lecture 12 chapter 5 gases
TRANSCRIPT
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.
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