Unit 4Sections A7-A9

In which you will learn about:•Kinetic molecular theory

•Pressure and volume relationships

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A.7 Atoms & Molecules in Motion• Making observations is the first step in “doing

science”– A more difficult task is crafting a theory that explains all

observations and that also predicts the outcomes of investigations yet to be completed

• One such theory concerns the motion of atoms and molecules within all states of matter– Remember, scientific laws describe the behavior of

events in nature, but they do not provide explanations for the observed behavior.

– Scientific theories and models attempt to offer how-type explanations on phenomena in the natural world.

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States of Matter

• What do you already know about the three states of matter from observing them?– A solid has a definite shape and its structure is

rigid– A liquid flows and depends on its container to

define its shape– A gas does not have a definite

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• The atoms, molecules, or ions that make up solids are held closely to one another– Particles vibrate about a fixed position– Tightly packed in an orderly fashion (except for

ice) and cannot move past one another• The molecules and ions within liquids are

more mobile– Molecules can move past one another– Intermolecular forces prevent them from moving

too far apart• Remember, IMFs are attractive forces between

molecules that are NOT bonds

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What We Care About Right Now: Gases

• Most molecules in the gaseous state are not as strongly attracted to each other– In contrast to particles in solids and liquids, particles

in gases are very far apart– Their size is negligible compared to the great

distances that separate them– Gases molecules move in straight-line paths at very

high speeds• Change direction only when a collision occurs (remember,

when the collisions are with the container walls, we measure it as pressure)

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Kinetic Energy

• Gas molecules move at average speeds that depend on how much kinetic energy they possess– Kinetic energy = energy of motion = 1/2mv2 (where m

is mass and v is velocity)– Traveling at the same velocity, a more massive object

has a greater kinetic energy than a less massive object– When comparing the speeds of gases, we can use

Graham’s Law which will be explained in detail later

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Kinetic Molecular Theory (KMT)

• KMT explains the behavior of gas molecules in motion. It is based on four postulates (statements accepted as the basis for further reasoning and study):– 1) Gases consist of tiny particles whose size is negligible

compared with the great distances that separate the molecules from each other

– 2) Gas molecules are in constant, random motion.– 3) Molecular collisions are elastic (no gain or loss in total

kinetic energy during collisions)– 4) At a given temperature, gas molecules have a range of

kinetic energies; however, the average kinetic energy is constant and depends on the temperature of the sample

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Putting KMT Into Action:A.8 Pressure-Volume Behavior of Gases

• Earlier, when you pushed down on a sealed syringe filled with gas, you observed that a gas sample can easily be compressed– The volume of a gas sample is easily changed

when an external pressure is applied

• As you decreased the volume of the gas within the syringe, the molecules collided more often with the walls, increasing the pressure

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Boyle’s Law

• As discussed in the previous slide, as volume decreases, pressure increases (and vice versa).

• An inverse relationship is one where an increase in one variable results in the decrease of the other, but the product of the two variables remains the same.

• P x V = k• Better known as P1V1 = P2V2

• What would a graph of Boyle’s Law look like?

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Example Problem• You know that initially a gas sample occupies a

volume of 8.0 mL and exerts a pressure of 1.0 atm. How would the pressure of the gas sample changes if its volume were increased to 10.9 mL?

• Use the GUESS method.• P1 = 1.0 atm, V1 = 8.0 mL, V2 = 10.9 mL, P2 = ?• P1V1 = P2V2 --> P2 = P1V1/ V2 plug and chug to

get P2 = 0.73 atm• CHECK: Volume increased and pressure

decreased which is in accordance with Boyle’s law.

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A.9 Predicting Gas Behavior: Pressure-Volume (HOMEWORK)

• 1) Explain each of the following observations:– A. Even if they have ample supplies of oxygen gas,

airplane passengers experience discomfort when the cabin undergoes a drop in air pressure.

– B. New tennis balls are sold in pressurized containers.

– C. After descending from a high mountain, the capped, half-filled plastic water bottle from which you drank while standing at the summit now appears dented or slightly crushed.

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More Homework• 2) You buy helium gas in small pressurized cans

to inflate party balloons. The can label indicates that the container delivers 7100 mL of helium gas at 100.0 kPa pressure. The volume of the gas container is 492 mL.– A. Do you think that the initial pressure of helium gas

inside the can is greater or less than 100.0 kPa? Explain.

– B. Calculate the initial pressure of helium gas inside the container.

– C. Was your prediction in 2a correct?

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Last Question• 3) Two glass bulbs are separated by a closed valve. The

0.50-L bulb on the left contains a gas sample at a pressure of 6.0 atm. The 1.7-L bulb on the right is evacuated; it contains no gas:– A. Draw a model of gas molecules in the two glass bulbs before

and after the middle valve is opened.– B. Explain your model in terms of kinetic molecular theory.– C. Predict, in general, what will happen to the total volume of

the gas sample if you open the middle valve. Explain.– D. Predict, in general, what will happen to the total pressure of

the gas sample if you open the middle valve. Explain.– E. Calculate the actual pressure of the gas sample after the

middle valve is opened.

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