Finding what fraction of molecules have speeds over a certain value

In summary, the problem involves finding the number of oxygen gas molecules with speeds between 375 m/s and 380 m/s, given a sample with a molar mass of 32 g/mol, containing 5.0 moles, and at a temperature of 500 K. The Maxwell Boltzmann distribution can be used to calculate the probability of molecules having a certain speed, and by integrating over the given speed range, the number of molecules with speeds in that range can be determined.
  • #1
Erubus
22
0

Homework Statement


A sample of oxygen gas with molar mass 32 g/mol contains 5.0 moles and is at a temperature of 500 K. How many moles of the gas have speeds between 375 m/s and 380 m/s?

Homework Equations


Maxwell Boltzmann Distribution:
f(v) = 4[itex]\pi[/itex][[itex]\frac{M}{2pi RT}[/itex]]^(3/2) * v^2 * e^[(-Mv^2)/(2RT)]

The Attempt at a Solution


I know that this function gives the probablility of having the molecules at some speed v, but I'm not sure how to translate this over a range or how to calculate the number of moles over this range.
 
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  • #2
Do you know how to use the M-B distribution to find out how many molecules have a speed greater than 380 m/s?

Do you know how to use the M-B distribution to find out how many molecules have a speed greater than 375 m/s?
 
  • #3
I figured it out, thanks!
 

FAQ: Finding what fraction of molecules have speeds over a certain value

1. How do you determine the fraction of molecules with speeds over a certain value?

To find the fraction of molecules with speeds over a certain value, we first need to know the total number of molecules in the system. Then, we need to measure the number of molecules that have speeds over the specified value. The fraction can then be calculated by dividing the number of molecules with speeds over the specified value by the total number of molecules.

2. What is the importance of knowing the fraction of molecules with speeds over a certain value?

Knowing the fraction of molecules with speeds over a certain value is important in understanding the dynamics and behavior of a system. It can also provide insights into the energy distribution of the molecules and can be used to make predictions about the system's behavior.

3. How do you measure the speed of molecules in a system?

The speed of molecules can be measured using various techniques such as thermal cameras, laser spectroscopy, or particle tracking methods. These methods involve measuring the displacement or emission of particles and using mathematical equations to calculate their speed.

4. Can the fraction of molecules with speeds over a certain value change over time?

Yes, the fraction of molecules with speeds over a certain value can change over time. This can be due to various factors such as changes in temperature, pressure, or interactions with other molecules. Therefore, it is important to constantly monitor and analyze the speed distribution of molecules in a system.

5. How does the speed of molecules affect the properties of a system?

The speed of molecules can affect the properties of a system in many ways. For example, in a gas system, the average speed of molecules is directly proportional to the temperature. In a chemical reaction, the speed of reactant molecules can determine the rate of the reaction. Changes in the speed of molecules can also affect the viscosity, density, and other physical properties of a system.

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