Lec 16: Kinetic Theory of Gases
How do we measure kinetic motion?
temperature
most probable speed
the peak of the curve; The speed at which the most molecules move in a gas; the maximum in the Maxwell-Boltzmann distribution of speeds.
When you lower the temp or raise the pressure, what happens to gases
they are no longer ideal; there are some attractive/repulsive forces, inelastic, KE ≠ temp, not rapid motion, slower
In what direction will the Maxwell Boltzmann distribution shift if the temperature of a gas decreases?
to the left; If the temperature of a gas decreases, the kinetic energy average will also decrease because molecules will have lower speeds, so the distribution shifts toward the lower speeds (to the left).
What is 3/2R
The proportionality constant with R as the gas constant
gases are composed of large number of gas particles that behave like hard, spherical objects in a state of constant, rapid motion
gases are mostly empty space
What do you use the KE equation for?
For a single particle that is moving across an area
Maxwell-Boltzmann distribution
Shows the spread of energies that molecules of gas or liquid have at a particular temperature
KE is proportional to the temp in K
all gases have the same KE at a given temp regardless of chemical identity
gases collide randomly and are perfectly elastic. They do not lose momentum to friction or heat
kinetic energy remains the same as long as temp is constant
Ideal Gas Law
the relationship PV=nRT, which describes the behavior of an ideal gas
According to Charles's law, volume and temperature are directly proportional because as temperature increases:
the volume must increase to keep constant pressure
When are gases like an ideal gas?
High temperature, low pressure
KE = 3/2RT
Temperature is a measure of the average kinetic energy KE, of the gas particles.
Which of the following is NOT a postulate of the kinetic molecular theory of gases?
The average kinetic energy of gas molecules is proportional to the pressure of the gas; The average kinetic energy of gas molecules is not proportional to the pressure of the gas, but rather to the absolute temperature of the gas, or the temperature in units of Kelvin.
What is u = √3RT / M
a kind of average speed; different gases (O and He) will have different values because there is an inverse relationship between u (speed) and molar mass (M). Particles with a lower molar mass will travel at a faster speed (higher U). Heavier particles will travel slower speed at the same temp (lower U).
According to the kinetic molecular theory, where does the pressure exerted by a gas in a container come from?
collisions between the gas molecules and the container walls
Which of the following can be explained by the kinetic molecular theory? Select all that apply.
Boyle, Charles, Amonton, Avogadro, and Dalton; The kinetic molecular theory shows how individual gas particles interact with one another and can be used to describe the individual gas laws of Boyle, Charles, Amonton, Avogadro, and Dalton.
What are the postulates of KMT?
1) gases are composed of molecules that are in continuous motion 2) molecules composing the gas are negligibly small compared to the distances between them 3) pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls 4) gas molecules exert no attractive or repulsive forces on each other or the container walls 5) average kinetic energy of the gas molecules is proportional to the kelvin temperature of the gas.
Ideal gases have 4 postulates:
1. Gases are composed of molecules that are in constant random motion. 2. The molecules composing the gas are negligibly small compared to the distances between them 3. Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic
What does temp of gas depend on?
How fast the gas particles are moving
What is the KE equation for one mole of the particles?
KE = 3/2RT; 2 gases (like O and He) will have the same KE at the same temp. 3/2 and R are constants, so KE is only dependent on temp
How do you find the average kinetic energy for all the particles of the same chemical identity rather than an individual particle?
Multiply by avogadro's number in order to get the molar mass
Do gas particles have attractive and repulsive forces according to KMT?
No; In kinetic molecular theory, we will assume that gas particles do not interact with one another when they are near.
translational kinetic energy
The energy of a system due to the motion of the systems center of mass
Between Ar and Kr, which has the more narrow distribution of molecular velocity?
The greater the mass, the more slowly the particles move. Slower moving particles have fewer velocities within which to distribute all the particles, so a great quantity of particles will end up moving at or near the most probable speed, which will be illustrated with a taller, narrower distribution curve.
Maxwell-Boltzmann distribution molar mass
The heavier the molecule, the slower it moves. Lower speed and smaller distribution of speeds.
no attractive or repulsive forces between the particles
They bounce to fast to attract/repel
At a given temperature, which noble gas will have the narrowest curve for distribution of molecular velocity? He, Ne, Ar, Kr, Xe
Xe; At a given temperature, all gases have particles with the same average kinetic energy. Gases composed of lighter molecules have more high-speed particles and a higher urms, with a speed distribution that peaks at relatively higher velocities. Gases consisting of heavier molecules have more low-speed particles, a lower urms, and a speed distribution that peaks at relatively lower velocities. Therefore, since Xe has the largest molar mass, it will have the narrowest curve for distribution of molecular velocity.
According to kinetic molecular theory, gas particles:
are of negligible size and are elastic; The space between gas particles is so great compared to the diameter of one particle, that we consider the volume occupied by gas particles to be negligible. They also do not lose KE during collisions
Kinetic molecular theory explains Dalton's law by stating that in a typical mixture of gases:
gas particles are far away from one another; If the particles are very sparse, then the pressure exerted by a particular gas will be independent of the presence of other gases, and thus the total pressure will just be the sum of the partial pressures of the gases present in the mixture.
If you keep the temp constant and identify different chemical identities,
lighter molecules move faster and have a wider distribution of speeds since they collide more often and travel different speeds after colliding
The molecular speed in a sample of gas that is exhibited by the greatest number of molecules is called the:
most probable speed
rotational motion
motion of a body that spins about an axis particles rotate about their axis
translational motion
movement in which an entire molecule moves in a definite direction particles moves from point a to b
vibrational motion
movement of the atoms within a molecule in which they move periodically toward and away from one another vibrate in one spot
How do you find KE for the molar mass of a particle?
multiply the KE equation by avogadro's number KE = 1/2Na mu^2 Na = avogadro's number m = mass of each individual particle Na x m = M (molar mass) KE = 1/2Mu^2
How do you find the mean square speed?
set the equations equal to each other 1/2Mu^2 = 3/2RT set it in terms of the average speed (root mean square speed) u = √3RT / M
the average speed
the average of all speeds that molecules are traveling at
Kinetic Theory of Gases
the constant motion of particles in a gas allows a gas to fill a container of any shape or size
As temperature increases, the curve describing the distribution of molecular velocities for a sample of gas will:
widen; With increasing temperature there will be a greater range of velocities available to the gas particles, and the distribution curve will flatten out, reaching farther to the right.