14.3 ideal gases > 1 copyright © pearson education, inc., or its affiliates. all rights...

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

14.3 Ideal Gases >14.3 Ideal Gases >

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Chapter 14The Behavior of Gases

14.1 Properties of Gases

14.2 The Gas Laws

14.3 Ideal Gases

14.4 Gases: Mixtures and Movements



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How can you blanket a stage with fog?

CHEMISTRY & YOUCHEMISTRY & YOU

Solid carbon dioxide, or dry ice, can be used to make stage fog.



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How can you calculate the amount of a contained gas when the pressure, volume, and temperature are specified?

Ideal Gas LawIdeal Gas Law

Ideal Gas Law



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Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure.




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• The volume occupied by a gas at a specified temperature and pressure depends on the number of particles.




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• The number of moles of gas is directly proportional to the number of particles.




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• The number of moles of gas is directly proportional to the number of particles.

• Moles must be directly proportional to volume.




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You can introduce moles into the combined gas law by dividing each side of the equation by n.




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You can introduce moles into the combined gas law by dividing each side of the equation by n.• This equation shows that (P V)/(T n) is a

constant.




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You can introduce moles into the combined gas law by dividing each side of the equation by n.

P1 V1 P2

V2T1 n1 T2 n2

=

• This equation shows that (P V)/(T n) is a constant.

• This constant holds for what are called ideal gases—gases that conform to the gas laws.




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If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R).

P V

T nR =




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• Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K).

P V

T nR =




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• Insert the values of P, V, T, and n into (P V)/(T n).

P V

T nR = =

101.3 kPa 22.4 L273 K 1 mol




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• Insert the values of P, V, T, and n into (P V)/(T n).

P V

T nR = =

101.3 kPa 22.4 L273 K 1 mol

R = 8.31 (L·kPa)/(K·mol)




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The gas law that includes all four variables—P, V, T, n—is called the ideal gas law.

P V = n R T

PV = nRT

or




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When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas.




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At 34oC, the pressure inside a nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball?

Sample Problem 14.5Sample Problem 14.5

Using the Ideal Gas Law



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Use the ideal gas law (PV = nRT) to calculate the number of moles (n).

KNOWNSP = 212 kPa

V = 0.148 L

T = 34oC

R = 8.31 (L·kPa)/(K·mol)

UNKNOWNn = ? mol N2

Analyze List the knowns and the unknown.

1




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Convert degrees Celsius to kelvins.

Calculate Solve for the unknown.2

T = 34oC + 273 = 307 K




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State the ideal gas law.


P V = n R T




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Rearrange the equation to isolate n.


n = R TP V

Isolate n by dividing both sides by (R T):

=R T

n R T

P V

R T

P V = n R T




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Substitute the known values for P, V, R, and T into the equation and solve.


n = 1.23 10–2 mol N2

n = 8.31 (L·kPa) / (K·mol) 307 K

212 kPa 0.148 L

n = R TP V




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• A tennis ball has a small volume and is not under great pressure.

• It is reasonable that the ball contains a small amount of nitrogen.

Evaluate Does the result make sense?3




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A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain?


Using the Ideal Gas Law



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Calculate the number of moles (n) using the ideal gas law. Use the molar mass of methane to convert moles to grams. Then convert grams to kilograms.

KNOWNSP = 1.50 103 kPa

V = 2.24 103 L

T = 315 K

R = 8.31 (L·kPa)/(K·mol)

molar massCH4 = 16.0 g

UNKNOWNm = ? kg CH4

Analyze List the knowns and the unknown.

1




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State the ideal gas law.


P V = n R T

Rearrange the equation to isolate n.

n = R TP V




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Substitute the known quantities into the equation and find the number of moles of methane.


n = 8.31 (L·kPa)/(K·mol) 315 K

(1.50 106 kPa) (2.24 106 L)

n = 1.28 106 mol CH4




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Do a mole-mass conversion.


1.28 106 mol CH4

16.0 g CH4

1 mol CH4

= 20.5 106 g CH4

= 2.05 107 g CH4




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Convert from grams to kilograms.


2.05 106 g CH4 1 kg

103 g= 2.05 104 kg CH4




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• Although the methane is compressed, its volume is still very large.

• So it is reasonable that the cavern contains a large amount of methane.

Evaluate Does the result make sense?3




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How would you rearrange the ideal gas law to isolate the temperature, T?

PV nR

T = A.nR PV

T = C.

PR nVT = B.

RV nP

T = D.



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How would you rearrange the ideal gas law to isolate the temperature, T?

PV nR

T = A.nR PV

T = C.

PR nVT = B.

RV nP

T = D.



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Ideal Gases and Real GasesIdeal Gases and Real Gases

Ideal Gases and Real GasesUnder what conditions are real gases

most likely to differ from ideal gases?



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An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.



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An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.• Its particles could have no volume.



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An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.• Its particles could have no volume.

• There could be no attraction between particles in the gas.



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There is no gas for which these assumptions are true.

• So, an ideal gas does not exist.



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At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas.



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• The particles in a real gas have volume.



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• There are attractions between the particles.



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• There are attractions between the particles.

• Because of these attractions, a gas can condense, or even solidify, when it is compressed or cooled.



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Real gases differ most from an ideal gas at low temperatures and high pressures.




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Interpret GraphsInterpret Graphs

This graph shows how real gases deviate from the ideal gas law at high pressures.



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What are the characteristics of an ideal gas?



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What are the characteristics of an ideal gas?

The particles of an ideal gas have no volume, and there is no attraction between them.



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Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made?




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Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made?


Dry ice doesn’t melt—it sublimes. As solid carbon dioxide changes to gas, water vapor in the air condenses and forms a white fog. Dry ice can exist because gases don’t obey the assumptions of kinetic theory at all conditions.



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Key Concepts and Key EquationKey Concepts and Key Equation

When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas.

Real gases differ most from an ideal gas at low temperatures and high pressures.

Key Equation: ideal gas law

P V = n R T or PV = nRT



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Glossary TermsGlossary Terms

• ideal gas constant: the constant in the ideal gas law with the symbol R and the value 8.31 (L·kPa)/(K·mol)

• ideal gas law: the relationship PV = nRT, which describes the behavior of an ideal gas



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Kinetic Theory

BIG IDEABIG IDEA

• Ideal gases conform to the assumptions of kinetic theory.

• The behavior of ideal gases can be predicted by the gas laws.

• With the ideal gas law, the number of moles of a gas in a fixed volume at a known temperature and pressure can be calculated.

• Although an ideal gas does not exist, real gases behave ideally under a variety of temperature and pressure conditions.



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END OF 14.3END OF 14.3

14.3 ideal gases > 1 copyright © pearson education, inc., or its affiliates. all rights...

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