[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.40,0:00:02.23,Default,,0000,0000,0000,,- [Instructor] Collision theory
Dialogue: 0,0:00:02.23,0:00:05.13,Default,,0000,0000,0000,,can be related to\NMaxwell-Boltzmann distributions.
Dialogue: 0,0:00:05.13,0:00:07.59,Default,,0000,0000,0000,,And first we'll start\Nwith collision theory.
Dialogue: 0,0:00:07.59,0:00:09.97,Default,,0000,0000,0000,,Collision theory says that\Nparticles must collide
Dialogue: 0,0:00:09.97,0:00:13.86,Default,,0000,0000,0000,,in the proper orientation and\Nwith enough kinetic energy
Dialogue: 0,0:00:13.86,0:00:17.37,Default,,0000,0000,0000,,to overcome the activation energy barrier.
Dialogue: 0,0:00:17.37,0:00:21.13,Default,,0000,0000,0000,,So let's look at the reaction\Nwhere A reacts with B and C
Dialogue: 0,0:00:21.13,0:00:24.42,Default,,0000,0000,0000,,to form AB plus C.
Dialogue: 0,0:00:24.42,0:00:28.24,Default,,0000,0000,0000,,On an energy profile, we\Nhave the reactants over here
Dialogue: 0,0:00:28.24,0:00:29.58,Default,,0000,0000,0000,,in the left.
Dialogue: 0,0:00:29.58,0:00:33.66,Default,,0000,0000,0000,,So A, atom A is colored red,
Dialogue: 0,0:00:33.66,0:00:36.59,Default,,0000,0000,0000,,and we have molecule BC over here,
Dialogue: 0,0:00:36.59,0:00:39.79,Default,,0000,0000,0000,,So these two particles must collide
Dialogue: 0,0:00:39.79,0:00:43.15,Default,,0000,0000,0000,,for the reaction to occur,
Dialogue: 0,0:00:43.15,0:00:45.40,Default,,0000,0000,0000,,and they must collide with enough energy
Dialogue: 0,0:00:45.40,0:00:48.07,Default,,0000,0000,0000,,to overcome the activation energy barrier.
Dialogue: 0,0:00:48.07,0:00:51.21,Default,,0000,0000,0000,,So the activation energy\Non an energy profile
Dialogue: 0,0:00:51.21,0:00:52.25,Default,,0000,0000,0000,,is the difference in energy
Dialogue: 0,0:00:52.25,0:00:56.01,Default,,0000,0000,0000,,between the peak here, which\Nis the transition state
Dialogue: 0,0:00:56.01,0:00:57.61,Default,,0000,0000,0000,,and the energy of the reactants.
Dialogue: 0,0:00:57.61,0:01:01.81,Default,,0000,0000,0000,,So this energy here is\Nour activation energy.
Dialogue: 0,0:01:01.81,0:01:04.03,Default,,0000,0000,0000,,The minimum amount of energy necessary
Dialogue: 0,0:01:04.03,0:01:06.77,Default,,0000,0000,0000,,for the reaction to occur.
Dialogue: 0,0:01:06.77,0:01:09.83,Default,,0000,0000,0000,,So if these particles\Ncollide with enough energy,
Dialogue: 0,0:01:09.83,0:01:13.92,Default,,0000,0000,0000,,we can just get over this\Nactivation energy barrier
Dialogue: 0,0:01:13.92,0:01:17.65,Default,,0000,0000,0000,,and the reactions can turn\Ninto our two products.
Dialogue: 0,0:01:20.02,0:01:22.09,Default,,0000,0000,0000,,If our reactant particles\Ndon't hit each other
Dialogue: 0,0:01:22.09,0:01:25.34,Default,,0000,0000,0000,,with enough energy, they\Nsimply bounce off of each other
Dialogue: 0,0:01:25.34,0:01:27.07,Default,,0000,0000,0000,,and our reaction never occurs.
Dialogue: 0,0:01:27.07,0:01:30.82,Default,,0000,0000,0000,,We never overcome this\Nactivation energy barrier.
Dialogue: 0,0:01:30.82,0:01:33.42,Default,,0000,0000,0000,,As an analogy, let's think\Nabout hitting a golf ball.
Dialogue: 0,0:01:33.42,0:01:35.31,Default,,0000,0000,0000,,So let's imagine we have a hill,
Dialogue: 0,0:01:35.31,0:01:37.15,Default,,0000,0000,0000,,and on the right side of the hill,
Dialogue: 0,0:01:37.15,0:01:39.05,Default,,0000,0000,0000,,somewhere is the hole down here,
Dialogue: 0,0:01:39.05,0:01:42.70,Default,,0000,0000,0000,,and the left side of the\Nhill is our golf ball.
Dialogue: 0,0:01:42.70,0:01:45.72,Default,,0000,0000,0000,,So we know we have to hit this\Ngolf ball with enough force
Dialogue: 0,0:01:45.72,0:01:47.92,Default,,0000,0000,0000,,to give it enough kinetic energy
Dialogue: 0,0:01:47.92,0:01:49.97,Default,,0000,0000,0000,,for it to reach the top of the hill
Dialogue: 0,0:01:49.97,0:01:53.05,Default,,0000,0000,0000,,and to roll over the hill\Nand go into the hole.
Dialogue: 0,0:01:53.05,0:01:55.32,Default,,0000,0000,0000,,So we can imagine this hill
Dialogue: 0,0:01:55.32,0:01:58.58,Default,,0000,0000,0000,,as being a hill of potential energy.
Dialogue: 0,0:01:58.58,0:02:02.08,Default,,0000,0000,0000,,And this golf ball needs to\Nhave enough kinetic energy
Dialogue: 0,0:02:02.08,0:02:06.35,Default,,0000,0000,0000,,to turn into enough potential\Nenergy to go over the hill.
Dialogue: 0,0:02:09.39,0:02:11.23,Default,,0000,0000,0000,,If we don't hit our golf ball hard enough,
Dialogue: 0,0:02:11.23,0:02:13.73,Default,,0000,0000,0000,,it might not have enough\Nenergy to go over the hill.
Dialogue: 0,0:02:13.73,0:02:16.16,Default,,0000,0000,0000,,So if we hit it softly,\Nit might just roll halfway
Dialogue: 0,0:02:16.16,0:02:18.47,Default,,0000,0000,0000,,up the hill and roll back down again.
Dialogue: 0,0:02:18.47,0:02:23.47,Default,,0000,0000,0000,,Kinetic energy is equal to 1/2 MV squared.
Dialogue: 0,0:02:24.77,0:02:26.63,Default,,0000,0000,0000,,And so M would be the\Nmass of the golf ball
Dialogue: 0,0:02:26.63,0:02:28.79,Default,,0000,0000,0000,,and V would be the velocity.
Dialogue: 0,0:02:28.79,0:02:30.35,Default,,0000,0000,0000,,So we have to hit it with enough force
Dialogue: 0,0:02:30.35,0:02:33.77,Default,,0000,0000,0000,,so it has enough as a high enough velocity
Dialogue: 0,0:02:33.77,0:02:35.19,Default,,0000,0000,0000,,to have a high enough kinetic energy
Dialogue: 0,0:02:35.19,0:02:37.08,Default,,0000,0000,0000,,to get over the hill.
Dialogue: 0,0:02:38.74,0:02:40.16,Default,,0000,0000,0000,,Let's apply collision theory
Dialogue: 0,0:02:40.16,0:02:42.81,Default,,0000,0000,0000,,to a Maxwell-Boltzmann distribution.
Dialogue: 0,0:02:42.81,0:02:45.37,Default,,0000,0000,0000,,Usually a Maxwell-Boltzmann distribution
Dialogue: 0,0:02:45.37,0:02:48.40,Default,,0000,0000,0000,,has fractional particles or\Nrelative numbers of particles
Dialogue: 0,0:02:48.40,0:02:52.79,Default,,0000,0000,0000,,on the y-axis and particle\Nspeed on the x-axis.
Dialogue: 0,0:02:52.79,0:02:55.16,Default,,0000,0000,0000,,And a Maxwell-Boltzmann distribution
Dialogue: 0,0:02:55.16,0:03:00.16,Default,,0000,0000,0000,,shows us the range of speeds\Navailable to the particles
Dialogue: 0,0:03:01.38,0:03:02.84,Default,,0000,0000,0000,,in a sample of gas.
Dialogue: 0,0:03:02.84,0:03:04.16,Default,,0000,0000,0000,,So let's say we have,
Dialogue: 0,0:03:04.16,0:03:06.42,Default,,0000,0000,0000,,here's a particulate diagram over here.
Dialogue: 0,0:03:06.42,0:03:07.82,Default,,0000,0000,0000,,Let's say we have a sample of gas
Dialogue: 0,0:03:07.82,0:03:10.29,Default,,0000,0000,0000,,at a particular temperature T.
Dialogue: 0,0:03:10.29,0:03:12.98,Default,,0000,0000,0000,,These particles aren't\Ntraveling at the same speed,
Dialogue: 0,0:03:12.98,0:03:15.79,Default,,0000,0000,0000,,there's a range of\Nspeeds available to them.
Dialogue: 0,0:03:15.79,0:03:19.82,Default,,0000,0000,0000,,So one particle might be\Ntraveling really slowly
Dialogue: 0,0:03:19.82,0:03:22.09,Default,,0000,0000,0000,,so we'll draw a very short arrow here.
Dialogue: 0,0:03:22.09,0:03:24.45,Default,,0000,0000,0000,,A few more might be\Ntraveling a little faster,
Dialogue: 0,0:03:24.45,0:03:28.19,Default,,0000,0000,0000,,so we'll draw the arrow longer\Nto indicate a faster speed.
Dialogue: 0,0:03:28.19,0:03:31.31,Default,,0000,0000,0000,,And maybe one particle\Nis traveling the fastest.
Dialogue: 0,0:03:31.31,0:03:34.29,Default,,0000,0000,0000,,So we'll give this\Nparticle the longest arrow.
Dialogue: 0,0:03:36.13,0:03:38.40,Default,,0000,0000,0000,,We can think about the\Narea under the curve
Dialogue: 0,0:03:38.40,0:03:40.31,Default,,0000,0000,0000,,for a Maxwell-Boltzmann distribution
Dialogue: 0,0:03:40.31,0:03:43.85,Default,,0000,0000,0000,,as representing all of the\Nparticles in our sample.
Dialogue: 0,0:03:43.85,0:03:47.92,Default,,0000,0000,0000,,So we had this one particle\Nhere moving very slowly,
Dialogue: 0,0:03:47.92,0:03:50.45,Default,,0000,0000,0000,,and so if we look at\Nour curve and we think
Dialogue: 0,0:03:50.45,0:03:52.12,Default,,0000,0000,0000,,about the area under the curve
Dialogue: 0,0:03:52.12,0:03:54.07,Default,,0000,0000,0000,,that's at a low particle speed,
Dialogue: 0,0:03:54.92,0:03:57.41,Default,,0000,0000,0000,,this area is smaller than\Nother parts of the curve.
Dialogue: 0,0:03:57.41,0:03:59.64,Default,,0000,0000,0000,,So that's represented here\Nby only this one particle
Dialogue: 0,0:03:59.64,0:04:01.49,Default,,0000,0000,0000,,moving very slowly.
Dialogue: 0,0:04:01.49,0:04:03.62,Default,,0000,0000,0000,,We think about this\Nnext part of the curve,
Dialogue: 0,0:04:03.62,0:04:06.61,Default,,0000,0000,0000,,most, this is a large\Namount of area in here
Dialogue: 0,0:04:06.61,0:04:09.64,Default,,0000,0000,0000,,and these particles are\Ntraveling at a higher speed.
Dialogue: 0,0:04:09.64,0:04:14.64,Default,,0000,0000,0000,,So maybe these three\Nparticles here would represent
Dialogue: 0,0:04:15.55,0:04:17.87,Default,,0000,0000,0000,,the particles moving at a higher speed.
Dialogue: 0,0:04:17.87,0:04:21.67,Default,,0000,0000,0000,,And then finally, we had\Nthis one particle here,
Dialogue: 0,0:04:21.67,0:04:23.61,Default,,0000,0000,0000,,We drew this arrow longer than the others.
Dialogue: 0,0:04:23.61,0:04:26.44,Default,,0000,0000,0000,,So this particle's traveling\Nfaster than the other one.
Dialogue: 0,0:04:26.44,0:04:29.75,Default,,0000,0000,0000,,So maybe this area under the curve up here
Dialogue: 0,0:04:29.75,0:04:31.85,Default,,0000,0000,0000,,is represented by that one particle.
Dialogue: 0,0:04:33.52,0:04:34.89,Default,,0000,0000,0000,,We know from collision theory,
Dialogue: 0,0:04:34.89,0:04:37.76,Default,,0000,0000,0000,,that particles have to\Nhave enough kinetic energy
Dialogue: 0,0:04:37.76,0:04:42.76,Default,,0000,0000,0000,,to overcome the activation\Nenergy for a reaction to occur.
Dialogue: 0,0:04:42.85,0:04:46.61,Default,,0000,0000,0000,,So we can draw a line\Nrepresenting the activation energy
Dialogue: 0,0:04:46.61,0:04:48.84,Default,,0000,0000,0000,,on a Maxwell-Boltzmann distribution.
Dialogue: 0,0:04:48.84,0:04:52.72,Default,,0000,0000,0000,,So if I draw this line,\Nthis dotted line right here,
Dialogue: 0,0:04:52.72,0:04:57.06,Default,,0000,0000,0000,,this represents my activation energy.
Dialogue: 0,0:04:57.06,0:04:59.60,Default,,0000,0000,0000,,And instead of particle\Nspeed, you could think
Dialogue: 0,0:04:59.60,0:05:02.40,Default,,0000,0000,0000,,about the x-axis as being\Nkinetic energy if you want.
Dialogue: 0,0:05:02.40,0:05:05.48,Default,,0000,0000,0000,,So the faster a particle is traveling,
Dialogue: 0,0:05:05.48,0:05:07.69,Default,,0000,0000,0000,,the higher its kinetic energy.
Dialogue: 0,0:05:07.69,0:05:11.39,Default,,0000,0000,0000,,And so the area under the curve
Dialogue: 0,0:05:11.39,0:05:13.01,Default,,0000,0000,0000,,to the right of this dash line,
Dialogue: 0,0:05:13.01,0:05:14.64,Default,,0000,0000,0000,,this represents all of the particles
Dialogue: 0,0:05:14.64,0:05:19.64,Default,,0000,0000,0000,,that have enough kinetic energy\Nfor this reaction to occur.
Dialogue: 0,0:05:21.82,0:05:24.30,Default,,0000,0000,0000,,Next, let's think about what\Nhappens to the particles
Dialogue: 0,0:05:24.30,0:05:27.77,Default,,0000,0000,0000,,in our sample when we\Nincrease the temperature.
Dialogue: 0,0:05:27.77,0:05:29.24,Default,,0000,0000,0000,,So when we increase the temperature,
Dialogue: 0,0:05:29.24,0:05:32.35,Default,,0000,0000,0000,,the Maxwell-Boltzmann\Ndistribution changes.
Dialogue: 0,0:05:32.35,0:05:36.03,Default,,0000,0000,0000,,So what happens is the peak height drops
Dialogue: 0,0:05:36.03,0:05:40.36,Default,,0000,0000,0000,,and our Maxwell-Boltzmann\Ndistribution curve gets broader.
Dialogue: 0,0:05:40.36,0:05:43.37,Default,,0000,0000,0000,,So it looks something like\Nthis at a higher temperature.
Dialogue: 0,0:05:45.38,0:05:47.21,Default,,0000,0000,0000,,So we still have some particles traveling
Dialogue: 0,0:05:47.21,0:05:48.82,Default,,0000,0000,0000,,at relatively low speeds, right?
Dialogue: 0,0:05:48.82,0:05:50.44,Default,,0000,0000,0000,,Remember it's the area under the curve.
Dialogue: 0,0:05:50.44,0:05:53.58,Default,,0000,0000,0000,,So maybe that's represented\Nby this one particle here,
Dialogue: 0,0:05:54.44,0:05:56.52,Default,,0000,0000,0000,,and next, let's think about the area
Dialogue: 0,0:05:56.52,0:06:00.18,Default,,0000,0000,0000,,to the left of this dash line for Ea.
Dialogue: 0,0:06:00.18,0:06:02.75,Default,,0000,0000,0000,,So we want to make these\Nparticles green here
Dialogue: 0,0:06:02.75,0:06:05.18,Default,,0000,0000,0000,,as we have some particles traveling
Dialogue: 0,0:06:05.18,0:06:06.51,Default,,0000,0000,0000,,a little bit of faster speeds.
Dialogue: 0,0:06:06.51,0:06:09.25,Default,,0000,0000,0000,,So let me go ahead and draw\Nthese arrows a little bit longer
Dialogue: 0,0:06:09.25,0:06:12.33,Default,,0000,0000,0000,,but notice what happens to\Nthe right of this dash line.
Dialogue: 0,0:06:12.33,0:06:14.88,Default,,0000,0000,0000,,We think about the area under the curve
Dialogue: 0,0:06:14.88,0:06:17.96,Default,,0000,0000,0000,,for the magenta curve.
Dialogue: 0,0:06:17.96,0:06:21.35,Default,,0000,0000,0000,,Notice how the area is bigger\Nthan in the previous example.
Dialogue: 0,0:06:21.35,0:06:24.45,Default,,0000,0000,0000,,So maybe this time we have\Nthese two particles here
Dialogue: 0,0:06:24.45,0:06:25.90,Default,,0000,0000,0000,,traveling at a faster speed.
Dialogue: 0,0:06:25.90,0:06:28.15,Default,,0000,0000,0000,,So I'm gonna draw these arrows longer
Dialogue: 0,0:06:28.15,0:06:30.27,Default,,0000,0000,0000,,to indicate they're\Ntraveling at a faster speed.
Dialogue: 0,0:06:30.27,0:06:33.78,Default,,0000,0000,0000,,And since they're to the\Nright of this dash line here,
Dialogue: 0,0:06:33.78,0:06:36.69,Default,,0000,0000,0000,,both of these particles\Nhave enough kinetic energy
Dialogue: 0,0:06:36.69,0:06:40.84,Default,,0000,0000,0000,,to overcome the activation\Nenergy for our reaction.
Dialogue: 0,0:06:40.84,0:06:44.53,Default,,0000,0000,0000,,So we can see when you\Nincrease the temperature,
Dialogue: 0,0:06:44.53,0:06:46.73,Default,,0000,0000,0000,,you increase the number of particles
Dialogue: 0,0:06:46.73,0:06:48.58,Default,,0000,0000,0000,,that have enough kinetic energy
Dialogue: 0,0:06:48.58,0:06:51.32,Default,,0000,0000,0000,,to overcome the activation energy.
Dialogue: 0,0:06:52.84,0:06:54.09,Default,,0000,0000,0000,,It's important to point out
Dialogue: 0,0:06:54.09,0:06:56.77,Default,,0000,0000,0000,,that since the number of\Nparticles hasn't changed,
Dialogue: 0,0:06:56.77,0:06:59.48,Default,,0000,0000,0000,,all we've done is increase\Nthe temperature here,
Dialogue: 0,0:06:59.48,0:07:02.36,Default,,0000,0000,0000,,the area under the curve remains the same.
Dialogue: 0,0:07:02.36,0:07:06.42,Default,,0000,0000,0000,,So the area under the curve\Nfor the curve in yellow,
Dialogue: 0,0:07:06.42,0:07:08.88,Default,,0000,0000,0000,,is the same as the area under the curve
Dialogue: 0,0:07:08.88,0:07:12.01,Default,,0000,0000,0000,,for the one drawn in magenta.
Dialogue: 0,0:07:12.01,0:07:14.64,Default,,0000,0000,0000,,The difference of course\Nis the one in magenta
Dialogue: 0,0:07:14.64,0:07:15.95,Default,,0000,0000,0000,,is at a higher temperature,
Dialogue: 0,0:07:15.95,0:07:18.37,Default,,0000,0000,0000,,and therefore there are more\Nparticles with enough energy
Dialogue: 0,0:07:18.37,0:07:20.79,Default,,0000,0000,0000,,to overcome the activation energy.
Dialogue: 0,0:07:20.79,0:07:23.03,Default,,0000,0000,0000,,So increasing the temperature
Dialogue: 0,0:07:23.03,0:07:25.78,Default,,0000,0000,0000,,increases the rate of reaction.