Pressure and Mass: Calculating Oxygen and Helium Molecules in a Tank

In summary, the conversation discusses the pressure change in a storage tank when replacing N2 with CO2, and also the number of molecules, average kinetic energy, and RMS speeds of oxygen and helium molecules in a scuba tank filled with a mixture of the two gases. The solution involves using the PV=NkT equation and calculating the number of molecules using the given conditions. The results show that the average kinetic energy of oxygen is higher than that of helium, and the RMS speeds of oxygen and helium are 810m/s and 393m/s respectively.
  • #1
qomoco
12
0

Homework Statement


A storage tank contains 29.5 kg of N2 at a pressure of 3.87. What will thep ressure be if the N2 is replaced with an equal mass of CO2


Homework Equations


PV=nRT
PV=NKT
PV=nNkT


The Attempt at a Solution




I know CO2 mass is going to be 25kg.


Another one:



A scub tank has a volume of 3500.0 cm cubed. For very deep dives, the tank is filled with 50%(by volume) pure oxygen and 50% helium.
A)how many molecules are in the tnak of each type of molecule if it is filled at 20.0 C to a gauge pressure of 11 atm.
B) how does the average kinetic engergy of the oxygen molecules compare to the average kinetic energy of the helium?
C) calculate the rms speeds for eacdh type of molecule

Attempt:
I used PV=NkT
set (.0035m)(101000Pa)(11)=N(1.38x10^-23)(293K)

and found N=9.6x10^23
 
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  • #2
molecules B) The average kinetic energy of oxygen will be higher than the average kinetic energy of heliumC) Using rms speed=sqrt 3/2 kT/mThe rms speed of oxygen is 810m/s and the rms speed of helium is 393m/s.
 
  • #3
molecules of gas in the tank.

For part B, the average kinetic energy of a gas molecule is directly proportional to its temperature. Since both oxygen and helium are at the same temperature in the tank, they will have the same average kinetic energy.

For part C, the root mean square (rms) speed of a gas molecule is given by the equation vrms=√(3RT/M), where R is the gas constant, T is the temperature, and M is the mass of the molecule. Plugging in the values for oxygen and helium, we get vrms (O2)= 465.2 m/s and vrms (He)= 1177.3 m/s. This shows that helium molecules have a higher rms speed compared to oxygen molecules, due to their lower mass.
 

Related to Pressure and Mass: Calculating Oxygen and Helium Molecules in a Tank

1. How is pressure calculated in a tank of oxygen and helium molecules?

In order to calculate the pressure in a tank of oxygen and helium molecules, you must first determine the total number of molecules present. This can be done by using the ideal gas law, which states that pressure is equal to the number of moles of gas multiplied by the gas constant and the temperature. Once you have the total number of molecules, you can use the formula for pressure, which is force per unit area, to determine the pressure in the tank.

2. How do you calculate the mass of oxygen and helium molecules in a tank?

In order to calculate the mass of oxygen and helium molecules in a tank, you must know the number of molecules present and their individual molecular weights. This can be done by using the Avogadro's number, which represents the number of molecules in one mole of a substance. Once you have the total number of molecules and their molecular weights, you can use the formula for calculating mass, which is mass = number of molecules * molecular weight.

3. What is the difference between oxygen and helium molecules in terms of pressure and mass?

Oxygen and helium molecules have different molecular weights, which means that they will have different masses in the same volume of gas. This also means that they will exert different pressures in the tank, as the pressure is directly proportional to the number of molecules present. Additionally, helium molecules are smaller and lighter than oxygen molecules, so they will take up more space and exert less pressure compared to the same number of oxygen molecules.

4. How does temperature affect the pressure and mass of oxygen and helium molecules in a tank?

According to the ideal gas law, temperature is directly proportional to pressure, meaning that an increase in temperature will result in an increase in pressure. This will also affect the mass of the molecules in the tank, as an increase in temperature will cause the molecules to move faster and take up more space, resulting in a higher mass calculation.

5. What are some potential risks associated with handling tanks of oxygen and helium molecules?

One potential risk is the high pressure inside the tank, which can cause explosions if not handled properly. Another risk is the potential for oxygen and helium to mix together, creating a dangerous combination that can cause a fire or explosion. It is also important to handle these tanks with caution as they may contain compressed gases that can be harmful if inhaled or come into contact with skin.

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