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1. The Gas Laws
Learning Goals
I will be able to describe
Boyle’s, Charles’ and Gay-
Lussac’s Laws relating T, P
and/or V and be able to
calculate unknown values
using the equations derived
from these laws, as well as
the combined gas law.

2. Gas Laws
One of the most amazing things about gases is that, despite wide
differences in chemical properties, all the gases more or less obey the
gas laws. Gases, when contained in a closed system, exhibit perfectly
elastic collision wherein there is no observed loss of energy. The gas laws
deal with how gases behave with respect to pressure, volume,
temperature. Gases are the only state of matter that can be compressed
very tightly or expanded to fill a very large space because of diffusion
accompanied by an increase in temperature, like in the case of a hot air
balloon. To quantify the physical quantities used involving gas laws such
as pressure, temperature, and volume we will make use of the SI units
and derivatives and some useful conversion factors.

3. Pressure is force per unit area, calculated by dividing the
force by the area on which the force acts. The Earth's gravity
acts on air molecules to create a force, that of the air
pushing on the Earth. This is called atmospheric pressure.
The units of pressure that are used are Pascal (Pa) named
after Blaise Pascal, standard atmosphere (atm), and torr. The
SI unit is Pa which is equivalent to N/m².
Conversion Factors and Equivalents
1 atm = 760 torr
= 76.0 cmHg
= 760 mmHg
= 1.013 x 105 Pa (exactly 101,325 Pa)

4. For laboratory work, the atmosphere is
very large. A more convenient unit is the
torr. From the above conversion factors,
760 torr equals 1 atm. A torr is the same
unit as the mmHg (millimeter of
mercury). It is the pressure that is
needed to raise a tube of mercury 1
millimeter.

5. 1. Intro to Boyle’s Law
 Imagine that you hold the tip of a s
yringe on the tip of your finger so n
o gas can escape. Now push dow
n on the plunger of the syringe.
What happens to the volume in the
syringe?
What happens to the pressure the
gas is exerting in the syringe?

6. 1. Boyle’s Law

7. 1. Boyle’s Law
 The pressure and volume of a gas
are inversely proportional (as one i
ncreases, the other decreases, an
d vice versa
• at constant mass & temp
P
V

8. 1. Boyle’s Law
Boyle’s Law leads to the mathematical e
xpression: *Assuming temp is constant
P1V1=P2V2
Where P1 represents the initial pressure
V1 represents the initial volume,
And P2 represents the final pressure
V2 represents the final volume

9. Example Problem:
1. If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and co
mpress the gas until its volume is 4.8 L, what will the new pressure
inside the piston be?

10. You Try:
2. I have added 15 L of air to a balloon at sea level (1.0 atm). If I take t
he balloon with me to Manila, where the air pressure is 0.85 atm, w
hat will the new volume of the balloon be?

11. 2. Intro to Charles’ Law
Imagine that you put a ballo
on filled with gas in liquid nit
rogen
What is happening to the te
mperature of the gas in the
balloon?
What will happen to the volu
me of the balloon?

12. 2. Charles’ Law

13. V
T
2. Charles’ Law
The volume and absolute te
mperature (K) of a gas are
directly proportional (an incr
ease in temp leads to an inc
rease in volume)
• at constant mass & press
ure

14. 2. Charles’ Law

15. 2. Charles’ Law
 Charles’ Law leads to the mathema
tical expression:
*Assuming pressure remains constant

16. Example Problem:
Sample Problem 1
A container holds 78.0 mL of nitrogen at 23°C and a pressure of
728 mmHg. What will be its volume if the temperature increa
ses to 32°C?

17. You Try:
Sample Problem 2
A sample of chlorine gas occupies 448 cm3at 25° C. At what te
mperature will it occupy 336 cm³ if the pressure remains cons
tant?

18. 3. Intro to Gay-Lussac’s Law
 Imagine you have a balloon insi
de a container that ensures it h
as a fixed volume. You heat th
e balloon.
What is happening to the temp of
the gas inside the balloon?
What will happen to the pressure
the gas is exerting on the balloo
n?

19. P
T
3. Gay-Lussac’s Law
The pressure and absolute t
emperature (K) of a gas are
directly proportional (as tem
perature rises, so does pres
sure)
• at constant mass & volum
e

20. 2. Gay-Lussac’s Law
 Gay-Lussac’s Law leads to the mat
hematical expression:
*Assuming volume remains constant
Egg in a bottle to show Gay-Lussac's Law:
T & P relationship:
http://www.youtube.com/watch?v=r_JnUBk1JPQ

21. Example Problem:
Sample Problem 1
A 12.0 L of a gas is found to exert 1.4 atm at 35.0°C. What wou
ld be the needed temperature in Celsius to change the pressur
e to standard pressure?

22. You Try:
A sample of a gas is collected at 38.0°C and 827.0 mmHg. Whe
n the temperature is changed to standard conditions, what is t
he new pressure?

23. Ideal Gas Law
Gases are composed of billions and billions of constantly moving gas
molecules that can collide and interact with each other. It is very difficult
to accurately describe a real gas, so people created the concept of an
ideal gas, which helps model and predict the behavior of gases.
The term ideal gas refers to a hypothetical gas composed of molecules
which follow a few rules:
1. Ideal gas molecules do not attract or repel each other. The only
reaction between ideal gas molecules could be an elastic collision upon
impact with each other or an elastic collision with the walls of
the container.
2. Ideal gas molecules themselves take up no volume. The gas takes up
volume since the molecules expand into a large region of space, but the
ideal gas molecules are approximated as point particles that have no
volume in and of themselves.

24. There are no gases that are exactly ideal, but there are
plenty of gases that are close enough that the concept of an
ideal gas is an extremely useful approximation for many
situations. In fact, for temperatures near room temperature
and pressures near atmospheric pressure, many of the gases
we care about are very nearly ideal.
If the pressure of the gas is too large (e.g. hundreds of times
larger than atmospheric pressure), or the temperature is too
low (e.g. -200°C) there can be significant deviations from the
ideal gas law.

25. The Ideal Gas Law makes use of the following values under
STP (Standard Temperature and Pressure):
PV=NRT where P is the pressure of the gas, V is the volume
taken by the gas, T is the temperature of the gas, R is the
constant gas, and n is the number of mole in the gas.
P = 1 atm (pressure of the gas)
V = 22.4 L
n = 1 mole
R=0.0821 L.atm/mol-K (Universal Gas Constant)
T =273 K

26. Example problem:
SAMPLE PROBLEM 1
What is the pressure exerted by 0.65 mole of a gas inside a 7.5 L
container at 22°C?

27. You try:
SAMPLE PROBLEM 2
Find the molecular mass of a gas if 3.75 g of the gas occupies a
volume of 10.5 L at 24°C and 820 torr.

28. How Did You Do?
Part B:
Learning Goals
I will be able to describe
Boyle’s, Charles’ and Gay-
Lussac’s Laws relating T, P
and/or V and be able to
calculate unknown values
using the equations derived
from these laws, as well as
the combined gas law.