Calculating vrms of Helium in Mixture of Gases

In summary, to find the root-mean-square velocity for Helium atoms in a gas mixture containing Helium and Oxygen molecules, we can use the equation 1/2mv^2=1/2mv^2 and solve for velocity of He. However, the masses needed for this calculation would depend on whether the molecule is polyatomic or monatomic, and can be found by looking at a periodic table. A useful reference for this calculation can be found at http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kinthe.html#c3.
  • #1
sheri1987
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Homework Statement



A gas bottle contains a mixture of Helium and Oxygen molecules (O2 is diatomic). The root-mean-square velocity for the O2 molecules is 482 m/s. Find vrms for the Helium atoms.


Homework Equations



1/2mv^2=1/2mv^2

and solve for velocity of He, however, i am not sure what numbers to plug in for the mass.

The Attempt at a Solution



I filled everything in but the masses, I know that oxygen is diatomic, or O2, but what does that mean I put in for the mass? Do I need to use the mass numbers by looking at a periodic table?
 
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Yes, in order to calculate the vrms for Helium, you will need to use the mass of Helium. The mass of Helium is 4.003 atomic mass units (amu) or 4.003 grams per mole (g/mol). This can be found on a periodic table.

The equation for calculating vrms is: vrms = √(3RT/M), where R is the gas constant (8.314 J/mol*K) and T is the temperature in Kelvin.

Since the temperature is not given in the homework statement, you will need to use the given information about the root-mean-square velocity for O2 molecules. The root-mean-square velocity is related to the average kinetic energy of the molecules, which is directly proportional to the temperature. Therefore, you can use the given velocity of 482 m/s to calculate the temperature in Kelvin using the equation: v^2 = 3RT/M.

Once you have calculated the temperature, you can plug in the values for R, T, and M (mass of Helium) into the equation for vrms and solve for the velocity of Helium.

I hope this helps. Remember to always check your units and make sure they are consistent throughout the calculation. Good luck with your homework!
 

1. How is the root mean square velocity (vrms) of helium calculated in a mixture of gases?

The vrms of helium in a mixture of gases is calculated using the equation vrms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of helium.

2. What is the significance of calculating the vrms of helium in a mixture of gases?

Calculating the vrms of helium in a mixture of gases allows us to understand the behavior and movement of helium atoms within the gas mixture. It can also help determine the contribution of helium to the overall kinetic energy of the mixture.

3. Can the vrms of helium be affected by the presence of other gases in the mixture?

Yes, the vrms of helium can be affected by the presence of other gases in the mixture. This is because the vrms is dependent on the temperature and molar mass of the gas, both of which can be influenced by the other gases present.

4. How does the temperature of the gas mixture impact the vrms of helium?

The vrms of helium is directly proportional to the square root of the temperature. This means that as the temperature of the gas mixture increases, the vrms of helium will also increase.

5. Is there a difference in calculating the vrms of helium in a mixture of gases compared to calculating it in a pure helium gas?

Yes, there is a difference in calculating the vrms of helium in a mixture of gases compared to a pure helium gas. In a mixture of gases, the molar mass used in the equation will be the average of the molar masses of all the gases present, while in a pure helium gas, the molar mass used will be the molar mass of helium alone.

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