume. Thanks.
 
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  • #2
Neglect the tube volume.
 
  • #3



I am happy to provide a response to your inquiry. Based on the given information, it is important to note that the total pressure and partial pressure of gases in a closed system are dependent on the volume, temperature, and number of moles of gases present.

To answer your questions, let's go through each part step by step:

a) To determine the number of moles of each gas present, we can use the ideal gas law equation PV = nRT. Rearranging it to solve for n, we get n = PV/RT. Plugging in the values for each gas, we get 0.600 atm * 2.4 L / (0.08206 L atm/mol K * 300 K) = 0.0589 moles of hydrogen and 1.40 atm * 6.8 L / (0.08206 L atm/mol K * 300 K) = 0.204 moles of helium.

b) When the valve is opened, the two cylinders will be connected and the gases will mix together. The total pressure will be the sum of the individual pressures of each gas. So, the total pressure will be 0.600 atm + 1.40 atm = 2.00 atm.

c) To determine the partial pressures of each gas, we can use Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas. So, when the valve is opened, the partial pressure of hydrogen will be 0.600 atm and the partial pressure of helium will be 1.40 atm.

Regarding your question about the volume, yes, we can add the individual volumes of the two cylinders to get the total volume when the valve is opened. The connecting tube between the two cylinders does not add any additional volume, as it is considered a negligible volume.

I hope this helps clarify your understanding of the total pressure and partial pressure of gases in a closed system. Let me know if you have any further questions.
 

1. What is partial pressure?

Partial pressure is the pressure exerted by a single gas in a mixture of gases. It is the contribution of that gas to the total pressure of the mixture.

2. How is partial pressure calculated?

Partial pressure can be calculated by multiplying the total pressure of the mixture by the mole fraction of the gas in the mixture. The mole fraction is the ratio of moles of the gas to the total moles of all gases in the mixture.

3. Why is partial pressure important?

Partial pressure is important because it helps us understand how individual gases contribute to the overall pressure of a gas mixture. It is also used in various scientific and industrial processes, such as gas chromatography and gas law calculations.

4. How does temperature affect partial pressure?

According to the Ideal Gas Law, as temperature increases, the kinetic energy of gas molecules increases, causing them to collide more frequently and with greater force. This results in an increase in the partial pressure of the gas in the mixture.

5. What is the relationship between partial pressure and concentration?

In a gas mixture, the partial pressure of a gas is directly proportional to its concentration. This means that as the concentration of a gas increases, so does its partial pressure, assuming all other factors remain constant.

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