Calculating RMS Speed of Helium & Oxygen Gas at 260K

In summary, the problem involves finding the ratio of the root-mean-square speeds of monatomic helium and diatomic oxygen in a gas tank. The equation V(rms) = sqrt(3kT/m) can be used, where k is Boltzmann's constant, T is temperature, and m is the mass of a molecule. The masses of He and O2 must be substituted correctly in order to find the correct ratio.
  • #1
ChloeYip
93
1

Homework Statement

(introduction course of university physics)[/B]

A 5.0- liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen

(O2), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and

16.0 g/mol, respectively. What is the ratio of the root- mean- square (thermal) speed of helium to

that of oxygen?

Answer: C

Homework Equations


V(rms) = sqrt(3kT/m)

The Attempt at a Solution


This is the only equation I found from my book about rms speed of gas, but the variables seems unrelated at all. I have no idea on how to do it.

Please tell me how to deal with it in a more detail way.
Thank you very much.
 
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  • #2
ChloeYip said:
1
This is the only equation I found from my book about rms speed of gas, but the variables seems unrelated at all.
Unrelated to what? This is actually the correct equation to use.
 
  • #3
but how to pluck in the numbers? what should i manipulate to get the required variables?
can you be more specific please?
thanks
 
  • #4
The question is
ChloeYip said:
What is the ratio of the root- mean- square (thermal) speed of helium to
that of oxygen?
Start with that. How do you write that ratio?

ChloeYip said:
but how to pluck in the numbers?
What are k, T, and m?
 
  • #5
DrClaude said:
How do you write that ratio?
just divide the two which substituded in the equation

of course I know I have to find out all the variables mentioned in the question and the equation in order to answer the question...
but I just have no idea how to figure them out...
can you be more specific? i can't even guess them out... please don't just simply ask me to calculate the answer, because that's exactly my problem for can't getting the answer!

DrClaude said:
What are k, T, and m?
k is Boltzmann constant
t is temperature
m is mass of a molecule
of course i know them, by just substitute them!, but how to find them out?

sqrt(3*1.38e-23*260/1)/sqrt((3*1.38e-23*260/16)=4
but the answer is 2.8

I REALLY have no idea
whats wrong by plucking them in
or if i did something totally in the wrong track

please be more specific on how to do!
like how you figure out the answer
or your steps to calculate it
i can't do anything further based on your question which that seems to be common sense

thank you very much
 
Last edited:
  • #6
ChloeYip said:
k is Boltzmann constant
t is temperature
m is mass of a molecule
of course i know them, by just substitute them!, but how to find them out?

sqrt(3*1.38e-23*260/1)/sqrt((3*1.38e-23*260/16)=4
What are the masses of the molecules? The atomic mass of He is not 1 and the molar mass of the O2 is not 16.
 
  • #7
oh yes thanks
 

FAQ: Calculating RMS Speed of Helium & Oxygen Gas at 260K

How do you calculate the RMS speed of helium and oxygen gas at 260K?

To calculate the RMS (root mean square) speed of helium and oxygen gas at 260K, you can use the following formula:
RMS Speed = √(3RT/M)
where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin (260K in this case), and M is the molar mass of the gas. For helium, M = 4.003 g/mol and for oxygen, M = 31.999 g/mol. Plug in these values and solve for the RMS speed.

Why is calculating the RMS speed important in studying gases?

Calculating the RMS speed allows us to understand the distribution of molecular velocities in a gas. This is important in studying the behavior and properties of gases, such as diffusion and effusion. It also helps us to better understand the kinetic theory of gases and the relationship between temperature and molecular motion.

Can the RMS speed of a gas change at different temperatures?

Yes, the RMS speed of a gas is directly proportional to the square root of the temperature. This means that as the temperature increases, the RMS speed also increases. This relationship is described by the Maxwell-Boltzmann distribution.

Is the RMS speed the same for all molecules in a gas?

No, the RMS speed is an average value that represents the speed of a gas molecule at a given temperature. Not all molecules in a gas will have the same speed, as their velocities follow a distribution curve. However, the RMS speed is the most probable speed for a molecule in the gas.

Is there a difference in the RMS speed of different gases at the same temperature?

Yes, the RMS speed of a gas is dependent on its molar mass. Heavier gases, such as oxygen, will have a lower RMS speed at the same temperature compared to lighter gases, such as helium. This is because heavier molecules have a lower average speed due to their larger mass.

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