chapter 10: gases - yolaholcombslab.yolasite.com/resources/chapter 10.pdf · chapter 10 gases john...

6/29/2012

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Gases

© 2009, Prentice-Hall, Inc.

Chapter 10

Gases

John Bookstaver

St. Charles Community College

Cottleville, MO

Chemistry, The Central Science, 11th edition

Theodore L. Brown; H. Eugene LeMay, Jr.;

and Bruce E. Bursten

Gases


Chapter 10 Problems

• Problems 16, 19, 26, 33, 39,49, 57, 61

Gases


THREE STATES

OF MATTER

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Gases


General Properties of Gases

• There is a lot of “free” space

in a gas.

• Gases can be expanded

infinitely.

• Gases occupy containers

uniformly and completely.

• Gases diffuse and mix

rapidly.

Gases


Gases: What Are They Like?

Flow readily and occupy

the entire volume of their

container

Vapor is the term used to denote the gaseous state

of a substance existing more commonly as a liquid

e.g., water is a vapor, oxygen is a gas

EOS

Many low molar mass molecular compounds are

gases – methane (CH4), carbon monoxide (CO)

Composed of widely separated particles in constant,

random motion

Gases


Common Gases

EOS

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Gases


Properties of Gases Gas properties can be

modeled using math. Model

depends on—

• V = volume of the gas (L)

• T = temperature (K)

• n = amount (moles)

• P = pressure

(atmospheres)

Gases


• The gaseous states of three

halogens.

• Most common gases are colorless

–H2, O2, N2, CO and CO2

Properties of Gases: Gas Pressure

Gases


The Concept of Pressure

• The pressure

exerted by a solid.

–Both cylinders have

the same mass

–They have different

areas of contact

P (Pa) = Area (m2)

Force (N)

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Gases


Gas Pressure

SI units express pressure in Newtons (N) per square

meters (m2) -- or N m–2

a.k.a. – Pascals (Pa)

Pressure is the force per unit area – consider the

unit pounds per square inch

EOS

A barometer is an instrument

used to measure atmospheric

pressure

Gases


Pressure

Pressure of air is

measured with a

BAROMETER

(developed by

Torricelli in

1643)

Gases


Units of Pressure

• mm Hg or torr

–These units are literally

the difference in the

heights measured in mm

(h) of two connected

columns of mercury.

• Atmosphere

–1.00 atm = 760 torr

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Gases


Pressure

Hg rises in tube until

force of Hg (down)

balances the force

of atmosphere

(pushing up).

P of Hg pushing

down related to

• Hg density

• column height

Gases


Pressure

Column height

measures P of

atmosphere

• 1 standard atm

= 760 mm Hg

= 29.9 inches Hg

= about 34 feet of

water

SI unit is PASCAL,

Pa, where 1 atm =

101.325 kPa

Gases


Examples of Pressure Units

Given these values, one can

generate conversion factors to

switch between units:

e.g., 760 mmHg = 1.01325 bar

EOS

mmHg

baror

bar

mmHg

760

01325.1

01325.1

760

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Gases


Liquid Pressure

• The pressure exerted

by a liquid depends

on:

– The height of the

column of liquid.

– The density of the

column of liquid. P = g ·h ·d

Gases


Barometers

Used to measure atmospheric pressure

The pressure exerted by a column

of mercury exactly 760 mm high is

defined as 1 atmosphere (atm)

EOS

Gases tend to settle under the

effects of gravity – pressure as

altitude

Gases


Barometric Pressure Standard Atmospheric Pressure

1.00 atm, 760 mm Hg, 760 torr, 101.325 kPa, 1.01325 bar

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Gases


Manometer

This device is used to

measure the difference

in pressure between

atmospheric pressure

and that of a gas in a

vessel.

Gases


Open-Ended Manometers

Open-ended manometers

compare gas pressure to

barometric pressure

EOS

Column height differences

are proportional to gas

pressure

Pgas = Pbar + Dh

Gases


Manometers

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Gases


Standard Pressure

• Normal atmospheric pressure at sea level

is referred to as standard pressure.

• It is equal to

– 1.00 atm

– 760 torr (760 mm Hg)

– 101.325 kPa

Gases


Simple Gas Laws

• Boyle 1662

P 1

V PV = constant

Gases


Pressure-Volume Relationship:

Boyle’s Law

For a given amount of a gas at

constant temperature, the

volume of the gas varies

inversely with its pressure

i.e., if V , then P

EOS

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Gases


Boyle’s Law

The volume of a fixed quantity of gas at

constant temperature is inversely proportional

to the pressure.

Gases


As P and V are

inversely proportional

A plot of V versus P results in a curve.

Since

V = k (1/P)

This means a plot of

V versus 1/P will be

a straight line.

PV = k

Gases


Relating Gas Volume and Pressure – Boyle’s Law. The

volume of a large irregularly shaped, closed tank can be

determined. The tank is first evacuated and then connected to a

50.0 L cylinder of compressed nitrogen gas. The gas pressure in

the cylinder, originally at 21.5 atm, falls to 1.55 atm after it is

connected to the evacuated tank. What is the volume of the

tank?

EXAMPLE

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Gases


EXAMPLE

P1V1 = P2V2 V2 = P1V1

P2

= 694 L Vtank = 644 L

Gases


Charles’s Law

• The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

A plot of V versus T will be a straight line.

• i.e., V

T = k

Gases


Temperature-Volume

Relationship: Charles’s Law

The volume of a fixed

amount of a gas at constant

pressure is directly

proportional to its Kelvin

temperature

i.e., if V , then T

or V/T = k

EOS

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Gases


Temperature-Volume

Relationship: Charles’s Law

Absolute zero is the

temperature obtained by

extrapolation to zero

volume

EOS

Absolute zero on the

Kelvin scale = –273.15 °C

and ...

273.15 K = 0 °C

Gases


Avogadro’s Law

• The volume of a gas at constant temperature

and pressure is directly proportional to the

number of moles of the gas.

• Mathematically, this means V = kn

Gases


Avogadro’s Hypothesis Equal volumes of gases at the same T

and P have the same number of

molecules.

V = n (RT/P) = kn

V and n are directly related.

twice as many

molecules

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Gases


Molar Volumes and Standard

Pressure and Temperature

Standard Temperature and

Pressure (STP) is defined

as

T = 0 oC and P = 1 atm

EOS

The molar volume of a gas is the

volume occupied by one mole of the

gas at STP

Gases


Avogadro’s Law

V n or V = c n

At STP

1 mol gas = 22.4 L gas

At an a fixed temperature and pressure:

Gases


Ideal-Gas Equation

V 1/P (Boyle’s law)

V T (Charles’s law)

V n (Avogadro’s law)

• So far we’ve seen that

• Combining these, we get

V nT

P

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Gases


The Ideal Gas Law

The constant of proportionality (k) is given the

symbol R

RknT

PV

EOS

For 1 mol of an ideal gas at STP …

R = 0.08206 L atm mol–1 K–1

Gases


Ideal-Gas Equation

The constant of

proportionality is

known as R, the

gas constant.

Gases


Ideal-Gas Equation

The relationship

then becomes

nT

P V

nT

P V = R

or

PV = nRT

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Gases


The Combined Gas Law

Given the various gas laws, all can be combined

into a single form …

V = k/P, V = kT, and V = kn

V a (nT)/P

knT

PV

For initial and final conditions:

EOS

2

22

1

11

nT

VPk

nT

VP

Gases


The General Gas Equation

R = = P2V2

n2T2

P1V1

n1T1

= P2

T2

P1

T1

If we hold the amount and volume constant:

Gases


Using the Gas Laws

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Gases


6-4 Applications of the Ideal Gas

Equation

PV = nRT and n = m

M

PV = m

M

RT

M = m

PV

RT

Molar Mass Determination

Gases


Determining a Molar Mass with the Ideal Gas Equation.

Polypropylene is an important commercial chemical. It is used

in the synthesis of other organic chemicals and in plastics

production. A glass vessel weighs 40.1305 g when clean, dry

and evacuated; it weighs 138.2410 when filled with water at

25°C (δwater = 0.9970 g cm-3) and 40.2959 g when filled with

propylene gas at 740.3 mm Hg and 24.0°C. What is the molar

mass of polypropylene?

Strategy:

Determine Vflask. Determine mgas. Use the Gas Equation.

EXAMPLE

Gases


Determine Vflask:

Vflask = mH2O dH2O = (138.2410 g – 40.1305 g) (0.9970 g cm-3)

Determine mgas:

= 0.1654 g

mgas = mfilled - mempty = (40.2959 g – 40.1305 g)

= 98.41 cm3 = 0.09841 L

EXAMPLE

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Gases


Use the Gas Equation:

PV = nRT PV = m

M

RT M = m

PV

RT

M = (0.9741 atm)(0.09841 L)

(0.6145 g)(0.08206 L atm mol-1 K-1)(297.2 K)

M = 42.08 g/mol

EXAMPLE

Gases


Densities of Gases

If we divide both sides of the ideal-gas

equation by V and by RT, we get

n

V

P

RT =

Gases


• We know that

– moles molecular mass = mass

Densities of Gases

• So multiplying both sides by the

molecular mass ( ) gives

n = m

P

RT

m

V =

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Gases


Densities of Gases

• Mass volume = density

• So,

Note: One only needs to know the

molecular mass, the pressure, and the

temperature to calculate the density of

a gas.

P

RT

m

V = d =

Gases


GAS DENSITY PV = nRT

n

V =

P

RT

m

M •V =

P

RT

where M = molar mass

d = m

V =

PM

RT

d and M proportional

and density (d) = m/V

Gases


Gas Densities

Gases are much less dense than liquids and solids

Because of the magnitude of the value, densities of

gases are reported in g/L

At STP, L

Md

4.22

EOS

At other conditions, use the combined gas law …

RT

MPd

the density of a gas is directly proportional

to molar mass and pressure, and inversely

proportional to its Kelvin temperature

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Gases


Gases in Chemical Reactions

• Stoichiometric factors relate gas

quantities to quantities of other reactants

or products.

• Ideal gas equation relates the amount of

a gas to volume, temperature and

pressure.

• Law of combining volumes can be

developed using the gas law.

Gases


Gases and Stoichiometry 2 H2O2(liq) ---> 2 H2O(g) + O2(g)

Decompose 1.1 g of H2O2 in a flask

with a volume of 2.50 L. What is the

pressure of O2 at 25 oC? Of H2O? Bombardier beetle

uses decomposition

of hydrogen peroxide

to defend itself.

Gases


Gases and Stoichiometry

2 H2O2(liq) ---> 2 H2O(g) + O2(g)

Decompose 1.1 g of H2O2 in a flask

with a volume of 2.50 L. What is the

pressure of O2 at 25 oC? Of H2O?

Solution Strategy:

Calculate moles of H2O2 and then

moles of O2 and H2O.

Finally, calc. P from n, R, T, and V.

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Gases



Decompose 1.1 g of H2O2 in a flask with a

volume of 2.50 L. What is the pressure of O2 at

25 oC? Of H2O?

Solution

1.1 g H2O2 • 1 mol

34.0 g 0.032 mol

0.032 mol H2O2 • 1 mol O2

2 mol H2O2

= 0.016 mol O2

Gases



Decompose 1.1 g of H2O2 in a flask with a

volume of 2.50 L. What is the pressure of O2 at

25 oC? Of H2O?

Solution

P of O2 = nRT/V

= (0.016 mol)(0.0821 L •atm/K •mol)(298 K)

2.50 LP of O2 = 0.16 atm

Gases


Gases and Stoichiometry

What is P of H2O? Could calculate as

above. But recall Avogadro’s hypothesis.

V n at same T and P

P n at same T and V

There are 2 times as many moles of H2O

as moles of O2. P is proportional to n.

Therefore, P of H2O is twice that of O2.

P of H2O = 0.32 atm

2 H2O2(liq) ---> 2 H2O(g) + O2(g)

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Gases


Mixtures of Gases

• Partial pressure

– Each component of a gas mixture exerts a

pressure that it would exert if it were in the

container alone.

• Gas laws apply to mixtures of gases.

• Simplest approach is to use ntotal, but....

Gases


Dalton’s Law of

Partial Pressures

• The total pressure of a mixture of gases

equals the sum of the pressures that

each would exert if it were present

alone.

• In other words,

Ptotal = P1 + P2 + P3 + …

Gases


Dalton’s Law

John Dalton

1766-1844

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Gases


Partial Pressure

Ptot = Pa + Pb +…

Va = naRT/Ptot and Vtot = Va + Vb+…

Va

Vtot

naRT/Ptot

ntotRT/Ptot

= = na

ntot

Pa

Ptot

naRT/Vtot

ntotRT/Vtot

= = na

ntot

na

ntot = a Recall

Gases


Mole Fraction

EOS

The mole fraction (x1) is the fraction of all the

molecules in a mixture that are of a given type

Consider the ratio of a component’s partial pressure

to total pressure

V, R, and T are all constant and drop out

1 1 11

1 2 ...tot tot

P n nx

P n n n

Gases


Collection of Gases over

Water

EOS

As essentially insoluble gas is passed into a container

of water, the gas rises because its density is much less

than that of water and the water must be displaced

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Gases


Collection of Gases over

Water

Assuming the gas is saturated with water vapor, the

partial pressure of the water vapor is the vapor

pressure of the water.

EOS

Pgas = Ptotal – PH2O(g) = Pbar – PH2O(g)

Ptotal = Pgas + PH2O(g)

Gases


Pneumatic Trough

Ptot = Pbar = Pgas + PH2O

Gases


Partial Pressures

• When one collects a gas over water, there is

water vapor mixed in with the gas.

• To find only the pressure of the desired gas,

one must subtract the vapor pressure of

water from the total pressure.

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Gases


Vapor Pressure as a

Function of Temperature

The combined gas law shows the

relationship between P and T at

constant n and V:

EOS

P nR

T V

As with Charles’s law for V and T,

P and T are directly proportional

Gases


Kinetic-Molecular Theory

This is a model that

aids in our

understanding of what

happens to gas

particles as

environmental

conditions change.

Gases


Main Tenets of Kinetic-

Molecular Theory

Gases consist of large numbers of

molecules that are in continuous,

random motion.

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Gases



Molecular Theory

The combined volume of all the

molecules of the gas is negligible

relative to the total volume in which the

gas is contained.

Gases



Molecular Theory

Attractive and

repulsive forces

between gas

molecules are

negligible.

Gases


KINETIC MOLECULAR THEORY (KMT)

Theory used to explain gas laws. KMT

assumptions are

• Gases consist of molecules in constant,

random motion.

• P arises from collisions with container

walls.

• No attractive or repulsive forces between

molecules. Collisions elastic.

• Volume of molecules is negligible.

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Gases


Kinetic Molecular Theory

Because we assume molecules are

in motion, they have a kinetic

energy.

KE = (1/2)(mass)(speed)2 At the same T, all gases have the same average KE.

As T goes up for a gas, KE also increases — and so does speed.

Gases



At the same T, all gases have the same

average KE.

As T goes up, KE also increases — and

so does speed.

Gases



Molecular Theory

Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.



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Gases



where u is the speed and M

is the molar mass.

• speed INCREASES with T

• speed DECREASES with M

Maxwell’s equation

root mean square speed

2uM

3RT

Gases


Distribution of Gas

Molecule Speeds

•Boltzmann plots

•Named for Ludwig

Boltzmann doubted

the existence of atoms.

• This played a role in

his suicide in 1906.

Gases


Velocity of Gas Molecules

Molecules of a given gas have a

range of speeds.



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Gases


Velocity of Gas Molecules Average velocity decreases with increasing

mass.

Gases



Molecular Theory

The average kinetic

energy of the

molecules is

proportional to the

absolute

temperature.

Gases


Effusion

Effusion is the

escape of gas

molecules

through a tiny

hole into an

evacuated

space.

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Gases


Effusion

The difference in the

rates of effusion for

helium and nitrogen,

for example,

explains a helium

balloon would

deflate faster.

Gases


Diffusion

Diffusion is the

spread of one

substance

throughout a space

or throughout a

second substance.

Gases


GAS DIFFUSION AND EFFUSION

Graham’s law governs

effusion and

diffusion of gas

molecules.

Thomas Graham, 1805-1869.

Professor in Glasgow and London.

Rate of effusion is

inversely proportional

to its molar mass.

M of A

M of B

Rate for B

Rate for A

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Gases


Effusion

At a given temperature, the rates

of effusion of gas molecules are

inversely proportional to the

square roots of their molar

masses

EOS

11 2

2 1

2

3

3

RT

Mrate M

rate MRT

M

Gases


Graham’s Law

• Only for gases at low pressure (natural escape, not a

jet).

• Tiny orifice (no collisions)

• Does not apply to diffusion.

A

BA

Brms

Arms

M

M

3RT/MB

3RT/M

)(u

)(u

Bofeffusionofrate

Aofeffusionofrate

• Ratio used can be:

– Rate of effusion (as above)

– Molecular speeds

– Effusion times

– Distances traveled by

molecules

– Amounts of gas effused.

Gases


Real Gases Under many conditions, real gases do not follow the

ideal gas law ...

-- Intermolecular forces of attraction cause the

measured pressure of a real gas to be less than

expected

-- When molecules are close together, the volume

of the molecules themselves becomes a

significant fraction of the total volume of a gas

EOS

2

2

n aP V nb nRT

V

van der Waals equation

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Gases


Deviations from Ideal Gas Law

• Real molecules

have volume.

• There are

intermolecular

forces.

–Otherwise a gas

could not become

a liquid.

Gases



Account for volume of

molecules and intermolecular

forces with VAN DER

WAALS’s EQUATION. Measured V = V(ideal) Measured P

intermol. forces

vol. correction

J. van der Waals,

1837-1923,

Professor of

Physics,

Amsterdam.

Nobel Prize 1910.

nRT V - nb V

2

n 2 a

P + ----- ) (

Gases



Cl2 gas has a = 6.49, b = 0.0562

For 8.0 mol Cl2 in a 4.0 L tank at 27 oC.

P (ideal) = nRT/V = 49.3 atm

P (van der Waals) = 29.5 atm

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Gases


van der Waals Equation

Corrections for real gas behavior are made using the

parameters a and b

a – accounts for intermolecular attractions in real gases

b – accounts for the real volumes of gases

EOS

Gases


Real Gases

In the real world, the

behavior of gases

only conforms to the

ideal-gas equation

at relatively high

temperature and low

pressure.

Gases


Real Gases

Even the same gas

will show wildly

different behavior

under high pressure

at different

temperatures.

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Gases


Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Gases


Corrections for Nonideal

Behavior

• The ideal-gas equation can be adjusted

to take these deviations from ideal

behavior into account.

• The corrected ideal-gas equation is

known as the van der Waals equation.

Gases


The van der Waals Equation

) (V − nb) = nRT n2a

V2 (P +

chapter 10: gases - yolaholcombslab.yolasite.com/resources/chapter 10.pdf · chapter 10 gases john...

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