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The Gaseous State of MatterChapter 12

Hein and Arena

Dr. Eugene Passer

Chemistry Department

Bronx Community College

© John Wiley and Company

Version 1.1

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The Kinetic-

Molecular Theory

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The Kinetic-Molecular Theory

• KMT is based on the motions of gasparticles.

• A gas that behaves exactly as outlinedby KMT is known as an ideal gas.

• While no ideal gases are found innature, real gases can approximateideal gas behavior under certainconditions of temperature and pressure.

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Principle Assumptions of the KMT

1. Gases consist of tiny particles with

mass but negligible volume.

2. The distance between particles is

large compared with the size of the

particles themselves.

3. Gas particles have no attraction for

one another.

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4. Gas particles move in straight linesin all directions, colliding frequentlywith one another and with the wallsof the container.

5. No energy is lost by the collision of agas particle with another gas particleor with the walls of the container.All collisions are perfectly elastic.

Principle Assumptions of the KMT

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6. The average kinetic energy forparticles is the same for all gases atthe same temperature, and its value isdirectly proportional to the Kelvintemperature.

Principle Assumptions of the KMT

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Kinetic Energy

21KE =

2mv

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Standard Temperature

and Pressure

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Standard Temperature and

Pressure

Standard Conditions

Standard Temperature and PressureSTP

273.15 K or 0.00oC

1 atm or 760 torr or 760 mm Hg

Selected common reference points of temperature and

pressure.

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Mole-Mass-Volume

Relationships

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• Volume of one mole of any gas at STP

= 22.4 L.

• 22.4 L at STP is known as the molar

volume of any gas (i.e. 22.4 L/mol.).

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The density of neon at STP is 0.900 g/L. What is the

molar mass of neon?

g = 20.2

mol

0.900 g

1 L

22.4 L

1 mol

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Ideal Gas Equation

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V aP

nTnRTV =

PPV = nRT

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V aP

nTnRTV =

PPV = nRT

atmospheres

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V aP

nTnRTV =

PPV = nRT

liters

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V aP

nTnRTV =

PPV = nRT

moles

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V aP

nTnRTV =

PPV = nRT

Kelvin

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V aP

nTnRTV =

PPV = nRT

Ideal Gas

ConstantL-atm

0.0821mol-K

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A balloon filled with 5.00 moles of helium gas is at a

temperature of 25oC. The atmospheric pressure is 750.

torr. What is the balloon’s volume?

Step 1. Organize the given information.

Convert temperature to kelvins.

K = oC + 273

K = 25oC + 273 = 298K

Convert pressure to atmospheres.

P = 750. torr 1 atm

x 760 torr

= 0.987 atm

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Step 2. Write and solve the ideal gas

equation for the unknown.

Step 3. Substitute the given data into the

equation and calculate.

A balloon filled with 5.00 moles of helium gas is at a

temperature of 25oC. The atmospheric pressure is 750.

torr. What is the balloon’s volume?

nRTV =

PPV = nRT

(0.987 atm)

(5.00 mol)V =

(0.0821 L×atm/mol×K)

(298 K)

= 124 L

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Determination of Molecular Weights

Using the Ideal Gas Equation g

molar mass = mol

gRTM =

PV

gmol =

molar mass

M = molar massg

n = mol = M

PV = nRTg

PV = RTM

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Calculate the molar mass of an unknown gas, if 0.020

g occupies 250 mL at a temperature of 305 K and a

pressure of 0.045 atm.

gRTM =

PV

V = 250 mL = 0.250 L g = 0.020 g

T = 305 K P = 0.045 atm

(0.020 g)M =

(0.082 L × atm/mol × K)

(305 K)

(0.250 L)

(0.045 atm)

g = 44

mol

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Gas Stoichiometry

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Gas Stoichiometry

Primary conversions involved in stoichiometry.

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The problem can be solved in one

continuous calculation.

What volume of oxygen (at STP) can be formed

from 0.500 mol of potassium chlorate?

2 KClO3 2KCl + 3 O2

3(0.500 mol KClO ) 2

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3 mol O

2 mol KClO

22.4 L

1 mol

2= 16.8 L O

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V aP

nTnRTV =

PPV = nRT

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2 Al(s) + 6 HCl(aq) 2AlCl3(aq) + 3 H2(g)

Step 1 Calculate moles of H2.

grams Al moles Al moles H2

What volume of hydrogen, collected at 30.0oC and

700. torr, will be formed by reacting 50.0 g of

aluminum with hydrochloric acid?

50.0 g Al1 mol Al

26.98 g Al

23 mol H

2 mol Al

2 = 2.78 mol H

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• Convert oC to K: 30.oC + 273 = 303 K

• Convert torr to atm:

2 Al(s) + 6 HCl(aq) 2AlCl3(aq) + 3 H2(g)

Step 2 Calculate liters of H2.

What volume of hydrogen, collected at 30.0oC and

700. torr, will be formed by reacting 50.0 g of

aluminum with hydrochloric acid?

700 torr1 atm

760 torr

= 0.921 atm

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What volume of hydrogen, collected at 30.0oC and

700. torr, will be formed by reacting 50.0 g of

aluminum with hydrochloric acid?

PV = nRT

nRTV =

P

• Solve the ideal gas equation for V

(0.921 atm)2(2.78 mol H )

V =

(0.0821 L-atm)

(303 K)

(mol-K)2 = 75.1 L H

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Real Gases

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Real Gases

• Deviations from the gas laws occur athigh pressures and low temperatures.

–At high pressures the volumes of the realgas molecules are not negligiblecompared to the volume of the gas

–At low temperatures the kinetic energy ofthe gas molecules cannot completelyovercome the intermolecular attractiveforces between the molecules.

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