Ch 5 Gases Student .pptx

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Why study gases?

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Pressure

• Uniformly fills any container.

• _{Mixes completely with any other gas.}

• _{Exerts pressure on its surroundings.}

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Pressure

• _{SI units = 1 Pascal (Pa) = Newton/meter}2

• _{1 standard atmosphere (1 atm)}

– _{101,325 Pa}

– _{760 mm Hg}

Pressure

force Pr essure =

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Pressure

The pressure of a gas is measured as 2.5 atm. Represent this pressure in both torr and pascals.

Pressure Conversions: An Example



_{2.5 atm}



760 torr _{= 1.9 10 torr}3 1 atm

 

_ _ 

 



_{2.5 atm}



101,325 Pa _{= 2.5 10 Pa}5 1 atm

 

_ _ 

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Pressure

Barometer

• _{Device used to measure}

atmospheric pressure.

• _{Mercury flows out of the}

tube until the pressure of the column of

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The Gas Laws of Boyle, Charles, and Avogadro

Robert Boyle studies the relationship between the pressure on a gas and volume of a gas

Boyle’s Law

Using a J-shaped tube closed at one end, which he reportedly set up in the multistory entryway of his house, Boyle studied the relationship between the pressure of the trapped gas and its volume.

• Adding mercury to the open end of the tube

• Increases pressure on the trapped gas

• Decreases the volume of the trapped gas

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The Gas Laws of Boyle, Charles, and Avogadro

Boyle’s Law

This is some of Boyles data

When we plot P vs V

We see that as

• Pressure goes down

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The Gas Laws of Boyle, Charles, and Avogadro

Boyle’s Law

If we plot the data as V vs 1/P

we get a straight line which intersects the Y axis at 0.

This is very helpful because can use the equation for a straight line to look at the relationship between V and P.

so if y = m x + b then V = k 1

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The Gas Laws of Boyle, Charles, and Avogadro

Boyle’s Law

so since V = 1

P k + 0

then V = k P

or VP = k

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• PV = k

– _{Specific temperature and number of}

moles (n)

• _{This means that the product of pressure}

and volume is always the same value for a given sample of gas at a given

temperature

Boyle’s Law

1 1 = 2 2

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Calculations Using Boyle’s Law

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 mmHg after its pressure is changed to 2200 mmHg at constant T and n?

P₁ = 550 mmHg P₂= 2200 mmHg V₁ = 8.0 L V₂ = ?

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The Gas Laws of Boyle, Charles, and Avogadro

Learning Check

A sample of helium gas occupies 12.4 L at

23°C and 0.956 atm. What volume will it

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Ideal Gases vs Real Gases

• _{Gases that obey Boyles Law are called “ideal gases” (Section 5.3)}

• PV = k

• Plot of PV vs P linear

• Ne and O₂ show only small deviations

from ideal behavior at low pressures

• CO₂ shows larger deviation from

ideal behavior

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The Gas Laws of Boyle, Charles, and Avogadro

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• What happened to the gas in the

balloon?

• _{A decrease in temperature was followed}

by a decrease in the volume of the balloon.

• _{There is a direct relationship between}

volume and temperature

• _{This is an observation}

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The Gas Laws of Boyle, Charles, and Avogadro

• Observation: The volume of a gas

depends on the temperature of the gas

– _{At constant pressure (P)}

– _{At constant number of moles (n)}

• _{What law summarizes observations}

like these?

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• Volume and Temperature (in Kelvin) are

directly related

– _(constant_P_and_n_).

• _V=bT₍_b_{is a proportionality constant)}

Charles’s Law

1 2

=

V V

T T

V

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Learning Check

Suppose a balloon containing 1.30 L of air at 24.7°C is placed into a beaker containing liquid nitrogen at –78.5°C. What will the

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• _{The volumes different gases with different numbers of moles all}

extrapolate to the same value

• _{- 273°C or 0K}

• _{0 K is called absolute zero.}

• _{At this point atoms or molecules have no volume and no molecular}

motion (where entropy reaches its minimum value)

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The Gas Laws of Boyle, Charles, and Avogadro

• In some problems 2 variables change and

you want to determine the value of the third variable

• _{ie pressure and volume change and you}

want to determine the new temperature

• _{To solve these problems we can combine}

Boyles and Charles Law

The Combined Gas Law

P

₁

V

₁

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The Ideal Gas Law

Exercise

At what temperature (in °C) does 121 mL of CO₂ at 27°C and 1.05 atm occupy a volume of 293 mL at a pressure of 1.40 atm? P1 = 1.05 atm P2 = 1.40 atm

V1 = 121 mL V2 = 293 mL T1 = 27°C T2 = ?

P₁V₁

T₁ = P2 V₂ T₂

T₂= P2V2T1

P₁V₁ so T2 = 1.40 atm

  293 m L  27+273  1.05 atm

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Return to TOC

Learning Check

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 is constant)?

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The Gas Laws of Boyle, Charles, and Avogadro

• Chapter 2 Avogadro postulated that equal

volumes of gases at the same temperature and pressure contain the same number of “particles.

• _{Avogadro’s law,}

• _{Volume and number of moles are directly related}

(constant T and P).

• _{V = an}₍_a_{is a proportionality constant)}

Avogadro’s Law

n n

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Learning Check

If 2.45 mol of argon gas occupies a volume

of 89.0 L, what volume will 2.10 mol of

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• We can bring all of these laws together into one

comprehensive law:

• _{Basically adding Avogadro’s Law to the}

combined gas law

PV = nRT

V = k

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The Ideal Gas Law

PV = nRT

When using the ideal gas law Volume has to be in L

Temperature has to be in K Pressure has to be in atm

This is because of the units of R

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The Ideal Gas Law

Learning Check

An automobile tire at 23°C with an internal volume of 25.0 L is filled with air to a total pressure of 3.18 atm. Determine the

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Learning Check

What is the pressure in a 304 L tank that

contains 5.670 kg of helium at 25°C?

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The Ideal Gas Law

• Which equation do I use?

• _{Write down initial and final conditions and look for}

what is missing?

• _{Units and Gas Law Problems}

• _{Don’t have to change units of pressure or volume}

– _{Units just have to be the same}

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Gas Stoichiometry

• For 1 mole of an ideal gas at 0°C and 1

atm, the volume of the gas is 22.42 L.

• _{STP =}_{standard temperature and pressure}

 0°C and 1 atm

 _{Therefore, the molar volume is 22.42 L}

at STP.

Molar Volume of an Ideal Gas



1.000 mol 0.08206 L atm/K mol 273.2 K

 



V = = = 22.42 L

1.000 atm

 

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Concept Check

A sample of oxygen gas has a volume of

2.50 L at STP. How many grams of O₂ are

present?

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•We can determine the molar mass of a gas from a measurement of the density

Molar Mass of a Gas

PV = nRT where n = g

molar mass

so PV= gRT

molar mass and P=

g RT molar mass

  V 

and since g

V  density

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 d = density of gas

 T = temperature in Kelvin

 P = pressure of gas

 R = universal gas constant

Molar Mass of a Gas

 





g L atm

K

g L mol K

= =

atm mol

Molar mass =

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Concept Check

The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L.

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Concept Check

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Dalton’s Law of Partial Pressures

• For a mixture of gases in a container,

P

_Total

= P

₁

+ P

₂

+ P

₃

+ . . .

• _{The total pressure exerted is the sum of}

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Dalton’s Law of Partial Pressures

Concept Check

Consider the following apparatus containing helium in both sides at 45°C. Initially the valve is closed.

–_{After the valve is opened, what is the pressure of}

the helium gas?

–_{There is more than one way to solve this.}

3.00 atm

3.00 L 2.00 atm

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Dalton’s Law of Partial Pressures

Concept Check

27.4 L of oxygen gas at 25.0°C and 1.30 atm, and 8.50 L of helium gas at 25.0°C

and 2.00 atm were pumped into a tank with a volume of 5.81 L at 25°C.

•_{Calculate the new partial pressure of}_oxygen_. •_{Calculate the new partial pressure of}_helium_.

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The Kinetic Molecular Theory of Gases

• So far we have considered “what

happens,” but not “why.”

• _Observations_{– direct relationship}

between volume and temperature

• _Laws_{– Charles Law}

– _{This is the What}

• _{Now we need a}_Theory

– _{This is the Why}

• _{In science, “what” always comes before}

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The Kinetic Molecular Theory of Gases

1) The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).

2) The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.

4) The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin

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The Kinetic Molecular Theory of Gases

Concept Check

You are holding two balloons of the same volume. One contains

helium, and one contains

hydrogen. Complete each of the following statements

with “different” or “the same”

and be prepared to justify your answer.

He

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The Kinetic Molecular Theory of Gases

Concept Check

•Complete the following

statement with “different” or “the same” and be prepared to justify your answer.

•_The_pressures_{of the gas} in the two balloons are

•_{__________.}

He

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Concept Check

•_The_temperatures_{of the} gas in the two balloons are __________.

He

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Concept Check

statement with “different” or

“the same” and be prepared to justify your answer.

•_The_{numbers of moles}_of the gas in the two balloons are

__________.

He

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The Kinetic Molecular Theory of Gases

Concept Check

•_The_densities _{of the gas in} the two balloons are

__________.

He

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Pressure and Volume - Molecular View of Boyle’s Law

P = (nRT) 1

V

Constant

For a given sample of gas at a given temperature (n and T are constant) that if the volume of a gas is decreased, the pressure increases.

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Pressure and Temperature – Molecular View

P = ( nR

V

) T

Constant

From the ideal gas law P directly proportional to T.

The KMT accounts for this behavior because when the temperature of a gas increases, the speeds of its particles

increase, the particles hitting the wall with greater force and greater frequency. Since the volume remains the same, this would result in increased gas pressure,

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The Kinetic Molecular Theory of Gases

Volume and Temperature - Molecular View of Charles’s Law

V

= ( nR

P

) T

Constant

The ideal gas law states that for a sample of gas at a constant P, the volume of the gas is directly proportional to the Kelvin temperature

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Volume and Number of Moles = Molecular View of Avagadro’s Law

V

= ( RT

P

) n

Constant

The ideal gas law predicts that the volume of a gas at a constant T and P depends directly on the n. This makes sense in terms of the KMT because an increase in the n at the same temperature would cause the pressure to increase if the volume were held constant. The only way to return the pressure to its original value is to increase the volume.

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The Kinetic Molecular Theory of Gases

Volume and Number of Moles = Molecular View of Avogadro’s Law

V

= ( RT

P

) n

Constant

Remember that the volume of a gas (at constant P and T) depends only on the number of gas particles present. The individual volumes of the particles are not a factor because the particle volumes are so small compared with the distances between the particles (for a gas behaving ideally).

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Mixture of Gases – Molecular View of Daltons Law

The observation that the total pressure exerted by a mixture of gases is the sum of the pressures of the individual gases is expected because the KMT assumes that all gas particles are

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Deriving The Ideal Gas Law

Can the ideal gas law be derived from the assumptions the KMT Yes!

And if you can do it

You will get extra credit on the next exam!

Your derivation must include

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The Kinetic Molecular Theory of Gases

P = 2 3

nN_A 1 2mu2 V          

P = pressure, n = moles, NA = Avogadro’s number, m is mass, u2 is the average of the square of the velocities of the particles, V = volume

KE

 avg = NA 1 2mu 2      

mu2 = the average kinetic energy of a gas particle. mu2 x NA, = average kinetic energy for a mole of gas particles

P = 2 3

n KE _avg V       

 becomes PVn = 23 KE avg

The fourth postulate of the KMT is that the average kinetic energy of the particles in the gas sample is directly proportional to the Kelvin

temperature.

PV

n = 23 KE avg so PV_n  T

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The Kinetic Molecular Theory of Gases

PV

n  T From KMT

PV

n  RT

From Experiment

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Concept Check

You have a sample of nitrogen

gas (N₂) in a container fitted with

a moveable piston that maintains a pressure of 6.00 atm. Initially, the gas is at 45°C in a volume of 6.00 L.

•_{You then cool the gas}

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The Kinetic Molecular Theory of Gases

Concept Check

Which best explains the final result that

occurs once the gas sample has cooled?

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Concept Check

The gas sample is then cooled to a

temperature of 15°C. Solve for the new

condition. (Hint: A moveable piston keeps the

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The Kinetic Molecular Theory of Gases

•KMT tells us that the Kelvin temperature indicates the average kinetic energy of the gas particles.

•The exact relationship between temperature and average kinetic energy can be obtained by combining equations (1) and (2).

•Equation (3) summarizes the meaning of the Kelvin temperature of a gas.

The Meaning of Temperature

PV

n  RT (1)

PV

n = 23 KE avg (2) KEavg 

3

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The Kinetic Molecular Theory of Gases

R = 8.3145 J/K·mol

(J = joule = kg·m2/s2)

T = temperature of gas (in K)

M = mass of a mole of gas in kg

• _{Final units are in m/s.}

Root Mean Square Velocity

urms = 3RT

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Concept Check

Calculate the root mean square velocity for the atoms in a sample of helium gas at

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Effusion and Diffusion

• Diffusion – the mixing of

gases.

• _{Effusion – describes the}

passage of a gas through a tiny orifice into an evacuated chamber.

• _{Rate of effusion measures the}

speed at which the gas is

transferred into the chamber.

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Effusion and Diffusion

• Rate of effusion is inversely proportional

to the square root of the molar mass

• M₁ and M₂ represent the molar masses of

the gases.

• _{Grahams Law of effusion}

Graham’s Law of Effusion

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Real Gases

• An ideal gas is theoretical

• _{No gas displays perfectly ideal behavior}

• _{We must correct for non-ideal gas}

behavior when:

– _{Pressure of the gas is high.}

– _{Temperature is low.}

• _{Under these conditions:}

– _{Concentration of gas particles is high.}

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Real Gases

Fig 5.25 Plots of PV/nRT Versus

P for Several Gases (200 K)

Fig 5.26 Plots of PV/nRT Versus P for Nitrogen Gas at Three Temperatures

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Real Gases

• _{For real gases:}

– _{Concentration of gas particles is high.} – _{Attractive forces become important.}

• _{We have to make two corrections to the ideal gas}

law

– _{The volume of the container is actually}

smaller because some of the the volume is taken up by the gas particles themselves

– _{The pressure is lower because the gas}

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Real Gases

Real Gases (van der Waals Equation)

[

P

obs

+

a

( / )

n V

2

]





V nb



 

nRT



corrected pressure

P

ideal



corrected volume

V

ideal

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Characteristics of Several Real Gases

Values of the van der Waals Constants for Some Gases

• _{The value of a reflects how}

much of a correction must be made to adjust the observed pressure up to the expected ideal pressure.

• _{A low value for a reflects}

weak intermolecular forces among the gas molecules.

• _{The value of b reflects the}

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Chemistry in the Atmosphere

• Two main sources:

 Transportation

 Production of electricity

• _{Combustion of petroleum produces CO,}

CO₂, NO, and NO₂, along with unburned

molecules from petroleum.

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Chemistry in the Atmosphere

• At high temperatures, N₂ and O₂ react to

form NO, which oxidizes to NO₂.

• The NO₂ breaks up into nitric oxide and

free oxygen atoms.

• Oxygen atoms combine with O₂ to form

ozone (O₃).

Nitrogen Oxides (Due to Cars and Trucks)

NO₂(g)

Radiant energy

NO(g)+O(g)

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Concentration for Some Smog

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• Sulfur produces SO₂ when burned.

• SO₂ oxidizes into SO₃, which combines

with water droplets in the air to form sulfuric acid.

Sulfur Oxides (Due to Burning Coal for Electricity)

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• Sulfuric acid is very corrosive and

produces acid rain.

• Use of a scrubber removes SO₂ from the

exhaust gas when burning coal.

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Ch 5 Gases Student .pptx

Table of Contents

Why study gases?

Pressure

The Gas Laws of Boyle, Charles, and Avogadro

The Gas Laws of Boyle, Charles, and Avogadro

The Gas Laws of Boyle, Charles, and Avogadro

Boyle’s Law

The Gas Laws of Boyle, Charles, and Avogadro

The Gas Laws of Boyle, Charles, and Avogadro

The Gas Laws of Boyle, Charles, and Avogadro

Charles’s Law

The Gas Laws of Boyle, Charles, and Avogadro

The Combined Gas Law

The Gas Laws of Boyle, Charles, and Avogadro

Learning Check

PV = nRT

The Ideal Gas Law

PV = nRT

The Ideal Gas Law

The Ideal Gas Law

Molar Volume of an Ideal Gas

Molar Mass of a Gas

Molar Mass of a Gas

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

Concept Check

The Kinetic Molecular Theory of Gases

Pressure and Volume - Molecular View of Boyle’s Law

The Kinetic Molecular Theory of Gases

Volume and Number of Moles = Molecular View of Avagadro’s Law

The Kinetic Molecular Theory of Gases

Mixture of Gases – Molecular View of Daltons Law

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases

Effusion and Diffusion

Effusion and Diffusion

Real Gases

Real Gases

Chemistry in the Atmosphere

Nitrogen Oxides (Due to Cars and Trucks)

Sulfur Oxides (Due to Burning Coal for Electricity)