Velocity Distributions - Online Tutor, Practice Problems & Exam Prep

The Maxwell-Boltzmann distribution curve demonstrates how gas molecules' velocities are influenced by temperature and molecular weight. As temperature rises, the probable speed increases, with molecules moving at higher velocities. For instance, at 330°C, a significant number of gas molecules travel at 800 m/s or more, compared to fewer at 30°C. Conversely, an increase in molecular weight results in a decrease in probable speed; heavier gases like Xenon move slower than lighter ones like Helium. The distribution curve broadens and lowers with higher temperatures, indicating a wider range of velocities, while it narrows and peaks higher for gases with greater molecular weights, reflecting a more limited range of velocities. Understanding these trends is crucial for comprehending the behavior of gaseous molecules under varying conditions.

Velocity Distributions

The shape of the Maxwell Boltzmann 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, at the very top of each curve we have our probable speed. Remember the probable speed is where majority the gases will reside, the velocity in which they move. And what we should see here is that for the curve at a higher temperature, the probable speed where a majority of them is moving looks like it's around 600 meters per second. 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? Well, 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 gases moving at 800 meters per second or higher. Not a great amount, but if we increase the temperature to 330�C, we see we have a bigger chunk of gases moving at 800 meters per second or greater. That's what happens. Increasing the temperature increase the velocity of many of the gases within each curve. So from this we can say as a temperature also increases, the curve gets more broad and lower, so more gases are able to move at a higher velocity. That's also what it's showing.

For factor two we have molecular weight, so for factor two we have 4 curves. For four gases we have helium which is around 4g per mole, neon which is around 20 grams per mole, argon which is around 40 grams per mole or so and finally xenon which is around 131g per mole. What can we see here? Well, for helium, we can see that its probable speed is around 700 or so meters per second. And then for Xenon, the one that weighs the most, it's probable speed is only around 100 or so meters per second.

So what trend 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 weigh more as a gas, it's harder for you to propel yourself, move yourself. And that's what we're seeing. Helium weighs the least. So it's it's easier for 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 curve. So we can say here as the molecular weight decreases, the curve gets more broad and lower, meaning more gases 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, a molecular weight on their velocities.

Velocity Distributions Example 1

For this example question, it says the graph illustrated below shows the distribution of molecular velocities. How many of the following statements is R true? Alright, so we have Let's take a look. We have 3 curves within this graph. We have the red curve, the blue curve and 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 A 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 Co. It would have the highest temperature.

Next, for a given gas sample, curve C represents gas molecules with the smallest molar mass. Well, we said that the lower your molar mass then the also more broad your curve gets. Since curve C is the most broad, it makes sense that it would have the smallest molar mass. So this is true. And then here we just said that curve C has the highest smallest molar mass, so it couldn't have the highest molar mass as well.

And then for four for a given gas sample, the more narrow the velocity distribution, the lower the temperature O. 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 your curve will become. We'd say here that curve A is the most narrow, therefore it would be at the lowest temperature O. This statement here is true. The more narrow the velocity distribution in terms of the curve then the lower the temperature is.

So out of the four statements, two of them are true. This makes option C the correct choice.