 ## General Chemistry

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

7. Gases

# Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution is a probability distribution curve that describes the speed of a gas at a specific temperature.

Distribution Curve
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concept

## Maxwell-Boltzmann Distribution 54s
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So the Maxwell bolts man distribution is a probability distribution that describes the speed of ideal gasses at a given temperature. So as temperature changes, the velocities of gas molecules will vary. Now, a probability distribution itself is just the region of the curve that shows the relative number of gas molecules. So we choose a temperature and we can get the relative number of gas molecules traveling at that velocity. Now to do this, we use a distribution function to determine these varying velocities, but it's beyond the scope of this class. So this complex formula, don't worry about it too much. You're not gonna see it within this course. Instead, we're gonna use our memory tool that just remember to a three for your velocity. So we'll see different types of velocities when looking at a distribution curve And we'll use 283 to help us remember which is which.
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concept

## Maxwell-Boltzmann Distribution 3m
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So like I said earlier, just remember to a three for your velocity. So here we have three different velocities, or speed that is involved with a distribution curve. So here we have to. Then we have eight, and then we have three. The first speed or velocity represents the speed at the top of the curve that represents the largest number of molecules with that speed. This is called your probable speed. So if you had to guess, you would say a majority of gas is within a container. Have this speed? Most likely. Next we have the average speed of gaseous molecules. What's another word for average? Mean, So here mean speed and it's equal to square root of eight rt over em Now. Next we have the speed that is the square root of the average speed squared, so that's just our root mean square speed. So if you've watched this video earlier, you know it's pretty familiar to us. So here root mean square speed equals square root of three rt over em. Now we're talking about M R T. M. Here represents the molar mass of the gas in kilograms per mole. So all of These are kilograms per mole because we're talking about speed or velocity. Remember, our our becomes 8.314 and will be jewels over moles times K. And then temperature is always is in Kelvin. When we're dealing with calculations Now, this probable speed means speed and root mean square speed can be transfixed or put onto a distribution curve. So let's take a look at this distribution curve here. So we're gonna say here that our distribution curve on our Y axis we have our probability distribution. This is can be seen as the likelihood off X number of gas molecules with within a container existing there. So and on our X axis, we have our velocity from zero all the way up to 13 50 m per second. We can see at the very top. We have our probable speed. So what, this is telling me? It's telling me at 400 m per second, most likely if you're gonna look at a particular gas, it has the most likely chance off following here around 400 m per second because that's where the curve is the highest. Next right next to it is we have our average or mean speed notice here that are probable speeds around 400 m per second and our average or mean speed is a little bit higher than that. And then even higher than both of them is our routing square speed. We see that it kind of falls close to 600 m per second. So here this distribution curve, this is showing us the varying velocities for collection of gasses and what we need to understand in terms of velocity of increasing velocity. We would say that root mean square speed we can see is the highest because it's closest to 600. Then we can see next would be our average or mean speed, and then we would see that are probable. Speed would be the lowest in terms of velocity when it comes to this chart. Okay, so that's the way we need to think about it in terms off the different types of velocities or speeds that exists at any given temperature. That's the whole idea behind the Maxwell distribution curve
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example

## Maxwell-Boltzmann Distribution Example 1 1m
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