Calculating the Mass of a Gas Molecule Using Kinetic Theory

In summary, to calculate the mass of a molecule of an ideal gas with a temperature of 320 K and an rms molecular speed of 1631 m/s, you can use the equation M = 3RT / u^2 or u = √(3kT/m) and then convert the molar mass to kg/molecule or use the value directly.
  • #1
dnl65078
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Homework Statement


A sample of an ideal gas is at a temperature of 320 K. The rms molecular speed at this temperature is measured as 1631 m/s. Calculate the mass of a molecule of this gas


Homework Equations



rms velocity , u = √(3RT/M )

The Attempt at a Solution



Given u = 1631 m / s
Temperature , T = 320 K
R = gas constant = 8.314 J/ mol . K
Molar mass of the gas molecule , M = 3RT / u 2
= 3 * 10^-3 Kg / mol
 
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  • #2
Right. You can convert to kg/molecule now, or you can use u=sqrt(3kT/m) instead of u=sqrt(3RT/M) and get the answer directly.
 
  • #3
so do i just multply by 6.02e23?
 

1. What is the Kinetic Theory Problem?

The Kinetic Theory Problem is a fundamental concept in physics that explains the behavior of particles in a gas. It states that the temperature of a gas is directly proportional to the average kinetic energy of its particles.

2. How does the Kinetic Theory Problem relate to the properties of gases?

The Kinetic Theory Problem explains the macroscopic properties of gases such as pressure, volume, and temperature in terms of the microscopic behavior of its particles. It helps to understand and predict how gases will behave under different conditions.

3. What are the assumptions of the Kinetic Theory Problem?

The Kinetic Theory Problem is based on three main assumptions: 1) Gas particles are in constant, random motion, 2) The particles have negligible volume, and 3) The particles do not interact with each other except during collisions.

4. How does the Kinetic Theory Problem explain the relationship between temperature and kinetic energy?

The Kinetic Theory Problem states that as the temperature of a gas increases, the average kinetic energy of its particles also increases. This is because at higher temperatures, the particles move faster and have more energy.

5. How is the Kinetic Theory Problem used in real-world applications?

The Kinetic Theory Problem is used in a variety of real-world applications, such as predicting the behavior of gases in different environments, understanding the properties of materials, and designing technologies like refrigerators and combustion engines.

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