1 Lecture 6 Gases Properties of Gases Gas Pressure Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

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Lecture 6 Gases

Properties of Gases

Gas Pressure

Copyright © 2007 by Pearson Education, Inc.Publishing as Benjamin Cummings

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Kinetic Theory of Gases

Assumptions about the behavior of gases: Gas particles are in constant motion and

move rapidly in straight lines until they collide

Gas particles are very far apart. Gases have no volume or very small

volume (true if pressure is low) As the temperature of gas increases, the

speed of the gas particles increase (Kinetic energy increases).

The size of the gas molecule will not affect the properties of the gas

Ideal Gas: one that obeys all of the above criteria


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Properties of Gases

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

TABLE 7.1

Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

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Gas pressure: the force acting on a specific area.

Pressure (P) = force

area Has units of atm, mm Hg, torr, lb/in.2 and

kilopascals (kPa).

1 atm = 760 mm Hg (exact)

1 atm = 760 torr

1 atm = 14.7 lb/in.2

1 atm = 101.325 kPa

Gas Pressure

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A. What is 475 mm Hg expressed in atm? 1) 475 atm

2) 0.625 atm 3) 3.61 × 105 atm

B. The pressure of 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

Learning Check

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Atmospheric Pressure

Atmospheric pressure Is the pressure

exerted by a column of air from the top of the atmosphere to the surface of the Earth.


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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. Copyright © 2007 by Pearson Education, Inc.

Publishing as Benjamin Cummings

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Barometer

A barometer Measures the

pressure exerted by the gases in the atmosphere.

Indicates atmospheric pressure as the height in millimeters of the mercury column.


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Relationship Between Properties of Gases Pressure and Volume (Boyle’s Law) Temperature and Volume (Charle’s Law) Temperature and Pressure (Gay-Lussac’s Law) The Combined Gas Law Volume and Moles (Avogadro’s Law) Partial Pressures (Dalton’s Law)

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Pressure and Volume (Boyle’s Law)

Boyle’s Law states that

or PV = K

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

If the pressure increases, volume decreases.

Robert Boyle, 1627-1691*


*http://www.iun.edu/~cpanhd/C101webnotes/gases/boyleslaw.html

P 1V

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In Boyle’s Law The product P x V is constant as long as T and n do

not change.

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

Boyle’s Law can be stated as

P1V1 = P2V2 (T, n constant)

PV Constant in Boyle’s Law

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Solving for a Gas Law Factor

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

P1V1 = P2V2 Boyle’s Law

To solve for V2 , divide both sides by P2.

P1V1 = P2V2

P2 P2

V1 x P1 = V2

P2

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Freon-12, CCl2F2, is used in refrigeration systems. What is the new volume (L) of a 8.0 L sample of Freon gas initially at 550 mm Hg after its pressure is changed to 2200 mm Hg at constant T?

Conditions 1 Conditions 2 P1 = 550 mm Hg P2 = 2200 mm Hg

V1 = 8.0 L V2 =

Calculation with Boyle’s Law

?

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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

2) Pressure increases


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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

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Learning Check

A sample of helium gas in a balloon has a volume of 10. L at a pressure of 0.90 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C?


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Temperature and Volume: Charles’ Law

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.


Jaques Alexander Cedar Charles (1746-1823)*

*http://www.iun.edu/~cpanhd/C101webnotes/gases/charleslaw.html

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For two conditions, Charles’ Law is written

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

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Learning Check

Solve Charles’ Law expression for T2.

V1 = V2

T1 T2

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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)?

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 in gascalculations.

Calculations Using Charles’ Law

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A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)?

1) 443°C

2) 170°C

3) - 82°C

Learning Check

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Use the gas laws to complete 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

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Gay-Lussac’s Law: P and T

In Gay-Lussac’s Law, The pressure exerted by a

gas is directly related to the Kelvin temperature.

V and n are constant. P1 = P2

T1 T2


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A gas has a pressure at 2.0 atm at 18°C. What

is the new pressure when the temperature is

62°C? (V and n constant)

Calculation with Gay-Lussac’s Law

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Vapor Pressure and Boiling Point

Vapor pressure is the

Pressure of gas molecules above the surface of a liquid.

At the boiling point, the vapor pressure becomes equal to the external pressure.


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The combined gas law uses Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law (n is constant).

P1 V1 = P2 V2

T1 T2

Combined Gas Law

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A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n constant)?

Combined Gas Law Calculation

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A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the volume(mL) of the gas at -95°C and a pressure of 802 mm Hg (n constant)

Learning Check

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Avogadro's Law: Volume and MolesAvogadro’s Law states that

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

T and P are constant.

V1 = V2

n1 n2


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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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The volumes of gases can be compared at STP,

(Standard Temperature and Pressure) when they

have The same temperature.

Standard temperature (T)

0°C or 273 K

The same pressure. Standard pressure (P)

1 atm (760 mm Hg)

STP

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Molar Volume

The molar volume of

a gas Is measured at

STP (standard temperature and pressure).

Is 22.4 L for 1 mole of any gas. .


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Molar Volume as a Conversion Factor

The molar volume at STP can be used to form conversion factors.

22.4 L and 1 mole

1 mole 22.4 L

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Using Molar Volume

What is the volume occupied by 2.75 moles N2 gas

at STP?

The molar volume is used to convert moles to liters.

2.75 moles N2 x 22.4 L = 61.6 L

1 mole


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A. What is the volume at STP of 4.00 g of CH4?

1) 5.60 L 2) 11.2 L 3) 44.8 L

B. How many grams of He are present in 8.00 L of

Hes at STP?

1) 25.6 g 2) 0.357 g 3) 1.43 g

Learning Check

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Gases in Chemical Reactions

The volume or amount of a gas at STP in a chemical

reaction can be calculated from

STP conditions.

Mole factors from the balanced equation.

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STP and Gas Equations

What volume (L) of O2 gas is needed to completely

react with 15.0 g of aluminum at STP?

4Al(s) + 3O2 (g) 2Al2O3(s)

Plan: g Al mole Al mole O2 L O2 (STP)

What volume (L) of O2 gas is needed to completely

react with 15.0 g of aluminum at STP?

4Al(s) + 3O2 (g) 2Al2O3(s)

Plan: g Al mole Al mole O2 L O2 (STP 22.4 L/1 mole)

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What mass of Fe will react with 5.50 L O2 at STP?

4Fe(s) + 3O2(g) 2Fe2O3(s)

Learning Check

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The relationship between the four properties (P, V, n, and T) of gases can be written equal to a constant R.

PV = RnT

Rearranging this expression gives the expression called the ideal gas law.

PV = nRT

Ideal Gas Law

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The universal gas constant, R Can be calculated using the molar volume of a gas at

STP. Calculated at STP uses 273 K,1.00 atm, 1 mole of a

gas, and a molar volume of 22.4 L.

P V

R = PV = (1.00 atm)(22.4 L)

nT (1 mole) (273K) n T = 0.0821 L atm

mole K

Universal Gas Constant, R

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Another value for the universal gas constant is obtained

using mm Hg for the STP pressure. What is the value

of R when a pressure of 760 mm Hg is placed in the R

value expression?

Learning Check

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Dinitrogen oxide (N2O), laughing gas, is used by dentists as an anesthetic. If a 20.0 L tank of laughing gas contains 2.86 moles N2O at 23°C, what is the pressure (mm Hg) in the tank?

Learning Check


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Learning Check

A cylinder contains 5.0 L of O2 at 20.0°C and 0.85 atm. How many grams of oxygen are in the cylinder?


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The partial pressure of a gas Is the pressure of each gas in a mixture. Is the pressure that gas would exert if it were by

itself in the container.

Partial Pressure (Dalton’s Law)

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Dalton’s Law of Partial Pressures indicates that Pressure depends on the total number of gas

particles, not on the types of particles.

The total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases.

PT = P1 + P2 + P3 +.....

Dalton’s Law of Partial Pressures

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Dalton’s Law of Partial Pressures


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For example, at STP, one mole of a pure gas in a volume of 22.4 L will exert the same pressure as one mole of a gas mixture in 22.4 L.

V = 22.4 L Gas mixtures

Total Pressure

0.5 mole O2

0.3 mole He0.2 mole Ar1.0 mole

1.0 mole N2

0.4 mole O2

0.6 mole He1.0 mole

1.0 atm 1.0 atm 1.0 atm

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Scuba Diving

When a scuba diver dives, the increased pressure causes N2(g)

to dissolve in the blood. If a diver rises too fast, the

dissolved N2 will form bubbles in the blood, a dangerous and painful condition called "the bends".

Helium, which does not dissolve in the blood, is mixed with O2 to prepare breathing mixtures for deep descents.


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Learning Check

A scuba tank contains O2 with a pressure of 0.450 atm and He at 855 mm Hg. What is the total pressure in mm Hg in the tank?


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For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mm Hg, what is the partial pressure of the helium?

1) 520 mm Hg

2) 2040 mm Hg

3) 4800 mm Hg

Learning Check

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Gases We Breathe

The air we breathe Is a gas mixture. Contains mostly

N2 and O2 and small amounts of other gases.

TABLE 7.7


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A.If the atmospheric pressure today is 745 mm Hg, what is the partial pressure (mm Hg) of O2 in the

air?

1) 35.6 2) 156 3) 760

B. At an atmospheric pressure of 714, what is the partial pressure (mm Hg) N2 in the air?

1) 557 2) 9.14 3) 0.109

Learning Check

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1 Lecture 6 Gases Properties of Gases Gas Pressure Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings