AP Chemistry

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Unit 3 - Intermolecular Forces& Properties

3.1 Intermolecular Forces 3.2 Properties of Solids 3.3 Solids, Liquids & Gases 3.4 Ideal Gas Law 3.5 Kinetic Molecular Theory 3.6 Deviation from Ideal Gas Law 3.7 Solutions & Mixtures 3.8 Representations of Solutions 3.9 Separation of Solutions & Mixtures Chromatography 3.10 Solubility 3.11 Spectroscopy & Electromagnetic Spectrum 3.12 Photoelectric Effect 3.13 Beer-Lambert Law

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This logo shows it is a Topic Question - it should only require knowledge included in this Topic and it should be giving practice in the Science Practice associated with this Topic.

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AP Chemistry

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3.5 Kinetic Molecular Model

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Kinetic Molecular ModelThe ideal-gas equation describes how gases behave but not why they behave as they do.

Why does a gas expand when heated at constant pressure?

Or why does its pressure increase when the gas is compressed at constant temperature?

To understand the physical properties of gases, we need a model that helps us picture what happens to gas particles when conditions such as pressure or temperature change.

Such a model, known as the kinetic-molecular theory of gases, was developed over a period of about 100 years, culminating in 1857 when Rudolf Clausius (1822–1888) published a complete and satisfactory form of the theory.

The kinetic-molecular theory (the theory of moving molecules) is summarized by the following statements:

① Gases consist of large numbers of molecules (atoms for Noble Gases) that are in continuous, random motion.

② The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

③ Attractive and repulsive forces between gas molecules are negligible.

④ Energy can be transferred between molecules during collisions but, as long as temperature remains constant, the average kinetic energy of the molecules does not change with time.

⑤ The average kinetic energy of the molecules is proportional to the absolute temperature.

At any given temperature the molecules of all gases have the same average kinetic energy.

KE = ½mv2

However, since molecules of different gases will have different masses

At same temperature the molecules of different gases have different speeds.

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The dependence of molecular speed on mass has two consequences.

The first is effusion, which is the escape of gas molecules through a tiny hole (b). The second is diffusion, (a) , which is the spread of one substance throughout a space or throughout a second substance. For example, the molecules of a perfume diffuse throughout a room.

Rate of effusion and diffusion increases as the mass decreases

HCl36.5 amu

NH3

17 amu

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3.5 Quick Check - AP FRQ Questions

1. A student is doing experiments with CO2(g). Originally, a sample of the gas is in a rigid container at 299K and 0.70atm. The student increases the temperature of the CO2(g) in the container to 425K. .

a) Describe the effect of raising the temperature on the motion of the CO2(g) molecules.

The response indicates that the average speed of the molecules increases as temperature increases

b) Calculate the pressure of the CO2(g) in the container at 425K.

The response shows a calculation similar to the following.

P1 / T1 = P2 / T2 0.70 atm / 425 K = P2 / 425 K P2 = 0.99 atm

c) In terms of kinetic molecular theory, briefly explain why the pressure of the CO2(g) in the container changes as it is heated to 425K

The response meets one or both of the following criteria. The response indicates that faster-moving gas particles collide more frequently with the walls of the container, thus increasing the pressure. The response indicates that faster-moving gas particles collide more forcefully with the walls of the container, thus increasing the pressure.

* d) The student measures the actual pressure of the CO2(g) in the container at 425K and observes that it is less than the pressure predicted by the ideal gas law. Explain this observation.

The response indicates that the attractive forces between CO2 molecules result in a pressure that is lower than that predicted by the ideal gas law.

* This question might be best left until after next section on deviations fron Ideal Gas.

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3.5 Practice Problems1. A 0.5 mol sample of He(g) and a 0.5 mol sample of Ne(g) are placed separately in two 10.0 L rigid containers at 25°C. Each container has a pinhole opening. Which of the gases, He(g) or Ne(g), will escape faster through the pinhole and why?

A He(g) will escape faster because the He(g) atoms are moving at a higher average speed than the Ne(g) atoms.

B Ne(g) will escape faster because its initial pressure in the container is higher.

C Ne(g) will escape faster because the Ne(g) atoms have a higher average kinetic energy than the He(g) atoms.

D Both gases will escape at the same rate because the atoms of both gases have the same average kinetic energy.

2. A rigid metal tank contains oxygen gas. Which of the following applies to the gas in the tank when additional oxygen is added at constant temperature?

A The volume of the gas increases.

B The pressure of the gas decreases.

C The average speed of the gas molecules remains the same.

D The total number of gas molecules remains the same.

E The average distance between the gas molecules increases.

3. A sample of an ideal gas is cooled from 50.0°C to 25.0°C in a sealed container of constant volume. Which of the following values for the gas will decrease?

I. The average molecular mass of the gas II. The average distance between the molecules III. The average speed of the molecules

A I only

B II only

C III only

D I and III

E II and III

O

O

O

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4. At standard temperature and pressure, a 0.50 mol sample of H2 gas and a separate 1.0 mol sample of O2 gas have the same

A average molecular kinetic energy

B average molecular speed

C volume

D effusion rate

E density

5. The diagram above shows the distribution of speeds for a sample of N2(g) at 25°C.

Which of the following graphs shows the distribution of speeds for a sample of O2(g) at 25°C (dashed line) ?

A B

C D

O

O

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6. Equal numbers of moles of He(g), Ar(g), and Ne(g) are placed in a glass vessel at room temperature. If the vessel has a pinhole-sized leak, which of the following will be true regarding the relative values of the partial pressures of the gases remaining in the vessel after some of the gas mixture has effused?

A PHe < PNe < PAr

B PHe < PAr < PNe

C PNe < PAr < PHe

D PAr < PHe < PNe

E PHe = PAr = PNe

7. The following question refers to the 1 L flasks shown below.

In which flask do the molecules have the greatest average speed?

A A B B C C D D E E

8. A 1L sample of helium gas at 25°C and 1atm is combined with a 1L sample of neon gas at 25°C and 1atm. The temperature is kept constant. Which of the following statements about combining the gases is correct?

A The average speed of the helium atoms increases when the gases are combined.

B The average speed of the neon atoms increases when the gases are combined.

C The average kinetic energy of the helium atoms increases when the gases are combined.

D The average kinetic energy of the helium atoms and neon atoms do not change when the gases are combined.

O

O

O

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9.

The graph above shows the distribution of molecular speeds for four different gases at the same temperature. What property of the different gases can be correctly ranked using information from the graph, and why?

A The densities of the gases, because as the density of a gas increases, the average speed of its molecules decreases.

B The pressures of the gases, because the pressure exerted by a gas depends on the average speed with which its molecules are moving

C The volumes of the gases, because at a fixed temperature the volume of a gas can be calculated using the equation PV=nRT .

D The molecular masses of the gases, because the gas molecules have the same average kinetic energy and mass can be calculated using the equation KEavg=½mv2 .

10.

The average kinetic energy of the gas molecules is?

A greatest in A B greatest in B

C greatest in C D the same in all three containers

O

O

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11.

The experimental apparatus represented above is used to demonstrate the rates at which gases diffuse. When the cotton balls are placed in the ends of a tube at the same time, the gases diffuse from each end and meet somewhere in between, where they react to form a white solid. Which of the following combinations will produce a solid closest to the center of the tube?

A HCl and CH3NH2

B HCl and NH3

C HBr and CH3NH2

D HBr and NH3

12.

The volume of a sample of air in a cylinder with a movable piston is 2.0 L at a pressure P1, as shown in the diagram above. The volume is increased to 5.0 L as the temperature is held constant. The pressure of the air in the cylinder is now P2. What effect do the volume and pressure changes have on the average kinetic energy of the molecules in the sample?

A The average kinetic energy increases.

B The average kinetic energy decreases.

C The average kinetic energy stays the same.

D It cannot be determined how the kinetic energy is affected without knowing P1 and P2.

O

O

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13.

The distribution of speeds of H2(g) molecules at 273 K and 1 atm is shown in the diagram above. Which of the following best shows the speed distribution of He(g) atoms under the same conditions of temperature and pressure?

A B

C D

14. The table below contains information about samples of four different gases at 273 K. The samples are in four identical rigid containers numbered 1 through 4.

Under the conditions given, consider containers 1, 2, and 4 only. The average speed of the gas particles is

A greatest in container 1 B greatest in container 2

C greatest in container 4 D the same in containers 1, 2, and 4

O

O

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15. Two flexible containers for gases are at the same tem perature and pressure. One holds 0.50 gram of hy drogen and the other holds 8.0 grams of oxy gen. Which of the following statements re garding these gas samples is FALSE?

A The volume of the hydrogen container is the same as the volume of the oxygen container.

B The number of molecules in the hydrogen con tainer is the same as the number of molecules in the oxygen container.

C The density of the hydrogen sample is less than that of the oxygen sample.

D The average kinetic energy of the hydrogen molecules is the same as the average kinetic en ergy of the oxygen molecules.

E The average speed of the hydrogen molecules is the same as the average speed of the oxygen molecules.

16. At 27°C, a rigid 2.0 L vessel is filled with N2(g) and sealed. The initial pressure of N2(g) is 720 mm Hg. The vessels is heated to 127°C and allowed to reach a constant pressure.

The gas particles in the vessel at 27°C are represented in the diagram above. The lengths of the arrows represent the speeds of the particles. Which of the following diagrams best represents the particles when the vessel is heated to 127°C?

A B

C D

O

O

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17.

The graph above shows the speed distribution of molecules in a sample of a gas at a certain temperature. Which of the following graphs shows the speed distribution of the same molecules at a lower temperature (as a dashed curve) ?

A B

C D

O