The graph below shows the distribution of molecular speeds for a gas at two different temperatur

step 1 So we have a graph here that represents two different things. We've got the molecular speed of a

The graph below shows the distribution of molecular speeds...

Key Concepts

Diffusion in Gases

Diffusion is the process by which gas molecules spread out from an area of higher concentration to lower concentration. It is inherently linked to the speed of the molecules; higher molecular speeds at elevated temperatures lead to faster diffusion as molecules traverse larger distances in a given time.

Temperature and Kinetic Energy

Temperature in a gas is directly related to the average kinetic energy of its molecules. Higher temperatures mean that the gas molecules, on average, possess greater kinetic energy, which results in higher speeds and a wider distribution of molecular speeds.

Maxwell-Boltzmann Distribution

This is a statistical distribution that describes the spread of molecular speeds in a gas. It shows that at a given temperature, molecules have a range of speeds, with most molecules moving around a most probable speed. As temperature increases, the distribution shifts so that a larger fraction of molecules move at higher speeds and the spread of speeds becomes broader.

Molecular Speed Distribution

This concept refers to the pattern of speeds that molecules in a gas exhibit. At lower temperatures, the distribution is narrower and centered at lower speeds, while at higher temperatures, the distribution widens and its peak shifts to higher speeds. This distinction helps in predicting gas behavior under different thermal conditions.

Transcript

00:01 So we have a graph here that represents two different things.

00:03 We've got the molecular speed of a gas on the x -axis, and we've got the relative number of molecules going at that speed on the y -axis.

00:11 Now, we want to know which curve fits a gas at a lower temperature.

00:17 So we need to make a couple connections.

00:20 We need to first know that a temperature's or a gases kinetic energy is directly proportionate to its temperature in, kelvin.

00:32 And we also need to know that as kinetic energy goes up, so does the speed.

00:39 So as kinetic energy goes up, so does the speed.

00:43 So that also means that as temperature increases, so to speed.

00:48 As temperature increases, kinetic energy increases, and so does speed.

00:52 As temperature decreases, gets colder, so does its kinetic energy goes slower, speed is slower.

01:01 So if we want to know which curve fits a gas at a lower temperature.

01:05 We have to look and see which one has a lower speed.

01:07 And we would say that our red curve does.

01:10 Our red curve is representative of a lower speed.

01:17 And in our second question, we want to know which curve depicts a gas of a higher kinetic energy.

01:24 So we've essentially just answered this question.

01:27 We know that a higher kinetic energy is going to be related to a higher temperature and a higher speed.

01:32 But we can explain this with a little bit of math, just a little bit.

01:37 So we've got kinetic energy, average kinetic energy, oops, wrong, so equals, okay, so an average kinetic energy equals two -thirds, two -thirds, r over n -a times t.

01:59 Now, we break this down.

02:01 We've got essentially three constants and our temperature.

02:05 We've got two -thirds, which is a constant.

02:07 We've got r, which is 8 .4 .4.

02:10 314 joules per mole times k.

02:16 And then we've got na, which is avogadro's number, and that is 6 .022 times 10 to the 23rd.

02:24 So looking at this, we've got essentially one big constant right here.

02:30 We've got two -thirds a constant, multiplied by r constant divided by n .a.

02:36 A constant.

02:37 All a constant.

02:37 So we know that ek is really only influenced by our temperature.

02:45 Ek and temperature are directly related by this logic.

02:48 Constant times a high temperature gives us a higher kinetic energy.

02:53 So our question, going back to that, which curve depicts a higher kinetic energy? well, we would say that the curve with the higher temperature and higher speed.

03:04 Because remember, we know that higher temperature and higher speed, higher kinetic energy all the same thing.

03:10 So increasing temperature, increasing kinetic energy, increase in speed.

03:16 The answer to which curve depicts a higher kinetic energy is going to be the one with the higher temperature and higher speed...

Please give Ace some feedback