What is the average velocity of the molecules in a gas?

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Homework Help Overview

The discussion revolves around calculating the average velocity of gas molecules, mean square speed, root mean square speed, and average kinetic energy of gas particles. The subject area includes gas laws and kinetic theory of gases.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to derive relationships between pressure, volume, temperature, and molecular speed. Questions about the dependencies of molecular speed and the mathematical expression of speed distribution in gases are raised.

Discussion Status

Some participants are sharing their working and reasoning, while others are questioning specific steps and assumptions in the calculations. There is an ongoing exploration of concepts without a clear consensus on the solutions.

Contextual Notes

Participants express uncertainty about the relationships between variables and seek clarification on their calculations. There is mention of specific values and conditions, such as pressure and temperature, that may influence the discussion.

CathyLou
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I'd really appreciate it if someone could please give me some hints over how to do the following questions as I'm currently really stuck.

8.

(a) What is the average velocity of the molecules in a gas?

(b) Explain your answer.

9. Two moles of He gas are at a pressure of 105 Pa and have a volume of 0.5m3.

(a) What is the mean square speed of the He atoms?

(b) What is the root mean square speed of the He atoms?

10. What is the average kinetic energy of the particles of a gas at 400ºC?

Thank you.

Cathy
 
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CathyLou said:
I'd really appreciate it if someone could please give me some hints over how to do the following questions as I'm currently really stuck.

8.

(a) What is the average velocity of the molecules in a gas?

(b) Explain your answer.

9. Two moles of He gas are at a pressure of 105 Pa and have a volume of 0.5m3.

(a) What is the mean square speed of the He atoms?

(b) What is the root mean square speed of the He atoms?

10. What is the average kinetic energy of the particles of a gas at 400ºC?
Why not show us what your thoughts are first?

What does the speed of molecules in a gas depend on? How is the distribution of speeds in a gas expressed mathematically?

AM
 
It is something to do with the mass of the gas and its volume or the pressure that it is under?
 
I'm now okay with number 10 but am still stuck on the others.

Here is my working so far for 9a:

PV = (1 x 105) x 0.5

PV = 50000

PV = nRT

So 50000 = 2 x 8.31 x T

T = 3008ºK

½ m x average speed squared = 3/2 k T

k = 1.38 x 10-23

so ½ m x average speed squared = 6.23 x 10-20

I'd really appreciate it if someone could please tell me what I've done wrong.

Thank you.

Cathy
 
Your method is correct but how does PV = 105 x 0.5 = 50000 :rolleyes:
 

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