Lecture 12 Chapter 5 Gases

• Announcements

• Pressure

• Gas Laws

• The Ideal Gas Law

• Kinetic Molecular Theory

Announcements• Seminar today – awesome• CAPA due Monday

Exams:High 91Mean 64

Scores in 90s 280s 1270s 1060s 1750s 8

< 50 15

If you had all day for the exam and could use your textbook, your score would have been?

1. 90 – 1002. 80 – 903. 70 – 804. 60 – 705. Below 60

What can I do?

• Remember exam was only 10 % of grade• Do an autopsy

– Tonight or tomorrow – go through in detail– Why did you miss questions you missed?

• Change study habits?– Read, lecture, homework– Less time on CAPA, do more problems

• No more than 20-30 minutes on each CAPA problem• Come get help if you need more – use extra time to do more problems

• Get more help– Tutors from ASC– Schedule time with me– Classmates, dormmates, etc.

Gasses

• Were rich area of science in 17th -19th centuries• High technology – balloons!

– Needed to understand gas behavior

• First define what we mean by Pressure– Force exerted on walls of container by collisions of gas

particleshttp://www.schulphysik.de/ntnujava/idealGas/idealGas.html

psi inlbsor pascals

mNoften

AreaForce

22 ====AFP

Measuring Pressure

• Pressure (P) – in a gas it is caused by molecular collisions with a container.

• The air around us is a huge reservoir of gas that exerts pressure on the Earth’s Surface

• The atmospheric pressure can be measured with a mercury barometer.

• Why does pressure sometimes have units of mmHg?

How do we measure the pressure of a gas in a closed container?

• We use a manometer.• In the U-shaped manometer, the difference

between the two mercury levels gives the pressure difference between the gas and atmospheric

• Not actually used much anymore due to Hg (yuck). We have other ways.

– Pressure of a gas often given as gauge pressure – the pressure above atmospheric. For example, 30 psi of pressure in your car tire is actually 45 total psi. (Ph in fig)

– Pressures are normally given as absolute pressure.

– Note that Ph could be negative.

Pressure – Units

PascalsmN

AreaForce

2 ====AFP

• Because the pressure at sea level is 760 mm Hg we define another unit called the atmosphere.– 1 atm = 760 mmHg– 1 atm = 14.7 psi

• Another common pressure unit is torr– 1 torr = 1 mm Hg– 1 atm = 760 torr

• The official SI unit is the pascal. – 1 atm = 101325 Pa

• Another SI unit is the bar. This is probably most often used today.– 1 atm = 1.01325 bar

Work by Robert Boyle (1662)Boyle’s law: The pressure of any gas changes in inverse proportion to its volume

PV /1∝

In 1783, Etienne and Joseph Montgolfierreleased a hot air balloon carrying a rooster, a duck, and a sheep over Paris.

When it landed, they had proved that living things could survive flight.

Later that year they flew a man over Paris

First “manned” flight:

All was glorious -- a cloudless sky above, a most delicious view around. . . . How great is our good fortune! I care not what may be the condition of the earth; it is the sky that is for me now.

— Prof. Jacques Alexandre CesareCharles, first free flight in a

manned hydrogen balloon, 1 December 1783.

TV ∝Charles’s Law (1787)

• Apparently figuring he could combine the best of both technologies, Pilatre de Rozier attempted flight in 1785 in a combination hydrogen and hot-air balloon.

• As one might imagine, this did not produced the intended result.

The last key idea –Avogadro’s Law (1811)

nV ∝

Ideal Gas Law

• Putting all these pieces together…

TV ∝PV /1∝ nV ∝

nRTPV =

At constant n, T constant n, P constant P, T

PnTR

PnTV =∝

R is the proportionality constant, called The Gas Constant

R = 0.08206 L·atm/mol·K = 8.314 J/mol·K

Note: L·atm J JEnergy23 →=====⋅ FddFd

AFVVPatmL

Ideal Gas Example

We have some container of gas at 350 K and 1 atm, and its volume is 10 L.

How many moles of gas do we have?

( )( )( )

nmol

nKatmL

KmolatmL

KKmol

atmLnLatm

nRTPV

=

=⋅

⋅⋅

⋅⋅

=⋅

=

348.035008206.0

10

35008206.0101

If we now compress this (0.348 mol) gas to a volume of 5 L and it warms to 400 K, what is the new pressure?

54321

25%25%25%25% 1. 0.228 atm

2. 2.28 atm3. 11.4 atm4. 57.1 atm

What Makes a Gas Ideal?

1. Each gas particle has infinitely small volume2. Interactions between gas particles are neglible

(see also p.177 – “key concepts”)

• Many regular gases behave ideally– N2

– Air (pretty much)– Most gases when V and/or T are large

• Note relationship of V and T to above two points• Also note that big V, T is same as P and/or n small

Kinetic Molecular Theory

• Gases are collections of many tiny particles– Always moving– Bumping into walls of container and each other

– The speed of the particles is related to their kinetic energy, which is related to the temperature

ABkineticmoleculekinetic N

RTTkEE23

23

, ===2

21 muEkinetic =

So, molecular speed is determined by mass and temperature!

A

B

AB mN

RTmTku

NRTTkmu 33or

23

23

21 2 ====

Speed Depends on m and T

Maxwell-Boltzmann Distribution

0

0.0005

0.001

0.0015

0.002

0.0025

0 500 1000 1500 2000 2500 3000 3500 4000

Speed (m/s)

Frac

tion

He T=300K

He T=1000K

Ar T=300 K

Note that different gases at the same temperature have the same ENERGY distributions! (the speed distributions are different)

Speed Distributions Can Be Measured

• Molecular Beam Appartus

• Cool speed distribution simulatorhttp://lorax.chem.upenn.edu./Education/MB/index.html

• The MB stands for Maxwell-Boltzmann

Today• Perform exam autopsy

By Monday• Read more of Chapter 5• Finish CAPA #7

– DO NOT DO PROBLEMS 3,4,5!• Work some extra HW problems from book

Rem

ember: Y

ou are done with the

homew

ork when you understand it!