Episode 18 starts with a recap of a recap: Reviewing Episode 7 Kinetic Molecular Theory (1:06)
Episode 18 starts with a recap of a recap: Reviewing Episode 7 Kinetic Molecular Theory (1:06) and the relationship between pressure, temperature and volume. Taking a closer look at temperature, it connects it to average kinetic energy (2:15), which can be calculated using mass and particle speed. The episode then describes graphs showing Maxwell-Boltzmann distributions of particle speed for different temperatures (2:55) as well as different gases at the same temperature (5:08).
Question: (6:27) Which of the following elements shows behavior that is the closest to the ideal gas behavior?
A.Helium B.Fluorine C.Oxygen D.Xenon
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Hi and welcome to the APsolute Recap: Chemistry Edition. Today’s episode will recap Kinetic Molecular Theory.
Lets Zoom Out:
Unit 3 - Intermolecular Forces and Properties
Topic - 3.5
Big idea - Structure and Properties
Introduction:
Kinetic Molecular Theory builds the foundation of understanding the behavior of gas. It helps us to explain the relationship between the gas particles on the particulate view with the measurable macroscopic properties like temperature, volume and pressure. And, it is not new: We’ve already introduced Kinetic Molecular Theory in episode 7! Today, we want to go deeper and talk about particle motion. So, let’s recap Kinetic Molecular Theory and gas behavior.
Let’s zoom in:
We are starting with a recap of the recap again: Let’s briefly summarize what we’ve discussed in Episode 7: Kinetic Molecular Theory is based on the following six assumptions or postulates: 1) Gases consist of a large number of particles that are in constant random motion 2) Gas particles move in straight lines unless they collide with another particle or the wall of a container 3) Most of the volume of a gas is empty space 4) The attractive and repulsive forces between gas particles as well as gas particles and the container wall are negligible 5) Collisions between particles as well as particles and the wall are elastic and no energy is lost and lastly, 6) The average kinetic energy of the gas particles solely depends on the temperature of the gas. In Episode 7, we tied the KMT to volume, pressure and temperature. So let’s recap: Under constant temperature, pressure and volume are inversely proportional; under constant pressure, the volume of a gas is directly proportional to the temperature and under constant volume, the pressure of a gas is directly proportional to the temperature.
Taking a closer look at temperature - As the KMT states, the average kinetic energy of the gas particles solely depends on the temperature of the gas and is therefore independent of the identity of the gas. That means, the higher the temperature, the higher the average kinetic energy of the particles. Kinetic Energy can be calculated using KE = ½ mass times velocity squared - now we have two new variables to discuss: mass and velocity aka speed of particles in meters/second.
To describe and predict the particle speed at any given temperature, we can use an equation named after its developing scientists: Maxwell-Boltzmann. When plotting a Maxwell-Boltzmann distribution function, you can get a graph that shows particle speed vs. the number of particles for different temperatures. Depending on the temperature, the curve can be a normal bell curve or, for lower temperatures, be skewed to the right. This curve also shows there is a variation: not all particles in the sample have the same particle speed at the same temperature. In a normal bell curve, the particle speed that most particles have is also the average speed.
The graph also shows that at a lower temperature, the speed of particles is lower and the distribution of speed within the sample is less. The particles have less energy. At higher temperatures, the curve flattens out: the molecules are moving faster and have more energy. And that affects pressure at constant volume in a rigid container! If you heat up a sample, the particles move faster and have a greater kinetic energy. Therefore, they hit the wall of the container more often and with greater force, which increases our pressure. If you have a flexible container, like a balloon for example, and you keep the pressure constant, this will increase the volume of your container.
When we plot the particle speed vs the number of particles for particles of different mass at the same temperature, like for the noble gases, we can see that lighter particles move faster and have a greater speed distribution. In our example: Helium atoms move faster than Argon atoms and both move faster than Xenon atoms.
And that makes sense when we look back at what we’ve just discussed: temperature is proportional to average kinetic energy. Our sample is at a constant temperature, therefore the kinetic energy stays constant. Looking at the equation of average kinetic energy, we can see that mass and velocity are directly proportional: if I increase the mass from Helium to Xenon, the speed of the particle decreases. It’s like a big moving day: when carrying a heavier box to the moving truck with the same amount of energy, you will move a lot slower! Pro tip: Do not put all books in the same box. Just sayin’.
To recap…
Kinetic Molecular Theory describes basic tenets about the behavior of gases. The average kinetic energy of particles is determined by temperature. At higher temperatures, the average particle speed and average kinetic energy is higher. Particles with lower mass move at higher particle speed on average at constant temperature.
Coming up next on the APsolute RecAP Chemistry Edition: Aqueous Solutions
Today’s Question of the day is about ideal behavior of gases.
Question: Which of the following elements shows behavior that is the closest to the ideal gas behavior?
A. Helium B. Fluorine C. Oxygen D. Xenon