Transcript Chapter 14: THE GAS LAWS

THE GAS LAWS
Kinetic Theory (Gases)
Assumptions
1. Gas particles do not attract or repel each other
2. Gas particles are much smaller than the
distances between them
3. Gas particles are in constant, random motion
4. No kinetic energy is lost when gas particles
collide with each other or the walls of their
container
5. All gases have the same average kinetic energy
at a given temperature
The Nature of Gases
• Actual gases do not follow suit with the
assumptions
• The assumptions are based on 4 factors:
– 1. number of particles present
– 2. temperature
– 3. pressure
– 4. volume of sample
• If one variable changes, it affects the other
three
Boyle’s Law
• Named for Robert Boyle (1627-1691)
– Irish Chemist
– Studied the relationship between volume and
pressure
– Proved that volume of a gas and the pressure of the
gas are inversely proportional
• Boyle’s Law- the volume of a given amount of
gas held at constant temperature varies
inversely with the pressure.
Boyle’s Law Cont’d
• Mathematically the equation is as follows:
P1V1=P2V2
Example Problem 14.1
• A sample of helium gas in a balloon is compressed
from 4.0 L to 2.5 L at a constant temperature. If the
pressure of the gas in the 4.0 L volume is 210kPa,
what will the pressure be at 2.5L?
ANSWER:
V1=4.0L
V2= 2.5L
P1V1=P2V2
P2= (P1V1) = (210kPa)(4.0L)= 340kPa
V2
2.5L
P1=210kPa
P2=???
Charles’ Law
• Named for Jacques Charles (French
physicist)
• 1746-1823
• Studied volume and temperature
• Observed that as temperature increases
so does the volume of a gas in a sample;
therefore, it is a direct relationship
• (Temperature is measured in KELVIN)
Charles’s Law Cont’d
• The volume of a given amount of gas is
directly proportional to its Kelvin
temperature at constant pressure
V1=V2
T1 T2
Tkelvin= 273 + TCelsius
Example Problem 14.2
• A gas sample at 40oC occupies a volume of 2.32
L. If the temperature is raised to 75oC, what will
the volume by assuming the pressure remains
constant?
T1=40oC +273= 313K
T2= 75oC + 273 = 348K
V1 = V2  V2=T2V1
T1 T2
T1
V1=2.32L
V2= ???
so V2= (348K)(2.32L)= 2.58L
313K
Gay-Lussac’s Law
• Named for Joseph Gay-Lussac
• Explored relationship between pressure
and temperature of a gas at a fixed
volume
• Equation:
P1=P2
T1 T2
Gay-Lussac’s Law Example
• The pressure of a gas in a tank is 3.20 atm
at 22oC. If the temperature rises to 60oC,
what will be the gas pressure in the tank?
P1=3.20 atm
T2=60oC + 273 = 333K
P1=P2
T1 T2
P2=T2P1
T1
T1= 22oC + 273 = 295K
P2=???
P2= (333K)(3.20atm) = 3.61 atm
295K
HOMEWORK due tomorrow
• Page 422 1-5
• Page 425 6-8
• Page 427 9-13
14.2 The Combined Gas Law
• Boyle’s, Charles’s and Gay-Lussac’s Law
can be COMBINED into one law
P1V1 =P2V2
T1
T2
Example 14.4
• A gas at 110kPa and 30oC fills a flexible container with an initial
volume of 2.0L. If the temperature is raised to 80oC and the
pressure increased to 440 kPa, what is the new volume?
P1=110kPa T1= 30oC +273= 303K
P2= 440 kPa T2=80oC + 273= 353K
P1V1=P2V2
T1
T2
V2= P1V1T2
P2T1
V1= 2.0L
V2=???
V2= (110kPa)(2.0L)(353K)= 0.58L
(440kPa)(303K)
Avogadro’s Principle
• States that equal volumes of gases at the
same temperature and pressure contain
equal numbers of particles
• Molar volume is the volume that one mole
occupies at 0oC and 1.00 atm of pressure
• These conditions are referred to as STP
(Standard Temperature and Pressure)
• Conversion Factor = 22.4L/1mol
Example 14.5
• Calculate the volume that 0.881 mol of gas
at STP will occupy.
XL = 0.881 mol x 22.4L = 19.7L
1mol
Example 14.6
• Calculate the volume that 2.0kg of
methane gas will occupy at STP.
XL = 2.0kgx 1000g x 1mol x 22.4L = 2.8x103L
1 kg 16.05g 1 mol
14.4 The Ideal Gas Law
• In addition to temperature, pressure, and
volume, the number of moles is another
way to describe a gas
• In the previous gas laws, care was taken
to observe a “fixed amount” of a gas
• If the number of moles of gas present is
changed, one of the other variables is
affected.
PV=nRT
•
•
•
•
•
P = pressure
V= volume
n= number of moles of gas present
R= ideal gas constant
T= temperature
• The value of the ideal gas constant (R) is
dependent on the units used for pressure
Numerical Values of R
Units of R
Numeri Units of
cal
P
Value of
R
Units of V
Units
of T
Unit
s of
n
L atm/mol K
0.0821
atm
L
K
mol
L kPa/mol K
8.314
kPa
L
K
mol
L mmHg/mol K
62.4
mm Hg
L
K
mol
Real vs. Ideal Gases
• Ideal gas- takes up no space and has no
intermolecular attraction
• In the real world, no true real gas is ideal
• In the real world, real gases have
intermolecular attraction
– Length of bonds
– Types of atoms
Example 14.7
• Calculate the number of
moles of gas contained in
a 3.0L vessel at 300K
with a pressure of 1.50
atm.
P=1.50 atm
V= 3.0L
n=?
R=0.0821Latm/molK
T=300K
PV=nRT
n=PV/RT
n=
(1.50 atm)(3.0L)
(0.0821Latm/molK) (300K)
n= 0.18 mol