Plan for Mon, 6 Oct 08• New schedule and practice problems for Ch 5,

6, 10• Exp 1 post-lab • Typo in Exp 2 pre-lab

• Lecture– Pressure (5.1)– Gas laws of Boyle, Charles, and Avogadro (5.2)– The ideal gas law ( 5.3)

• Exam 1 returned

Pressure

• Pressure is force per unit area:

• In SI units, pressure is expressed in newtons per square meter, N/m2, the pascal (Pa).

1 Pa = 1 N/m2

FP

A

Pressure Example• What is the pressure that one penny exerts on a table?

The penny has a radius of 9.3 mm, and weighs 2.5 g.• We need to find the force that the penny exerts, and the

area over which it exerts that force.• Force due to the penny:

F = (mass) x (accel. due to gravity)

= (2.5 x 10-3 kg) x (9.81 m/s2)

= 2.5 x 10-2 kg m/s2

= 2.5 x 10-2 N

Pressure Example (cont)• Cross-sectional area of the penny:

A = (radius)2

= (9.3 x 10-3 m)2

= 2.7 x 10-4 m2

• Therefore the pressure due to the penny is:

• The pascal is actually a pretty puny unit, so more often the kilopascal (kPa) is used.

2

4 2

2.5 10 N

2.7 10 mP

2

N93m

100 Pa

How do we measure the force of a gas?

Barometer

Petrucci pg. 177

Open to atmosphere

Closed

Vacuum

1 atm 1 atm

1 atm1 atm

Making a Mercury Barometer

A dish is filled with mercury. A long glass tube – closed at one end – is also filled with mercury.

Making a Mercury Barometer

Air bubbles are removed from the mercury in the tube.

Mercury is added until the tube is completely filled.

Making a Mercury Barometer

The tube is carefully upended and placed in the dish of mercury, so that none of the Hg in the tube falls out.

Some portion of the mercury will then flow out of the tube, until the pressure of the Hg is equal to the atmospheric pressure on the Hg in the dish.

Vacuum

Measuring the height of the Hg column will tell you what the atmospheric pressure is.

Making a Mercury Barometer

Units: “mm Hg” (milimeters of mercury)

Also known as “torr” after Evangelista Torricelli, inventer of the barometer.

ManometersManometers operate on the same principle as barometers, but they measure the pressure of an isolated gas sample rather than the whole atmosphere.

Pgas = PHg = h

hh h

Pgas = Patm – h Pgas = Patm + h

Note: Patm is obtained from a barometer.

Empirical Gas Laws

• Gases are relatively easy to measure and observe in a laboratory.

• This made the physical properties of gases a popular object of study in the 17th, 18th, and 19th centuries.

• Boyle, Charles, and Avogadro (yes, that Avogadro) determined fundamental connections between P, V, T and n for gases.

Boyle’s Law (c. 1650)

VP

1

or…

PV = constant

E&G pg. 179

Boyle studied the connection between P and V of gases.

Boyle’s Law (cont)

A gas for which PV = const is called “ideal.”

Charles’s Law (c. 1800)Charles studied the connection between T and V of gases.

Liquid nitrogen, T = 77 K

Blue balloon is placed in the liquid N2…

Cooling down the blue balloon decreases its volume

dramatically.

Charles’s Law

Vol vs. temp data for several gases. When these lines are extrapolated,

they all intersect at -273.15oC.

Same plot, except temperatures are given in Kelvin instead of Celcius.

V = bt + a V = bT

T = t + 273.15

t

The volume of an ideal gas is directly proportional to its

temperature measured in Kelvin

Avogadro’s Law

Volumes of gases that react do so in small whole number ratios: 2 vol H2 + 1 vol O2 = 2 vol H2O

Avogadro said this was so because the same volume of two different gases at the same T and P will have the same number of particles.

V = an

Empirical Gas Law Summary

• Boyle’s Law:

• Charles’s Law:

• Avogadro’s Law:

• Since V is directly proportional to 1/P, T, and n, V must also be directly proportional to the product:

1V

P

V T

V n

nTV

P

nTV R

P

add proportionality constant

Ideal Gas Law

PV nRTnTV R

P

P = pressure

V = volume

n = number of moles

R = “gas constant”

T = temperature in Kelvin

Common R values:L atm

0.082057mol K

L torr62.364

mol KJ

8.3145mol K

CHE161

CHE162

What is Ideality?• Molecules of an ideal gas do not attract or repel one another• The volume of an ideal gas molecule is negligible with respect to the

container• Essentially, an ideal gas is a collection of non-interacting point

particles.

Is this a reasonable approximation?Under what conditions would you expect ideality to fail?

high P molecules get too close, start interactinglow T same thing

• Over moderate T and P ranges, gases are fairly dilute, so the ideal gas law is a reasonable approximation.

DON’T FORGET YOU MUST NEVER USE CELCIUS TEMPRATURES! KELVIN ONLY!!