QuickNotes
The Kinetic Molecular Theory of Gases
Postulates:
The Relationship Between P and n
An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.
Boyle's Law (P = 1/v)
If we compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same. There is no change in the speed with which the particles move, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter period of time. Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas. Thus, the pressure of a gas becomes larger as the volume of the gas becomes smaller.
Charles' Law (V is directly proportional to T)
The average kinetic energy of the particles in a gas is proportional to the temperature of the gas. Because the mass of these particles is constant, the particles must move faster as the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each time they hit the walls, which leads to an increase in the pressure of the gas.
Avogadro's Hypothesis (V is directly proportional to N)
As the number of gas particles increases, the frequency of collisions with the walls of the container must increase. This, in turn, leads to an increase in the pressure of the gas.
Dalton's Law of Partial Pressures (Pt = P1 + P2 + P3 + ...)
The total number of collisions with the wall in this mixture is therefore equal to the sum of the collisions that would occur when each size of molecule bearing is present by itself. In other words, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
The root mean square speed measures the average speed of particles in a gas.
Example:
Calculate the root mean square (rms) speed in meters per second of argon atoms at 27o
To make sure you totally understand Kinetic Molecular Theory of Gases, check out this review video!
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- A gas consists of a collection of small particles traveling in straight-line motion and obeying Newton's Laws.
- The molecules in a gas occupy no volume (that is, they are points).
- Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during the collision).
- There are no attractive or repulsive forces between the molecules.
- The average kinetic energy of a molecule is 3kT/2. (T is the absolute temperature and k is the Boltzmann constant.)
The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.
The Relationship Between P and n
An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.
Boyle's Law (P = 1/v)
If we compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same. There is no change in the speed with which the particles move, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter period of time. Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas. Thus, the pressure of a gas becomes larger as the volume of the gas becomes smaller.
Charles' Law (V is directly proportional to T)
The average kinetic energy of the particles in a gas is proportional to the temperature of the gas. Because the mass of these particles is constant, the particles must move faster as the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each time they hit the walls, which leads to an increase in the pressure of the gas.
Avogadro's Hypothesis (V is directly proportional to N)
As the number of gas particles increases, the frequency of collisions with the walls of the container must increase. This, in turn, leads to an increase in the pressure of the gas.
Dalton's Law of Partial Pressures (Pt = P1 + P2 + P3 + ...)
The total number of collisions with the wall in this mixture is therefore equal to the sum of the collisions that would occur when each size of molecule bearing is present by itself. In other words, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
Root Mean Square Velocity
The root mean square speed measures the average speed of particles in a gas.
Calculate the root mean square (rms) speed in meters per second of argon atoms at 27o
- Use
the rms velocity equation and remember to use the proper values and units
for R to convert the molar mass into units of kilograms per mole (Kg/mol)
- The molar mass of argon 39.95 g/mol in the proper units is 0.03995 kg / mol. Son that units can be cancelled out in the calculations, expand the joule into its base units Kg.m2 / s2, when we substitute the value of R into rms equation, we get:
You think you are ready? Get out a calculator and take a mini-quiz. If you get a 100%, move onto the next concept! (Make sure you have an additional tab open to play at kahoot.it. You will need to keep 2 tabs open to play and view the questions.)
which observation indicates that the kinetic-molecular theory has limited use for describing a certain gas?
ReplyDeletehttp://sasuwaphysics.blogspot.com.ng/2016/08/which-observation-indicates-that.html