Kinetic Molecular Theory, Root mean square velocity, Diffusion and Effusion, and Non-Ideal Gases

What does KMT stand for?

Kinetic Molecular Theory

What is Kinetic Molecular Theory?

model developed to understand the behavior of gas

How is gas modeled in Kinetic Molecular Theory?

As a collection of particles in constant motion that collide elastically

How does a single particle move in a container in KMT?

It moves in a straight line until it collides with another particle or wall of the container

What is Postulate 1 of KMT?

The size of the particle is negligibly small, and the space between gas molecules is larger compared to their sizes

What does KMT assume about gas particles?

Particles of gas themselves occupy no volume, but have mass

What is Postulate 2 of KMT?

Average kinetic energy of a particle is PROPORTIONAL to temperature (in K)

In KMT, as average kinetic energy increases…

the temperature of gas increases

What is the motion of gas particles due to?

Thermal energy

In KMT, higher temperature results in…

greater overall motion → greater kinetic energy

In KMT, lower mass results in…

greater velocity

In KMT, larger mass results in…

lower velocity

In KMT, what is the relationship between mass and velocity

They are indirectly proportional to each other; as mass increases, velocity decreases.

In KMT, what is the relationship between temperature and Kinetic energy?

They are directly proportional to each other ; as temperature increases, so does kinetic energy 

In KMT, what is the relationship between particle pressure and moles?

They are directly proportional; as the number of moles increases, pressure increases, assuming temperature and volume are constant.

What is Postulate 3 in KMT?

The collision of the particles with another (or the wall of the container) are completely elastic 

Knowing the third postulate in KMT, what does it mean for energy in collision?

There may be an exchange in energy due to collision, but no loss in kinetic energy

According to KMT, particles of different masses have…

the same kinetic energy at same temperature

What does kinetic energy (KE) depend on?

mass and velocity

What is the formula for kinetic energy?

KE = 1/2 mv²

What would be the only way for particles of different masses to have the same kinetic energy?

They must have different velocities to compensate for their differences in mass.

In gas mixtures at given temperature, lighter particles of gas move [blank] (on average) tan heavier ones.

faster

In KMT, what is root mean square velocity defined as?

√u² or the average of the squares of the particle velocities 

urms = 

√(3RT/M)

Average Kinetic Energy is equal to

(3/2)RT

What does the gas constant R equal to in root mean square velocity?

8.314 J/(mol·K)

What units is molar mass represented by in root mean square velocity?

kg/mol

What is the relationship between Root mean square velocity (urms) of a collection of gas particles to temperature (in k)?

They are directly proportional to each other

What is the relationship between the root mean square velocity (urms) of a collection of gas particles to square root of molar mass (kg/mol)?

They are inversely proportional; as molar mass increases,  the root mean square velocity decreases.

What is Mean Fire Path?

the average distance molecule travels between collisions

Define diffusion

the process by which gas molecules spread out in a given space

What is rate of diffusion influenced by?

the root mean square velocity 

True or false: Heavier molecules (with lower urms) diffuse slower than lighters ones 

true

Define Effusion

the process by which gas escapes from a container into a vacuum though a small hole

What is rate of effusion related to?

the root mean square velocity

True or false: heavier velocity effuse slower than lighter ones

True

In Graham’s Law of Effusion, what is the relationship between rate of effusion and square root of molar mass?

They are inversely proportional 

What is the formula for rate of a?

rate a 1/√M

What is Graham’s Law of effusion?

rate A/rate B = √MB/√MA

Real gases behave near ideally at:

high temperatures, lower pressure, Ideal Gases, PV=nRT, and when molecules are far apart and don’t attract each other

Real gases do NOT behave ideally at: 

Low temperature, high pressure, real gases, [P+a(n/v)²] x [V-nb] = nRT, and when molecules are close together and attract