Kinetic Molecular Theory

A gas is seen as a collection of molecules or individual atoms that are in constant motion. The Kinetic-Molecular Theory tries to use data of real gases to predict how an ideal gas would behave if they existed.  

Examining the Kinetic-Molecular Theory

Concept: Understanding the Kinetic-Molecular Theory

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Video Transcript

Welcome back guys, in this new video, we’re going to take a look at the Kinetic Molecular Theory for gases.
Now, to better understand the behavior of gases, that’s why we use the Kinetic Molecular Theory. It’s a way of explaining what happens to gas particles as external pressures and temperatures influence them. We’re going to say a gas is not just simply a single thing, it’s a collection of particles that move together and are influenced by these pressures and temperatures on the outside of the container.
We’ve been talking about ideal gases this whole time, but what exactly is an ideal gas? Well, to be an ideal gas, you have to follow certain criteria or characteristics.
If we look, we’re going to say we have this vessel right here. Inside of this vessel, we have little black dots. Those little black dots represent individual gas particles. We have arrows pointing away from them because they’re moving in straight lines. They’re going to be bouncing off one another and bouncing off the walls on their containers. 

Ideal gases are imaginary and don’t actually exist. However, if they did exist then there would be certain characteristics that a gas would need to possess in order to be an ideal gas. 

Concept: The Characteristics of an Ideal Gas

5m
Video Transcript

The first criteria to be an ideal gas is, we’re going to say the size of the particle is significantly small when compared to the volume of the container.
What does this mean? That means if you look, look at all this volume inside this container. If you compare the size that’s free to the size of each gas particle, you’re going to say that gases really don’t take up that much room. That’s what it takes to be an ideal gas.
So the first criteria is the gases have to be very small and there has to be tons of room around because an ideal gas assumes that it’s alone. It acts as though it’s the only person there. That’s what an ideal gas is. An ideal gas is kind of like a diva, it only thinks that it’s by there by itself, no other gases are around, no other gases matter. The only thing that is important is that particle by itself.
So if we think of this, usually an ideal gas will take up about less than 1%, usually about 0.0% of the total volume. So, an ideal gas, an individual gas particle would take up usually less than this percentage of the total available space.
The next thing to be an ideal gas, we’re going to say the average kinetic energy of a particle is directly proportional to the temperature of the container in Kelvins. What the heck that does mean? Well that means, an ideal gas, when we increase the temperature that increases the average kinetic energy of that gas. We’ve said this before, we increase the temperature to a container, the gases absorb that thermal energy and convert it to kinetic energy. So, they have greater kinetic energy.
Now, this is going to be different from velocity. Velocity and kinetic energy are different. If we increase the temperature, we don’t increase the speed of those gas particles. All we’re doing is increasing their kinetic energy. We’re making them vibrate at a higher frequency, a higher level, so they’re shaking more. Velocity comes from weight not from temperature so remember that. Increasing the temperature increases the kinetic energy, not the velocity or speed. To increase the velocity or speed, you need to reduce the weight of the gases. The less you weigh, the faster you move.
Now, we’re going to say the collision of a particle with another gas particle or with the walls of a container are completely elastic. That means that when the gas particles are hitting one another or hitting the walls of the container, they bounce off, kind of like ping-pong balls inside of a container. They’re all bouncing around but none of them are sticking together. So to be an ideal gas, when you hit another ball, another gas particle, you’re not suppose to stick to it.
We are also going to say because they’re completely elastic, once they bounce off each other there’s a transferring of energy. So Gas A hits Gas B. Gas A is going to transfer its energy to Gas B. B is going to transfer its energy to Gas A. There’s a transfer of energies. So no energy is lost. This is what we mean by the third criteria to being a gas law.
And so what we are going to finally say is these are the three criteria you need to follow in order to be an ideal gas. Your professor more likely will give this to you as a theory question. So, you just have to remember, to be an ideal gas you have to be very smaller compared to the total volume. To be an ideal gas, your average kinetic energy is influenced by the temperature, not your speed or velocity. To be an ideal gas, you’re bouncing off the walls, you’re bouncing off other gases but you don’t stick. You are just bouncing around.

Example: Two identical 10.0 L flasks each containing equal masses of O2 and N2 gas are heated to the same temperature. Which of the following statements is/are true?  

The flask with the oxygen gas will have a greater overall pressure.

 

The nitrogen and oxygen gases will have the same average speed or velocity.

 

The nitrogen and oxygen gases will have the same average kinetic energy.

4m

Kinetic Molecular Theory Additional Practice Problems

At constant temperature, which of the following statement(s) is/are  TRUE according to the figure?            

I)  Every molecule of gas A has a faster speed than every molecule of gas D.

II) Gas D has the smallest molar mass.

III) Gas B has a smaller molar mass than gas C.

 

A) I only      

B) II only     

C) III only       

D) both I and III         

E) both II and III

Watch Solution

Consider two separate 1 L gas samples, both at the same temperature and pressure. The two gases have different molar masses. Which is true? 

1. The particles in both gas samples have different average kinetic energies.

2. You would need more information to be able to compare the average kinetic energies of these two gas samples.

3. The particles in both gas samples have the same average kinetic energies. 

Watch Solution

The graph (below) shows the distribution of molecular velocities.  How many of the statements are true?

  • At a given temperature, curve A represents gas particles with the smallest molar mass
  • For a given gas sample, curve D represents the highest temperature
  • At a given temperature, curve D represents gas particles with the highest molar mass
  • For a given gas sample, the broader the velocity distribution, the lower the temperature
  1. 0                      b) 1                  c) 2                  d) 3                  e) 4 
Watch Solution

Which of the gases in the graph below has the largest molar mass?

A) A

B) B

C) C

D) D

E) There is not enough information to determine.

Watch Solution

Which of the following statements is/are true molecules according to the Kinetic Molecular Theory?

i. increasing the amount of gas molecules increases the pressure by increasing the force of the collisions.
ii. decreasing the temperature of a gas decreases the pressure by increasing the force of the collisions.
iii. decreasing the volume of a gas increases pressure by increasing the frequency of the collisions.

a. i only
b. ii only
c. iii only
d. i and ii
e. ii and iii

Watch Solution

According to Kinetic Molecular Theory (KMT), which statement is   TRUE?

A. The density of a gas is usually comparable to the density of solids.

B. The average kinetic energy of a particle is proportional to the temperature in degree Celsius.

C. The collisions of particles with one another are completely elastic.

D. A single particle does not move in a straight line.

E. At constant temperature, the pressure of a gas in a container will decrease if the volume of the container decreases.

Watch Solution

Which of the following statements about the phases of matter is TRUE?

A) In both solids and liquids, the atoms or molecules pack closely to one another.

B) Solids are highly compressible.

C) Gaseous substances have long-range repeating order.

D) There is only one type of geometric arrangement that the atoms or molecules in any solid can adopt.

E) Liquids have a large portion of empty volume between molecules.

Watch Solution

The partial pressure of an ideal gas is equal to:

 

a) The pressure it would exert if it were at high pressure, same volume, and alone in a container.

b) The pressure it woudl exert if it were at low pressure, same volume, and alone in a container. 

c) The pressure it would exert if it occupied the same volume, alone in a container, at the same temperature. 

d) The pressure it would exert if it were at low temperature, same volume, and alone in a container. 

e) The pressure it would exert if it were at high temperature, same volume, and alone in a container. 

 

Watch Solution

At very high pressures (~ 1000 atm), the measured pressure exerted by real gases is greater than that predicted by the ideal gas equation. This is mainly because

a) such high pressures cannot be accurately measured.

b) real gases will condense to form liquids at 1000 atm pressure.

c) gas phase collisions prevent molecules from colliding with the walls of the container.

d) of attractive intermolecular forces between gas molecules.

e) the volume occupied by the gas molecules themselves becomes significant.

Watch Solution

If equal masses of O 2(g) and HBr(g) are in separate containers of equal volume and temperature, which one of the following statements is true?

 

a) The pressure in the O 2 container is greater than that in the HBr container.

b) There are more HBr molecules than O 2 molecules.

c) The average velocity of the O 2 molecules is less than that of the HBr molecules.

d) The average kinetic energy of HBr molecules is greater than that of O 2 molecules.

e) The pressures of both gases are the same. 

Watch Solution

Which is heavier, humid air or dry air? 

 Briefly explain your reasoning.

Watch Solution

Which of the following statements is false?

a. gases are highly compressible

b. distances between molecules of gases are very large compared to bond distances within molecules

c. non-reacting gas mixtures are homogeneous

d. gases expand spontaneously to fill the container they are placed in

e. gases have densities higher than solids

Watch Solution

An ideal gas differs from a real gas in that the particles of an ideal gas

 

a. have very large molecular volume

b. are assumed to occupy an infinitely small volume

c. have a molecular weight of zero

d. generally have no kinetic energy

e. do not exert any pressure

Watch Solution

A piece of metal, initially at room temperature, is heated. Neither a chemical change nor a physical change takes place. During this process what remains constant?

 

A. The density

B. The mass

C. The volume

D. All of these properties remain constant. 

Watch Solution

Which of the following statements are false?

a. Standard temperature and pressure are 25.0°C and 1.000 atm

b. The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to temperature

c. Gas molecules occupy –0.1% of the total volume of a container

d. In a given sample of an ideal gas. gas molecule behavior is dependent on molecular attraction and repulsion

e. Equal volumes of gases at the same temperature and pressure contain the same numbers of molecules

 

a) a, c, e

b) b, d

c) a, b, d

d) c, d, e

e) b, c, d

Watch Solution

The following information is to be used for the next three problems. A lab bench has three one liter stopped flasks. Flask A contains one mole of NH3 gas. Flask B contains one mole of N2 gas and Flask C contains one mole of SO 2 gas. All are at the same temperature. Which flask has molecules with the greatest average kinetic energy?

a. cannot be determined without more information

b. all are the same

c. A

d. B

e. C

 

Which flask has gas with the greatest density in g/L?

a. cannot be determined without more information

b. all are the same

c. A

d. B

e. C

 

Which flask has the molecules with the greatest average speed (velocity)?

a. cannot be determined without more information

b. all are the same

c. A

d. B

e. C

Watch Solution

For a substance that remains a gas under the conditions listed, deviation from the Ideal Gas Law would be most pronounced at

 

1. 0ºC and 2.0 atm.

2. 100ºC and 2.0 atm.

3. -100ºC and 2.0 atm.

4. 100ºC and 4.0 atm.

5. -100ºC and 4.0 atm. 

Watch Solution

Which of the following is one of the postulates of the kinetic theory of gases?

 

a. The average kinetic energy of the molecules of a gas depends only on the temperature and is independent of the mass of the molecules or the gas density.

b. A pure gas consists of a large number of identical molecules separated by distances that are large compared with their size

c. Temperature has meaning in a system of gaseous molecules only when their distribution of speeds is the Maxwell-Boltzmann distribution.

d. At constant temperature, the volume of a sample of gas is a liner function of its temperature.

e. The total pressure of a mixture of gases equals the sum of the portial pressures of the individual gases.

Watch Solution

At the particle level, why do most substances expand when heated?

a) The density of the particles increases

b) The density of the particles decreases

c) The particle motion increases and the spacing between the particles increases

d) The particle motion increases and the spacing between particles decreases

e) The substances undergo a chemical change

Watch Solution

A 250-mL glass bottle was filled with water at 20°C and capped tightly. It was then placed in a refrigerator where the average temperature was -5°C. The next morning the glass bottle was found to have a crack due to the expansion of the liquid. Assuming the glass bottle did not change size upon cooling, calculate the minimum amount of water initially in the bottle that produced the crack.

Density of water at 20°C = 0.998 g/cm 3.

Density of ice at -5°C = 0.916 g/cm 3.

a) 230-mL

b) 247-mL

c) 249.5-mL

d) 212-mL

e) 273-mL

Watch Solution

What is different for 100 mL of water at 0°C versus 100 mL of ice at 0°C?

 

A. Average kinetic energy of molecules.

B. The mass.

C. Arrangement of atoms within the molecule.

D. Size of H2O molecules. 

Watch Solution

Which of these properties is/are characteristic(s) of gases?

a) High compressibility

b) Relatively large distances between molecules

c) Formation of homogeneous mixtures regardless of the nature of gases

d) A and B, and C. 

Watch Solution

Consider the following gas samples:

Sample A: S 2(g); n = 1 mol; T = 800 K; P = 0.20 atm; and

Sample B: O 2(g); n = 2 mol; T = 400 K; P = 0.40 atm

Which one of the following statements is FALSE?

a) The volume of sample A is twice the volume of sample B.

b) The average kinetic energy of the molecules in sample A is twice the average kinetic energy of the molecules in sample B.

c) The fraction of molecules in sample A having a kinetic energy greater than some high fixed value is larger than the fraction of molecules in sample B having kinetic energies greater than that same high fixed value.

d) The mean square velocity of molecules in sample A will be twice as large as the mean square velocity of molecules in sample B.

e) Assuming identical intermolecular forces in the two samples. sample A should be more nearly ideal than sample B. 

Watch Solution

Which of the following statements is false?

a. Condensed states have much higher densities than gases.

b. Molecules are very far apart in gases and closer together in liquids and solids.

c. Gases completely fill any container they occupy and are easily compressed.

d. Vapor refers to a gas formed by evaporation of a liquid or sublimation of a solid.

e. Solid water (ice), unlike most substances, is denser than its liquid form (water).

Watch Solution