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Unit 5 Chapter 10

Gases

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Properties of Gases

• Three phases of matter

solid

liquid

gas

Definite shape and volume

Definite volume, shape of container

Shape and volume of container

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Gases

A gas consists of small particles that

• move rapidly in straight lines.

• have essentially no attractive (or repulsive) forces.

• are very far apart.

• have very small volumes compared to the volume of the container they occupy.

• have kinetic energies that increase with an increase in temperature.

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Properties of Gases

• A gas is a collection of molecules that are very far apart on average.

In air, gas molecules occupy only 0.1% of the total volume.

In liquids, molecules occupy ~ 70% of the total space.

• Gases are highly compressible.Volume decreases when pressure is applied.

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Properties of Gases

• Chemical properties of gases vary depending on their composition.– Air: ~ 78% N2 and ~ 21% O2

– CO2: colorless, odorless

– CO: colorless, odorless, highly toxic

– CH4: colorless, odorless, flammable

– NO2: toxic, red-brown, irritant

– N2O: colorless, sweet odor (laughing gas)

– Cl2: yellow/green, toxic

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Properties That Describe a Gas

Gases are described in terms of four properties: pressure (P), volume(V), temperature(T), and amount(n).

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• Pressure is the amount of force applied to an area.

Pressure

• Atmospheric pressure is the weight of air per unit of area.

P =FA

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Altitude and Atmospheric Pressure

Atmospheric pressure

• is about 1 atmosphere at sea level.

• depends on the altitude and the weather.

• is lower at high altitudes where the density of air is less.

• is higher on a rainy day than on a sunny day.

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Barometer

A barometer

• measures the pressure exerted by the gases in the atmosphere.

• indicates atmospheric pressure as the height in mm of the mercury column.

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Pressure

Many different units used to report pressure.

• millimeters of Hg (mm Hg)• inches of Hg (in. Hg)• pounds per square inch (psi)• atmosphere (atm)• torr (torr)• pascal (Pa) = SI base unit• kilopascal (kPa)

Must know units and

abbreviations!!

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Pressure

Relationships between different pressure units:

1 atm = 760 mm Hg

= 760 torr

= 29.92 in. Hg

= 14.7 psi

= 1.01325 x 105 Pa

= 101.325 kPa

Must be able to interconvert

between units.

Memorize the ones in red

You must know that 1 kPa = 1000 Pa

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A. What is 475 mm Hg expressed in atm?

1) 475 atm 2) 0.625 atm

3) 3.61 x 105 atm

475 mm Hg x 1 atm = 0.625 atm 760 mm Hg

Learning Check

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B. The pressure in a tire is 2.00 atm. What is this pressure in mm Hg?

1) 2.00 mm Hg 2) 1520 mm Hg 3) 22 300 mm Hg

2.00 atm x 760 mm Hg = 1520 mm Hg 1 atm

Learning Check

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More practice

The measured pressure inside the eye of a hurricane was 669 torr. What was the pressure in atm?

Given: 669 torr

Find: P (atm)

P (atm) = 669 torr x 1 atm = 0.880 atm760 torr

Conversion factor:1 atm = 760 torr

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Kinetic-Molecular Theory

• The behavior of gases can be described and explained using kinetic molecular theory.

– the “theory of moving molecules”

• You must know the basic ideas that are part of kinetic molecular theory.

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Kinetic Molecular Theory

• Gases consist of large numbers of molecules that are in continuous, random motion.

• The combined volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained.– i.e. the molecules are very far apart on average

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Kinetic Molecular Theory

• Attractive and repulsive forces between gas molecules are negligible.

• Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change as long as the temperature remains constant.– Collisions are perfectly elastic.

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Kinetic Molecular Theory• The average kinetic energy of the molecules is

proportional to the absolute temperature.– At any given temperature all molecules of a

gas have the same average kinetic energy.– As T (in K) increases,

KE increases.

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Gas Laws

• Four variables are needed to define the physical condition or state of any gas:– Temperature (T)– Pressure (P)– Volume (V)– Amount of gas (moles: n)

• Equations relating these variables are known as the

Gas Laws

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Boyle’s LawPressure and Volume

Boyle’s Law states that

• the pressure of a gas is inversely related to its volume when T and n are constant.

• if volume decreases, the pressure increases.

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In Boyle’s Law, the product P x V is constant as long as T and n do not change.

Boyle’s Law can be stated as

PV=constant

P1V1 = P2V2 (T, n constant)

P1V1 = 8.0 atm x 2.0 L = 16 atm L

P2V2 = 4.0 atm x 4.0 L = 16 atm L

P3V3 = 2.0 atm x 8.0 L = 16 atm L

PV Constant in Boyle’s Law

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The equation for Boyle’s Law can be rearranged tosolve for any factor.

P1V1 = P2V2 Boyle’s Law

Can find the change in volume if pressure changes:

To solve for V2 , divide both sides by P2.P1V1 = P2V2

P2 P2

V1 x P1 = V2

P2

Solving for a Gas Law Factor

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Learning Check

For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant).

1) pressure decreases

B (volume increases)

2) pressure increases

A (volume decreases)

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Learning Check

If a sample of helium gas has a volume of 120 mLand a pressure of 850 mm Hg, what is the newvolume if the pressure is changed to 425 mm Hg ?

1) 60 mL 2) 120 mL 3) 240 mL

Known: P1 = 850 mm Hg P2 = 425 mm Hg

V1 = 120 mL V2 = ??

P1V1=P2V2

V2 = V1 x P1 = 120 mL x 850 mm Hg = 240 mL

P2 425 mm Hg

Pressure ratioincreases volume

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Learning Check

A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C?

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Charles’ Law:Temperature and Volume

In Charles’ Law,

• the Kelvin temperature of a gas is directly related to the volume.

• P and n are constant.

• when the temperature of a gas increases, its volume increases.

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• Charles’ Law is written V T

Or: V1 V2 (P and n constant)

T1 T2

• Rearranging Charles’ Law to solve for V2

T2 x V1 = V2 x T2

T1 T2

V2 = V1 x T2

T1

Charles’ Law: V and T

= constant

=

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A balloon has a volume of 785 mL at 21°C. If the

temperature drops to 0°C, what is the new volume of

the balloon (P constant)?

1. Set up data table:Conditions 1 Conditions 2V1 = 785 mL V2 = ?

T1 = 21°C = 294 K T2 = 0°C = 273 K

Be sure to use the Kelvin (K) temperature ingas calculations.

Calculations Using Charles’ Law

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Calculations Using Charles’ Law (continued)

2. Solve Charles’ law for V2:

V1 = V2

T1 T2

V2 = V1 x T2

T1

V2 = 785 mL x 273 K = 729 mL 294 K

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Use the gas laws to complete sentence with

1) increases 2) decreases.

A. Pressure _______, when V decreases.

B. When T decreases, V _______.

C. Pressure _______ when V changes from 12 L to 24 L

D. Volume _______when T changes from 15 °C to 45°C

Learning Check

increases

increases

decreases

decreases

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Think!

Does the volume of a fixed quantity of gas decrease to half its original value when the temperature is lowered from 100C to 50C?

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Avogadro's Law: Volume and Quantity (Moles)

In Avogadro’s Law

• the volume of a gas is directly related to the number of moles (n) of gas.

• T and P are constant.

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Avogadro's Law: Volume and Quantity (Moles)

Vn = constant

or

V1n1

V2n2

=

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Learning Check

If 0.75 mole helium gas occupies a volume of 1.5 L, what volume will 1.2 moles helium occupy at the same temperature and pressure?

1) 0.94 L

2) 1.8 L

3) 2.4 L

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Solution

STEP 1 Conditions 1 Conditions 2 V1 = 1.5 L V2 = ??? n1 = 0.75 mol He n2 = 1.2 moles He

STEP 2 Solve for unknown V2

V2 = V1 x n2

n1

STEP 3 Substitute values and solve for V2.V2 = 1.5 L x 1.2 moles He = 2.4 L

0.75 mol He