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

• CathyLou
In summary, the conversation includes discussions about average velocity of molecules in a gas, mean square speed and root mean square speed of He atoms, and average kinetic energy of particles in a gas at 400ºC. The individual is seeking help on how to solve these questions and has shared their own working and asked for feedback.
CathyLou
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?

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

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?

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

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

The average velocity of molecules in a gas is the average speed of all the molecules in the gas. It is a measure of how fast the molecules are moving on average.

## How is the average velocity of molecules in a gas calculated?

The average velocity of molecules in a gas is calculated by taking the sum of all the velocities of the molecules and dividing it by the total number of molecules in the gas.

## Why is the average velocity of molecules in a gas important?

The average velocity of molecules in a gas is important because it helps us understand the behavior and properties of gases. It is also used in various calculations and equations in thermodynamics and fluid mechanics.

## Does the average velocity of molecules in a gas change?

Yes, the average velocity of molecules in a gas can change due to various factors such as changes in temperature, pressure, and volume of the gas. It is also affected by the type of gas and its molecular weight.

## How does the average velocity of molecules in a gas relate to temperature?

The average velocity of molecules in a gas is directly proportional to the square root of the temperature of the gas. This means that as the temperature increases, the average velocity of molecules in the gas also increases.

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