How many argon molecules have velocities between 250 m/s and 500 m/s?

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In summary, the conversation discusses a problem involving a sealed bottle with 1 mole of neon and 1 mole of argon gas at 1 atm and 295K. The Figure shows the velocity distributions of the molecules of each gas. The task is to find the number of molecules of argon with velocities between 250 m/s and 500 m/s. The solution involves using the equations for kinetic energy and probability to determine the area under the curve, with the hint that argon has a higher molar mass than neon. Ultimately, the correct answer can be obtained by manually calculating the area under the top curve on the graph.
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baubletop
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Homework Statement


A sealed bottle at 1 atm of pressure holds 1 mole of neon and 1 mole of argon gas at a temperature of 295K. The curves in the Figure (http://phlnx3.pas.rochester.edu/webwork2_files/CAPA_Graphics/Gtype43/prob01a.gif) show the distributions of velocities of the molecules of each gas.
Find the number of molecules of argon which have velocities between 250 m/s and 500 m/s.

Homework Equations


KE = (3/2)kT
P(v) dv [itex]\propto[/itex] 4πv^2 e^((-(1/2)mv^2)/kT) dv
Molar Mass of Argon = 0.03995 kg/mol

The Attempt at a Solution


Totally lost on how to set this one up. I get that I need some sort of bound on the probability of finding Argon between 250 and 500 m/s, and from there I can get an actual number, but for now I'm somewhat lost.
The graph might be giving me the answer right in front of me but I'm also having a hard time reading it (it doesn't help that it's not labeled which curve is which element...).
 
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  • #2
Argon has a higher molar mass than neon. What does that tell you about which curve is which? As a last resort, you can count area under the curve from 250 to 500.
 
  • #3
It should be the top curve since vrms would be lower than Neon. I thought it would be harder than that but I just manually calculated the area and got the right answer. Guess I was overthinking it. Thanks!
 

FAQ: How many argon molecules have velocities between 250 m/s and 500 m/s?

1. What is a "sealed bottle of gases"?

A sealed bottle of gases refers to a container that holds a mixture of gases that are confined within the bottle by a stopper or cap. The gases inside the bottle are not in contact with the surrounding air and are thus isolated from the environment.

2. How are gases trapped in a sealed bottle?

Gases are trapped in a sealed bottle by creating a vacuum inside the bottle and then filling it with the desired gas mixture. This vacuum creates a pressure difference between the inside and outside of the bottle, which keeps the gases from escaping.

3. What are the properties of gases in a sealed bottle?

The properties of gases in a sealed bottle are similar to those of gases in an open container. They have no definite shape or volume and can be compressed easily. However, the pressure inside the bottle may be different from atmospheric pressure due to the presence of other gases or changes in temperature.

4. How do gases behave in a sealed bottle?

Gases in a sealed bottle behave according to the ideal gas law, which states that the pressure, volume, and temperature of a gas are all related. As the temperature or pressure changes, the volume of the gas may also change to maintain equilibrium.

5. What are some uses of sealed bottles of gases?

Sealed bottles of gases are commonly used in scientific experiments and research, as well as in various industrial processes. They can also be used for storing and transporting gases safely, as the sealed container prevents any leaks or interactions with the environment.

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