**Velocity Distributions** represent probability distributions for a gas when examining their molar mass and temperature.

Velocity Distribution Curves

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concept

## Velocity Distributions

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the shape of the Maxwell bolts man distribution curve is dependent on two factors temperature and molecular weight. So for the first factor temperature, we have two curves, ones at 30°C and one's at 330°C. If we look at the apex with the very top of each curve, we have our probable speed. Remember the probable speed is where a majority of the gasses will reside. The velocity in which they move. What we should see here is that for the curve at a higher temperature, The probable speed where a majority of them was moving looks like it's around 600 m/s. But the probable speed for the curve at a lower temperature Is only around 400 or so meters per second. So what trend can we see here? What we can see here that as my temperature increases the molecules moving at a higher velocity also increase. If we take a look here for the green curve, we have just in this little portion here, this many gasses moving At 800 m/s or higher. Not a great amount, but if we increase the temperature two, we see we have a bigger chunk of gasses moving at m/s or greater. That's what happens, increasing the temperature, increase the velocity of many of the gasses within each curve. So from this we can say as the temperature also increases the curve gets more broad and lower. So more gasses are able to move at a higher velocity. That's also what it's showing Factor two We have molecular weight. So for factor too, We have four curves for four gasses. We have helium which is around four grams per mole Neon, which is around 20 g per mole Argon which is around 40 g from all or so. And finally Xenon, which is around 131 g per mole. What can we see here? Well, for helium, we can see that it's probable speed is around 700 or so meters per second and then for Xenon, the one that wins the most, it's probable speed is only around 100 or so meters per second. So which brand can we make here? Well, the trend we see here is that as the molecular weight increases, molecules moving at a higher velocity decreases. So if you wait more as a gas, it's harder for you to propel yourself, move yourself and that's what we're seeing. Helium weighs at least. So it's it's easier for it to move faster around Now. As a result of this, Also, in terms of molecular weight, we can see that helium, which weighs the least, also has the most broad her. So we can say here, as the molecular weight decreases, the curve gets more broad and lower meaning more gasses are able to get to a certain type of velocity as everyone else. Right? So these are the trends we need to realize when it comes to gaseous molecules when we factor in the effects of temperature and molecular weight on their velocities.

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example

## Velocity Distributions Example 1

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for this example. Question. It says the graph illustrated below shows the distribution of molecular velocities. How many of the following statements is our true? All right, So we have Let's take a look. We have three curves within this graph. We have the red curve, the blue curve in the green one. Here we can see that on our Y axis, we have the number of molecules, and then on our X axis we have our velocities. So for one at a given temperature curve, a is measured at the highest temperature, so curve is the red one. Remember, we said that the higher your temperature goes than the more broad, the more broad the curve gets the most broad one is the green curve curve C, so it would have the highest temperature. Next for a given gas sample. Courtesy represents gas molecules with the smallest Mueller Mass. What we said that the lower your Mueller Mass than the also more broad you're curve gets. Since Curve C is the most broad, it makes sense that it would have the smallest Mueller Mass. So this is true. And then here we just said that Curve C has the highest on smaller, smaller mass, so it couldn't have the highest smaller Massa's well and then for four forgiven gas sample. The more narrow the velocity distribution, the lower the temperature. So remember, we said, the higher your temperature gets, the more broad the curve becomes. So if we do the opposite, the lower your temperature gets, then the more narrow you're curve will become. We'd say here that curve A is the most narrow. Therefore, it would be at the lowest temperature. So this statement here is true. The more narrow the velocity distribution in terms of the curve in the lower the temperature is so out of the four statements, two of them are true. This makes options see the correct choice.

Additional resources for Velocity Distributions

PRACTICE PROBLEMS AND ACTIVITIES (4)

- Consider the following graph. (b) If A and B refer to the same gas at two different temperatures, which repres...
- Consider the following graph. (a) If curves A and B refer to two different gases, He and O2, at the same tempe...
- The graph shows the distribution of molecular velocities for two different molecules (A and B) at the same tem...
- The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (...