# Nitrogen Gas Molecule Speeds and Temperature Relationship

• weathercheck
In summary, the conversation discusses the percentage of molecules in an ideal gas with speeds less than various multiples of the root-mean-square velocity, specifically in the case of nitrogen gas with a molar mass of 28.0 g/mol. The question at hand is how to determine the temperature at which 94.7% of all nitrogen molecules have speeds less than 1500 m/s. The conversation includes an equation for calculating the root-mean-square velocity and a mention of a table in the textbook that provides information on the percentage of molecules with speeds below a certain multiple of the root-mean-square velocity.
weathercheck

## Homework Statement

Fractions of Molecules in an Ideal Gas with Speeds Less than Various Multiples of v/v_{\rm rms} in the textbook. The molar mass of {\rm{N}}_2 is 28.0 {\rm{ g/mol}}.

For a gas of nitrogen molecules {{\rm{N}}_2 } , what must the temperature be if 94.7\% of all the molecules have speeds less than 1500 \rm m/s?

## Homework Equations

Vrms = sqrt(3kt/m)

## The Attempt at a Solution

Really don't know where to start with the percentages and the relevance of the fracitons of molecules in an ideal gas with speeds less than various multiples etc??

Any help?

hmmmmmmmmm...

I suppose there is a table in your book which tells you that 94.7% will have a speed smaller than 2x the rms velocity. You now know that 94.7% has a speed smaller than 1500m/s.
It should be easy to get the rms speed from that and then the temperature from your equation

I have tried it.

It says 94.7% have a speed less than (v/v_rms = 1.6). this is confsuing me. What does this mean? Clearly from that I can find v_rms, and plug it into the given equation above.

How would you use the figure that I am given to find the Vrms ??

can you state exactly what is given in your book?

## What is the Kinetic Theory of Gases?

The Kinetic Theory of Gases is a scientific model that explains the behavior of gases based on the motion of the individual molecules. It states that gases are made up of tiny particles that are in constant, random motion and that the pressure exerted by a gas is a result of the collisions between these particles and the walls of the container.

## How does temperature affect the behavior of gases according to the Kinetic Theory?

According to the Kinetic Theory, as temperature increases, the average speed of gas molecules also increases. This means that the molecules collide with each other and the walls of the container more frequently, resulting in an increase in pressure.

## What is the relationship between volume and pressure in the Kinetic Theory of Gases?

The Kinetic Theory states that as the volume of a gas increases, the pressure decreases. This is because the molecules have more space to move around, decreasing the frequency of collisions and therefore, reducing the pressure. Similarly, as volume decreases, the pressure increases.

## Can the Kinetic Theory of Gases be used to explain the behavior of real gases?

While the Kinetic Theory of Gases is a simplified model, it can be used to explain the behavior of most gases under normal conditions. However, it does not take into account intermolecular forces or the volume occupied by the gas molecules, so it may not accurately predict the behavior of real gases at high pressures or low temperatures.

## How does the Kinetic Theory of Gases explain the relationship between temperature and volume?

According to the Kinetic Theory, as temperature increases, the average speed of gas molecules also increases. This means that the molecules exert more force on the walls of the container, causing the gas to expand and take up more volume. Conversely, as temperature decreases, the molecules have less energy and the gas occupies a smaller volume.

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