Chemistry 2045 Gasses

7/29/2019 Chemistry 2045 Gasses

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Gases

Our first look at large collections of

particles acting together!


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Gases & Atoms First

The simplest model of a gas has all the

molecules moving and acting independently.

But, with a large number of particles, their

average behavior is strictly delineated.

Only He, Ne, Ar, Kr, Xe, and Rn are atomic

gases.

Really, we are looking at a particles-first

approach here!


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Basic Ideas of This Chapter

We present the ideal gas first.

Gas molecules move independently.

Forces between molecules are nil.

Model seems very simple but it explains a greatdeal!

We shall end with a description of real gases.

Some intermolecular forces enter in. Structural effects (in terms of size) of molecules

also enter into our discussions.


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Studying the Behavior of Substances

To give a more general perspective, there arecertain things we can measure that lead tounderstanding the state of a system.

A short list: Pressure (P)

Volume (V)

Temperature (T) Amount of substance (mass or moles, wor n)

Composition (for mixtures; notation later)


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A Little Analysis

The properties listed on the previous slide arewhat we could call observables.

One thing we try to do in science is connectobservables together if possible.

Ideally, we can get an equation of state.

Having the equation of state, we then try to gofurther and explain itin terms ofindividual

particles. That is one of the main things we shall do in this

chapter.


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Our First Physical Property: P

P stands for pressure.

Pressure = force/unit area

On the average, you have 14.7 lb of air aboveyou.

This exerts the same pressure on you from all

sides! Why? (We explain this verbally.)


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Here is the explanation!

Pressure is caused by

particles (molecules)

hitting you.

When a moleculebounces off you, its

change of momentum is

the force exerted.

An equal number ishitting you from all sides!

Pressure is thus isotropic.


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Needless to say, the more particles,

the higher the pressure!


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Units of Pressure

We usually think of pressure in terms ofstandardatmospheric pressure.

The SI unit of pressure is the pascal (Pa).

This is 1 Pa = 1 N/m2. 1 atm 101325 Pa (exactly!)

The next slide shows some standard pressure

units. Ones with exact defintions are marked with an

asterisk (*).


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Some Pressure Units

Unit Abbreviation Std. Atmospheric Pressure

Pascal Pa (= 1 N/m2) 101325 Pa (*)

Pounds/in2 psi (or ) 14.6959488 psi

Torr (mm Hg) torr 760 torr (*)

Bar bar 1.01325 bar (*)

Inches of mercury in Hg 29.9212598

Atmosphere atm 1 atm (*)


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Measuring Pressure

Various instruments are

used nowadays.

For measuring air

pressure, the traditionalinstrument is the

mercury barometer.


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Measuring Gas Pressures

Pressures are measuredby manometers.

Some of these aremechanical but the

traditional instrumentsuse columns of Hg.

At the right is an open-ended manometer.

Note that we have tocorrect for atmosphericpressure!


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Other types of Manometers

Simple Closed-End Manometer A McLeod Gauge (Low Pressures)


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We now look at some gas laws.

Remember our observable variables:

n, P, V, and T

For the various laws, we keep two of these

constant and note how the remaining two

are related.

We examine these in the next few slides...


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Boyles Law

Tand n held constant.

Vis inversely

proportional to P.

Or, PV = constant.

Boyle is watching us to

the right!


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A Depiction of Boyles Experiment


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For a gas subject to Boyles Law...


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Charless Law

Here, we hold n and P

constant and observe V

vs. T.

V T V= (const) T

Needless to say, Charles

very much approves ofus using his work!


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Here we see the experimental results!


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Note the intercept!

All gases extrapolate to the same point.

This is -273.15C.

This is also 0.00 K. In other words, this is the first place that the

concept ofabsolute zero appears.

T(K) = T(C) + 273.15


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For a gas subject to Charles Law...


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We see something similar for P.

IfVand n are held

constant, we can look at

P vs. T.

P T. Or, P = (const) T.

This the law of Gay-

Lussac (not mentionedin book).

Gay-Lussac...


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Pour Monsieur Gay-Lussac...


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Avogadros Law

Here, we hold P and Tconstant and observe Vvs. n.

This is really where theconcept of the molewas first proposed.

Credit for this goes toAvogadro...

...who, of course, is alsowatching us!


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Avogadros Law is also a simple

graph...


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For a gas obeying Avogadros Law...


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Here are the 3 laws as in the book...


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These can be combined to give...


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We make this an equation by putting

in a constant...


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How the text looks at this...


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Another view of the constant...


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Values ofR


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Note these exactconversion factors...


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We can exploit this sometimes to get a

combined gas law (verbal discussion)...


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We write the combined gas law on the

board...

We look at how this handles the following

Boyles Law case...

Charles Law case...

Avogadros Law case...

Single gas sample at different P, V, and T(same n)


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In all this...

Watch your units!

We especially need to

watch R!

Also, how do we besthandle changes in

pressure, temperature,

and energy units.

We shall now discuss

some of these topics!


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We have two definitions of the mole

we shall be using...


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How many particles in a mole?

NA = 6.0221415 1023 mol-1


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Some Delightful Applications!

I. Molar Volume

II. Gas Density

III. Molar Mass (molecular weight) of a Gas


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Molar Volume


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Special Condition: STP

STP means standard temperature at pressure

P = 1 atm (exactly)

T= 0.00C = 273.15K

Under these conditions, V= 22.4Lfor all idealgases!


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A More Precise Calculation (n = 1)


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All IdealGases the Same! (AIGATS!)


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Density: General Definition pHirst!

density = mass/volume

Units:

g/L (gases)

g/mL (liquids & solids)

kg/m3 (SI unit)


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Density of a gas...


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Molar Mass of a Gas

This is important!

This is a method of

determining molar mass

(aka molecularweight)

The equation is to the

right...


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Gas Mixtures & Partial Pressures

Ideal gases in a mixture exert their pressures

independently.

This is called Daltons Law of Partial Pressures.

We show some math in the next slide...


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Look at a mixture of gases A, B, C, & D

Thi l d i i


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This leads to a concentration unit,

mole fraction (for a given gas, i)


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Useful Relations...


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Collecting Gases over Water

A common method of

collecting gaseous

products of reactions.

Works well as long asthe gas is not soluble in

water!

This is the first time that

we encounter vapor

pressure.


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Yes, water is a liquid but...


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Example: Collecting H2 over water


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Gas Stoichiometry

Before we get started on

this, please remember

that we have two

definitions for a mole:

In terms of mass.

In terms of the ideal gas

law.


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A Thank You to John Dalton!

In his prime! After too much pHun with gases!


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Shortcut Method for Stoichiometry

1) Write the balanced chemical equation.

2) Place the relevant coefficients below theequation.

3) Place the relevant number of moles abovethe equation.

4) Construct the needed equation from ratios.

5) Solve this equation for whatever you arelooking for (pressure, moles, mass, volume,etc.)


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A Picture of the Shortcut Method


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Comparing Moles via Ratios


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An Abstract Example

How many grams ofB are

needed to produce VmL

of a gas, C, at a given P

and T?

The way to set this up is

shown to the right.


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Two ways to do these problems!

I. Write the balanced chemical equation (BCE)

and construct the algebraic solution for a

given problem by use of ratios.

II. Use conversion factors as shown in the book.


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The Kinetic Theory of Gases

This is a very simple model.

But it gives a lot of profound conclusions.

Coupled with quantum mechanics, it actually

predicts the ideal gas law.

We shall skip the QM however!

And look at other things more relevant to us!


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Some Postulates...

I. The size of gas particles is negligibly small.

II. The average kinetic energy of a particle is

proportional to the temperature (in K).

III. All collisions between particles and with the

walls of the container are completely elastic.


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pHun with equations!


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pHun (continued)...


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pHun (it goes on!)...


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pHeeling the Pressure?


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Remember the 2nd Postulate?


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Lets put it in!


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And...................

pHinally putting in THE constant


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pHinally, putting in THE constant

gives...


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Lets Look at a Gas in Action...


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Time to Call in Some Mechanics!


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Major Point!

In a gas at a given temperature, lighter particles

travel faster (on average) than do heavier ones!

BUT, all have the same (average) kinetic energy!


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Remember...


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Root Mean Square Velocity

To make sense of this we need the


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To make sense of this, we need the

MOLE!


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Some Razzle-Dazzle Math!

f


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pHinal Equation for RMS Speed...

h h !!!


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Watch your units here!!!

R = 8.314472 J/molK

MSIis in kg/mol (!)

(This is the SI unit for MW)

Tis in Kelvins.

( )


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Example: Nitrogen gas (N2) at 25.00C

l 2 00C


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Example: He gas at 25.00C

F S k f C l


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For Sake of Completeness...

Average Velocity Most Probable Velocity

A C i


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A Comparison...

A G hi l Vi


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A Graphical View

A d th i


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And another view...

T P t L k At N


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Two Processes to Look At Now

Diffusion

This is the process whereby

two gases mix.

Basically, the molecules mix

while colliding.

This is influenced by the meanfree path (discussed shortly).

Effusion

This is the rate of escape of

molecules through a pin hole

into a vacuum.

How this (and diffusion) are

handled by kinetic theory is

shown in the next slide.

O Pi t f Diff i


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One Picture of Diffusion...

A d th (dj ?)


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And another (dj vu?)...

A Pi t f Eff i


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A Picture of Effusion

B th P F ll G h L


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Both Processes Follow Grahams Law

The rate of effusion(diffusion) is inversely

proportional to the

square root of the

molar mass.

Derivation on next slide.

In the meantime, meet

Thomas Graham!

A Sh t D i ti


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A Short Derivation

Mean Free Path


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Mean Free Path

Until now, we havebeen ignoring molecular

size.

But molecules docollide and do have size.

The distance a molecule

travels between

collisions is called themean free path.

An Equation for Mean Free Path ()


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An Equation for Mean Free Path ()

is the molecularcollision diameterin m.

P is the pressure in

pascals. R is in J/molK.

This is just a bonus

equation and will not be

on exams!

Example: Mean free path in O


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Example: Mean free path in O2

We shall assume STP. The molecular diameter

of O2 is 361 pm.

We shall analyze theunits on the board.

(Under the conditionsof this problem, O2travels about 180molecular diametersbefore colliding.)

A Bonus: The Speed of Sound


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A Bonus: The Speed of Sound

Monatomic Gas Diatomic Gas

Examples (25 00C)


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Examples (25.00 C)

Helium Nitrogen

Real Gases


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Real Gases

These differ from ideal gases in the followingways:

Real molecules are not pointsthey have size.

There are attractive forces between the molecules.

Conditions for a gas to behave like an


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ideal gas...

High temperature (explain why!)

Low pressure (again, explain this!)

Experimental Molar Volumes (STP)


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Experimental Molar Volumes (STP)

We look at Ar and pressure


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We look at Ar and pressure...

Correcting for Molecular Volume


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Correcting for Molecular Volume

Ideal Gas Volume Correction

We look at Xe and Pressure


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We look at Xe and Pressure...

Correcting Pressure for Effects of


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Intermolecular Forces

Ideal Behavior Pressure Correction

Multiplying the Corrected Values Together Gives


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the van der Waals Equation

Ifn = 1, this takes on a simpler form!


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(Vm is the molar volume.)

This is a semi-empirical equation


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This is a semi-empirical equation...

The form of theequation comes from

good physical

arguments.

But, a and b must be

obtained

experimentally.

A table of these is tothe right...

A little chalk talk


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A little chalk talk ...

The vdw equation is anequation of state forreal gases.

It is about the simplest

one that works well. But, it is not perfect!

There are many otherequations!

As you can see, van derWaals was proud of it!

Another view of real gas behavior


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Another view of real gas behavior

Z = PV/RT is called thecompressibility factor

of a gas.

Z = 1 for an ideal gas.

Real gases are much

more interesting!

See the slide to the

right (gases at 273K)...

The End of Gases!


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The End of Gases!

Yes, that

is

enough!

Chemistry 2045 Gasses

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