Lecture 5

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Transcript Lecture 5

Chemistry: A Molecular Approach

, 2nd Ed.

Nivaldo Tro

Chapter 5 Gases

April Senger MALMSTROM Park University Great Falls Montana Copyright © 2011 Pearson Education, Inc .

The Structure of a Gas

• • • Gases are composed of particles that are flying around very fast in their container(s) The particles in straight lines until they encounter either the container wall or another particle, then they bounce off If you were able to take a snapshot of the particles in a gas, you would find that there is a lot of empty space in there Copyright © 2011 Pearson Education, Inc .

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Gases Pushing

• • • Gas molecules are constantly in motion As they move and strike a surface, they push on that surface  push = force If we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting 

pressure

= force per unit area Copyright © 2011 Pearson Education, Inc .

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The Effect of Gas Pressure

• • • The pressure exerted by a gas can cause some amazing and startling effects Whenever there is a pressure difference, a gas will flow from an area of high pressure to an area of low pressure  the bigger the difference in pressure, the stronger the flow of the gas If there is something in the gas’s path, the gas will try to push it along as the gas flows Copyright © 2011 Pearson Education, Inc .

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Air Pressure

• • The atmosphere exerts a pressure on everything it contacts  the atmosphere goes up about 370 miles, but 80% is in the first 10 miles from the earth’s surface This is the same pressure that a column of water would exert if it were about 10.3 m high Copyright © 2011 Pearson Education, Inc .

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Atmospheric Pressure Effects

• • Differences in air pressure result in weather and wind patterns The higher in the atmosphere you climb, the lower the atmospheric pressure is around you  at the surface the atmospheric pressure is 14.7 psi, but at 10,000 ft it is only 10.0 psi Copyright © 2011 Pearson Education, Inc .

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Pressure Imbalance in the Ear

If there is a difference in pressure across the eardrum membrane, the membrane will be pushed out – what we commonly call a “popped eardrum” Tro: Chemistry: A Molecular Approach, 2/e 7 Copyright © 2011 Pearson Education, Inc .

The Pressure of a Gas

• • Gas pressure is a result of the constant movement of the gas molecules and their collisions with the surfaces around them The pressure of a gas depends on several factors  number of gas particles in a given volume  volume of the container  average speed of the gas particles Copyright © 2011 Pearson Education, Inc .

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Measuring Air Pressure

• • • We measure air pressure with a

barometer

Column of mercury supported by air pressure Force of the air on the surface of the mercury counter balances the force of gravity on the column of mercury gravity Copyright © 2011 Pearson Education, Inc .

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Common Units of Pressure

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Example 5.1: A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg?

Given: Find: Conceptual Plan:

132 psi mmHg psi atm mmHg

Relationships: Solution:

1 atm = 14.7 psi, 1 atm = 760 mmHg

Check:

because mmHg are smaller than psi, the answer makes sense Tro: Chemistry: A Molecular Approach, 2/e 11 Copyright © 2011 Pearson Education, Inc .

Practice —Convert 45.5 psi into kPa

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Practice —Convert 45.5 psi into kPa

Given: Find: Conceptual Plan:

645.5 psi kPa psi atm kPa

Relationships: Solution:

1 atm = 14.7 psi, 1 atm = 101.325 kPa

Check:

because kPa are smaller than psi, the answer makes sense Tro: Chemistry: A Molecular Approach, 2/e 13 Copyright © 2011 Pearson Education, Inc .

Boyle’s Law

Robert Boyle (1627 –1691) • • • • Pressure of a gas is inversely proportional to its volume  constant T and amount of gas  graph P vs V is curve  graph P vs 1/V is straight line As P increases, V decreases by the same factor P x V = constant P 1 x V 1 = P 2 x V 2 Copyright © 2011 Pearson Education, Inc .

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Boyle’s Law: A Molecular View

• • • Pressure is caused by the molecules striking the sides of the container When you

decrease the volume

of the container with the same number of molecules in the container, more molecules will hit the wall at the same instant This results in

increasing the pressure

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Boyle’s Law and Diving

• Because water is more dense than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atm  at 20 m the total pressure is 3 atm • If your tank contained air at 1 atm of pressure, you would not be able to inhale it into your lungs  you can only generate enough force to overcome about 1.06 atm Tro: Chemistry: A Molecular Approach, 2/e 16 Scuba tanks have a regulator so that the air from the tank is delivered at the same pressure as the water surrounding you.

This allows you to take in air even when the outside pressure is large.

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Boyle’s Law and Diving

• • • If a diver holds her breath and rises to the surface quickly, the outside pressure drops to 1 atm According to Boyle’s law, what should happen to the volume of air in the lungs?

Because the pressure is decreasing by a factor of 3, the volume will expand by a factor of 3, causing damage to internal organs.

Always Exhale When Rising!!

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Example 5.2: A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm?

Given:

V 1 =7.25 L, P 1 = 4.52 atm, P 2 = 1.21 atm

Find:

V 2 , L

Conceptual Plan:

V 1 , P 1 , P 2 V 2

Relationships:

P 1 ∙ V 1 = P 2 ∙ V 2

Solution: Check:

because P and V are inversely proportional, when the pressure decreases ~4x, the volume should increase ~4x, and it does Tro: Chemistry: A Molecular Approach, 2/e 18 Copyright © 2011 Pearson Education, Inc .

A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78x 10 3 mL, what was it originally?

Given:

V 2 =2780 mL, P 1 = 762 torr, P 2 = 0.500 atm

Find:

V 1 , mL

Conceptual Plan:

V 2 , P 1 , P 2 V 1

Relationships:

P 1 ∙ V 1 = P 2 ∙ V 2 , 1 atm = 760 torr (exactly)

Solution: Check:

because P and V are inversely proportional, when the pressure decreases ~2x, the volume should increase ~2x, and it does Tro: Chemistry: A Molecular Approach, 2/e 19 Copyright © 2011 Pearson Education, Inc .

Charles’s Law

Jacques Charles (1746 –1823) • Volume is directly proportional to temperature  constant P and amount of gas  graph of V vs. T is straight line • • • As T increases, V also increases Kelvin T = Celsius T + 273 V = constant x T  if T measured in Kelvin Copyright © 2011 Pearson Education, Inc .

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Charles’s Law – A Molecular View

• • The pressure of gas inside and outside the • • At high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – become larger Tro: Chemistry: A Molecular Approach, 2/e Copyright © 2011 Pearson Education, Inc .

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Example 5.3: A gas has a volume of 2.57 L at 0.00 °C. What was the temperature at 2.80 L?

Given: Find:

V 1 =2.57 L, V 2 = 2.80 L, t 2 = 0.00 °C t 1 , K and °C

Conceptual Plan:

V 1 , V 2 , T 2 T 1

Relationships: Solution: Check:

because T and V are directly proportional, when the volume decreases, the temperature should decrease, and it does Tro: Chemistry: A Molecular Approach, 2/e 22 Copyright © 2011 Pearson Education, Inc .

The temperature inside a balloon is raised from 25.0 °C to 250.0 °C. If the volume of cold air was 10.0 L, what is the

Given:

V 1 volume of hot air?

=10.0 L, t 1 = 25.0 °C L, t 2 = 250.0 °C

Find:

V 2 , L

Conceptual Plan:

V 1 , T 1 , T 2 V 2

Relationships: Solution: Check:

when the temperature increases, the volume should increase, and it does Tro: Chemistry: A Molecular Approach, 2/e 23 Copyright © 2011 Pearson Education, Inc .

Avogadro’s Law

Amedeo Avogadro (1776 –1856) • Volume directly proportional to the number of gas molecules 

V

= constant x

n

 constant P and T  more gas molecules = larger volume • • Count number of gas molecules by

moles

Equal volumes of gases contain equal numbers of molecules 

the gas doesn’t matter

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Example 5.4:A 0.225 mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L?

Given:

V 1 = 4.65 L, V 2 = 6.48 L, n 1 = 0.225 mol

Find:

n 2 , and added moles

Conceptual Plan:

V 1 , V 2 , n 1 n 2

Relationships: Solution: Check:

because n and V are directly proportional, when the volume increases, the moles should increase, and they do Tro: Chemistry: A Molecular Approach, 2/e 25 Copyright © 2011 Pearson Education, Inc .

    

Ideal Gas Law

By combining the gas laws we can write a general equation

R

is called the

gas constant

The value of

R

depends on the units of P and V  we will use 0.08206 and convert P to atm and V to L The other gas laws are found in the ideal gas law if two variables are kept constant Allows us to find one of the variables if we know the other three Tro: Chemistry: A Molecular Approach, 2/e 26 Copyright © 2011 Pearson Education, Inc .

Example 5.6: How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25 °C?

Given: Find: Conceptual Plan:

V = 3.24 L, P = 24.3 psi, t = 25 °C n, mol P, V, T, R n

Relationships: Solution: Check:

1 mole at STP occupies 22.4 L, because there is a much smaller volume than 22.4 L, we expect less than 1 mole of gas Tro: Chemistry: A Molecular Approach, 2/e 27 Copyright © 2011 Pearson Education, Inc .

Standard Conditions

• Because the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these

standard conditions

 STP • • Standard pressure = 1 atm Standard temperature = 273 K  0 °C Copyright © 2011 Pearson Education, Inc .

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A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at standard conditions?

Given:

V 1 = 10.0L, P 1 = 44.1 psi, t 1 = 27 °C, P 2 = 1.00 atm, t 2 = 0 °C

Find:

V 2 , L

Conceptual Plan:

P 1 , V 1 , T 1 , R n P 2 , n, T 2 , R V 2

Relationships: Solution: Check:

1 mole at STP occupies 22.4 L, because there is more than 1 mole, we expect more than 22.4 L of gas Tro: Chemistry: A Molecular Approach, 2/e 29 Copyright © 2011 Pearson Education, Inc .

Practice —Calculate the volume occupied by 637 g of SO 2 (MM 64.07) at 6.08 x 10 4 mmHg and –23 °C

.

Given:

m SO2 = 637 g, P = 6.08 x 10 4 mmHg, t = −23 °C,

Find: Conceptual Plan:

V

, L g n P, n, T, R V

Relationships: Solution:

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Molar Volume

• Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L  6.022 x 10 23 molecules of gas  notice: the gas is immaterial • We call the volume of 1 mole of gas at STP the

molar volume

 it is important to recognize that one mole measures of different gases have different masses, even though they have the same volume Copyright © 2011 Pearson Education, Inc .

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Molar Volume

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Molar Mass of a Gas

• One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law Tro: Chemistry: A Molecular Approach, 2/e 33 Copyright © 2011 Pearson Education, Inc .

Example 5.8: Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55 °C and 886 mmHg

Given:

m=0.311g, V=0.225 L, P=886 mmHg, t=55 °C,

Find: Conceptual Plan:

P, V, T, R n n, m MM

Relationships: Solution:

T(K) = 55°C + 273.15

T = 328 K

Check:

the unit is correct, the value is reasonable Tro: Chemistry: A Molecular Approach, 2/e 34 Copyright © 2011 Pearson Education, Inc .

Practice — What is the molar mass of a gas if 12.0 g occupies 197 L at 380 torr and 127 °C?

Given:

m=12.0 g, V= 197 L, P=380 torr, t=127 °C,

Find: Conceptual Plan:

P, V, T, R n n, m MM

Relationships: Solution: Check:

the unit is correct and the value is reasonable Tro: Chemistry: A Molecular Approach, 2/e 35 Copyright © 2011 Pearson Education, Inc .

Mixtures of Gases

• • When gases are mixed together, their molecules behave independent of each other  all the gases in the mixture have the same volume  all completely fill the container  each gas’s volume = the volume of the container  all gases in the mixture are at the same temperature  therefore they have the same average kinetic energy Therefore, in certain applications, the mixture can be thought of as one gas  even though air is a mixture, we can measure the pressure, volume, and temperature of air as if it were a pure substance  we can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules Copyright © 2011 Pearson Education, Inc .

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Composition of Dry Air

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• •

Partial Pressure

The pressure of a single gas in a mixture of gases is called its

partial pressure

We can calculate the partial pressure of a gas if  we know what fraction of the mixture it composes and the total pressure  or, we know the number of moles of the gas in a container of known volume and temperature • The sum of the partial pressures of all the gases in the mixture equals the total pressure  Dalton’s Law of Partial Pressures  because the gases behave independently Copyright © 2011 Pearson Education, Inc .

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The partial pressure of each gas in a mixture can be calculated using the ideal gas law

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Example 5.9: Determine the mass of Ar in the

Given:

mixture P He = 0.275 atm, V = 1.00 L, T=298 K V = 1.00 L, T=298 K = 662 mmHg,

Find:

mass Ar , g

Conceptual

P tot , P He , P Ne

Plan:

P Ar = P tot – (P He P Ar + P Ne ) P Ar , V, T n A r m A r

Relationships: Solution: Check:

the units are correct, the value is reasonable Tro: Chemistry: A Molecular Approach, 2/e 40 Copyright © 2011 Pearson Education, Inc .

Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe

Given:

P tot = 3.9 atm, V = 8.7 L, T = 598 K, Xe = 0.17 mol

Find:

P Ne , atm

Conceptual Plan:

n Xe , V, T, R P Xe P tot , P Xe P Ne

Relationships: Solution: Check:

the unit is correct, the value is reasonable Tro: Chemistry: A Molecular Approach, 2/e 41 Copyright © 2011 Pearson Education, Inc .

Properties of Gases

• • • Expand to completely fill their container Take the shape of their container Low density  much less than solid or liquid state • • • Compressible Mixtures of gases are always homogeneous Fluid Copyright © 2011 Pearson Education, Inc .

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Kinetic Molecular Theory

• • The particles of the gas (either atoms or molecules) are constantly moving • The attraction between particles is negligible When the moving gas particles hit another gas particle or the container, they do not stick; but they bounce off and continue moving in another direction  like billiard balls Copyright © 2011 Pearson Education, Inc .

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Kinetic Molecular Theory

• There is a lot of empty space between the gas particles  compared to the size of the particles • The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature  as you raise the temperature of the gas, the average speed of the particles increases  but don’t be fooled into thinking all the gas particles are moving at the same speed!!

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Gas Properties Explained – Pressure

• • Because the gas particles are constantly moving, they strike the sides of the container with a force The result of many particles in a gas sample exerting forces on the surfaces around them is a constant pressure Tro: Chemistry: A Molecular Approach, 2/e 45 Copyright © 2011 Pearson Education, Inc .

Gas Properties Explained – Indefinite Shape and Indefinite Volume

Because the gas molecules have enough kinetic energy to overcome attractions, they keep moving around and spreading out until they fill the container.

As a result, gases take the shape and the volume of the container they are in.

Copyright © 2011 Pearson Education, Inc .

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Gas Properties Explained Compressibility

Because there is a lot of unoccupied space in the structure of a gas, the gas molecules can be squeezed closer together Tro: Chemistry: A Molecular Approach, 2/e 47 Copyright © 2011 Pearson Education, Inc .

Gas Properties Explained – Low Density

Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume; the result is they have low density Copyright © 2011 Pearson Education, Inc .

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Density & Pressure

• • Pressure is the result of the constant movement of the gas molecules and their collisions with the surfaces around them When more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure  also higher density Copyright © 2011 Pearson Education, Inc .

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• • •

Gas Laws Explained – Boyle’s Law

Boyle’s Law says that the volume of a gas is inversely proportional to the pressure Decreasing the volume forces the molecules into a smaller space More molecules will collide with the container at any one instant, increasing the pressure Tro: Chemistry: A Molecular Approach, 2/e 50 Copyright © 2011 Pearson Education, Inc .

• • •

Gas Laws Explained – Charles’s Law

Charles’s Law says that the volume of a gas is directly proportional to the absolute temperature Increasing the temperature increases their average speed, causing them to hit the wall harder and more frequently  on average To keep the pressure constant, the volume must then increase Copyright © 2011 Pearson Education, Inc .

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Gas Laws Explained – Avogadro’s Law

• Avogadro’s Law says that the volume of a gas is directly proportional to the number of gas molecules • Increasing the number of gas molecules causes more of them to hit the wall at the same time • To keep the pressure constant, the volume must then increase Copyright © 2011 Pearson Education, Inc .

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Gas Laws Explained – Dalton’s Law of Partial Pressures

• • • • Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures Kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact Therefore the molecules behave independently of each other, each gas contributing its own collisions to the container with the same average kinetic energy Because the average kinetic energy is the same, the total pressure of the collisions is the same Copyright © 2011 Pearson Education, Inc .

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Dalton’s Law & Pressure

• Because the gas molecules are not sticking together, each gas molecule contributes its own force to the total force on the side Tro: Chemistry: A Molecular Approach, 2/e 54 Copyright © 2011 Pearson Education, Inc .

Diffusion and Effusion

• • • • The process of a collection of molecules spreading out from high concentration to low concentration is called

diffusion

The process by which a collection of molecules escapes through a small hole into a vacuum is called

effusion

The rates of diffusion and effusion of a gas are both related to its rms average velocity For gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of its molar mass Copyright © 2011 Pearson Education, Inc .

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Effusion

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