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

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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?  

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

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

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

4m

Kinetic Molecular Theory Additional Practice Problems

Which of the following gases has the lowest average speed at 25°C?

a. H2Se

b. PH3

c. C2H6

d. F

Watch Solution

Identify the gas particle that travels the fastest. 

a. Ne

b. Cl2

c. N2

d. CO

e. H2  

Watch Solution

Five samples of helium gas are described in the table below. Rank the samples in order of increasing average kinetic energy of the atoms in them. That is, select "1" next to the sample in which the helium atoms have the lowest average kinetic energy. Select "2" next to the sample in which the helium atoms have the next lowest average kinetic energy, and so on. 

Watch Solution

List the physical characteristics of gases.

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Select the gas with the highest average kinetic energy per mole at 298 K.

a. O2
b. CO2
c. H2O
d. H2
e. All have the same average kinetic energy.

Watch Solution

Which of the following is a postulate of the kinetic molecular theory of gases?

a. The volume occupied by the individual particles that compose a gas is very small. However, the distances between gas particles are comparable to the sizes of the gas particles, so the volume occupied by the individual gas particles cannot be assumed to be negligible.

b. The particles that compose a gas are so small compared to the distances between them that the volume of the individual particles can be assumed to be negligible.

c. Despite being very small, the volume occupied by the individual particles that compose a gas cannot be assumed to be negligible.

d. Because the distances between gas particles are so small relative to the sizes of the gas particles themselves, the volume of the individual particles can be assumed to be negligible.

Watch Solution

Which gas molecules have the highest average kinetic energy at a given temperature?

a) HBr

b) NO2

c) C2H6

d) all have the same

Watch Solution

Which of the following statements is/are true? Check all that apply.

a) There are gas molecules that move slower than the average speed.

b) There are gas molecules that move faster than the average speed.

c) All the gas molecules in a sample have the same kinetic energy.

d) The average kinetic energy of gas molecules increases with temperature.

f) The average speed of gas molecules increases with temperature.

Watch Solution

Rank these real gases according to how closely they resemble an ideal gas. CO, N  2, Ne, He, NH3

Watch Solution

Deviations from the ideal gas law are less at:

a. high temperatures and high pressures

b. high temperatures and low pressures

c. low temperatures and high pressures

d. low temperatures and low pressures

Watch Solution

Under which conditions will a gas behave most ideally?

1. high T and low P 

2. low V and low P

3. high P and low V

4. high T and low V

5. low n and high P

6. high T and high n

7. high n and high P

8. high V and low T

9. high n and high V

Watch Solution

Consider two cylinders of gas. One cylinder contains N2 at 2 atm and 25C. The other cylinder contains F2 at 1 atm and 50◦C. Which statements is/are true?

I) The N2 molecules and the F2 molecules have the same average kinetic energy.

II) Every molecule in the N2 sample has the exact same speed.

III) If the pressure of N2 was increased without a change in n or V, the temperature would have to increase.

IV) The N2 gas would behave less ideally if the pressure was increased.

Which of these statements is true?

1. III and IV only 

2. I and II only

3. II and III only

4. II and IV only

5. I and IV only

Watch Solution

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

According to the kinetic molecular theory, the pressure of a gas in a container decreases if the     

A) number of collisions with the container wall increases.

B) temperature of the gas increases.

C) another ideal gas is added to the container but volume is kept constant.

D) volume of the container increases.

Watch Solution

Under what conditions is a gas most likely to deviate from ideal behavior?

1. high temperatures

2. when considering noble gases

3. low density

4. high pressure

Watch Solution

A gas is showing a considerable amount of attractive forces. What is the likely value for the compressibility factor?

1. It will be slightly above one.

2. It will be slightly below one.

3. It will be equal to one.

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 gases has the highest average speed at 400K?

A) N2

B) O2

C) F2

D) Cl2

Watch Solution

Which of the following compounds will behave MOST like an ideal gas at low temperatures?

a. H2

b. SO2

c. H2O

d. CO2

e. I2

Watch Solution

In the figures below, if shaded and unshaded spheres represent atoms of different elements, which of the above drawings most likely represents a molecular compound at room temperature and a pressure of 1 atm?

A) drawing (a)     

B) drawing (b)     

C) drawing (c)     

D) drawing (d)

Watch Solution

A gas mixture at T = 300.K contains an equal number of moles of chlorine, (Cl  2), ethane (C2H6), nitrous oxide (N2O), and sulfur hexafluoride (SF6). Which gas molecules will have the highest average speed?

a. Cl2

b. C2H6

c. N2O

d. SF6

e. All of the molecules will have the same average speed

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

The graph shows the Maxwell distribution plots for a given gas at three different temperatures. Which plot corresponds to the highest temperature?

1. B

2. Cannot be determined from this type of plot.

3. C

4. A

Watch Solution

Liquids have a higher vapor pressure at a higher temperature because

1. the molar enthalpy of vaporization is decreased as the temperature is raised.

2. the more rapidly moving molecules in the gas phase exert a higher pressure on the container walls.

3. a higher temperature is required to supply the heat of vaporization of the liquid.

4. more molecules in the liquid have enough kinetic energy to escape from the surface.

5. the higher temperature may exceed the critical temperature of the liquid.

Watch Solution

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T1 and T2). Which temperature is greater? Explain. 

Watch Solution

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon.

b. The molecules or atoms of which gas have the greater average velocity?

Watch Solution

Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure. 

 Do the argon atoms, because they are more massive, exert a greater pressure on the walls of the container? Explain. 

Watch Solution

Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure. 

b. Do the atoms in the helium sample have the same average velocity as the atoms in the argon sample? 

Watch Solution

Which gas sample representation has the greatest pressure? Assume that all the samples are at the same temperature. Explain 

Watch Solution

Helium is preferable to hydrogen for filling balloons because helium is

a) less dense.

b) less expensive.

c) easier to obtain.

d) chemically inert.

Watch Solution

A change in temperature from 10°C to 20°C is found to double the rate of a particular chemical reaction. How did the change in temperature affect the reacting molecules?

(A) The average velocity of the molecules doubled

(B) The average energy of the molecules doubled

(C) The number of collisions per second doubled

(D) The number of molecules above the reaction energy threshold doubled. 

Watch Solution

Which set of temperature and pressure conditions will cause a gas occupying a volume of 300 mL to deviate from ideal gas behavior?

(A) 100°C and 4 atm

(B) 100°C and 2 atm

(C) —100°C and 4 atm

(D) 0°C and 2 atm

Watch Solution

Which gas has molecules with the greatest average molecular speed at 25°C?

A) Ar

B) N2

C) CO2

D) CH

E) Kr

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 pressure exerted by a gas is caused by 

a) collisions of the gas molecules with the container. 

b) the density of the gas molecules. 

c) the temperature of the gas molecules. 

d) intermolecular forces. 

e) the volume that the gas molecules occupy. 

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

A bottle of highly volatile perfume with molecular formula C5H8O4N2 spills inside a large infinitely expandable bubble and the bubble expands to its maximum size consistent with the fact that the perfume liquid/vapor equilibrium still exists i.e. the perfume “gas” molecules cause the bubble to expand with no work involved. How many molecules of perfume remain in the liquid phase?

a. not enough information is given to say

b. 22.4 liters

c. none should be left in the liquid phase

d. one mole

e. about one or two molecules

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

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

Which of the following is not part of the kinetic molecular theory?

 

a. Atoms are neither created nor destroyed by ordinary chemical reactions.

b. Attractive and repulsive forces between gas molecules are negligible.

c. Gases consist of molecules in continuous, random motion.

d. Collisions between gas molecules do not result in the loss of energy.

e. The volume occupied by all the gas molecules in a container is negligible compared to the volume of the container

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

The graph shows the distribution of molecular velocities. Which of the following statement is TRUE? 

Watch Solution

The pressure of a sample of gas describes:

 

A) the speed of the gas molecules

B) the number of gas molecules

C) the number of gas molecules in a set volume

D) the force of gas molecules hitting the surface

E) the mass of the gas molecules

Watch Solution

The average speed of a gas is dependent only on:

a. the temperature of the gas

b. the temperature and the mass of the gas

c. the temperature, the mass and the density of the gas

d. the mass of the gas

e. the density of the gas

Watch Solution

Which of the following statements about gases is true?

  1. Heavier gas particles effuse faster than lighter gas particles.
  2. Particles of different masses have the same average speed at a given temperature.
  3. The higher the temperature, the lower the average kinetic energy of a gas sample.
  4. At very high pressures, a gas will occupy a larger volume than predicted by the ideal gas law.
  5. Particles of lighter masses have a lower average speed then particles of a higher mass at a given temperature
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

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

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