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KINETICMOLECULAR
THEORY
Physical Properties of Gases:• Gases have mass• Gases are easily compressed• Gases completely fill their containers (expandability) •Gases diffuse rapidly •Gases exert pressure
Kinetic Molecular Theory
A theory that explains the physical properties of gases by describing
the behavior of the particles
KMT has 5postulates:
#1A gas consists of very small particles that
have mass. (molecules or atoms)
#2Gas particles are
very far apart from each other.
(therefore gases are easily compressed)
#3
Gas particles are in continuous, rapid, random motion.
#4Collisions of gas
particles (with each other and with container) are perfectly elastic(no energy lost)
#5The average energy of the gas particles
depends on the temperature of the
gas.
Measuring gases
• Experimental work in chemistry requires measurements of quantities . Like volume, temperature, pressure and amount. This quantities are variables.
We can measure gases in 4 ways:Measurement Unit
Amount of gas Moles
Volume (V) Liters (L)
Temperature (T) °C, °F, or K
Pressure (P) atm, kPa, Torr, mm Hg, or lb/in2
Temperature (T)
A measurement of the average kinetic energy of a substance, the temperature is related with speed of the molecules of the gas.
Higher temperatures cause gas particles to move faster
K = °C + 273
14°C = ? K14°C + 273 = 287K
To solve gas problems, the temp must always be
in Kelvin (K) !!!
Pressure (P)
The force per unit area on a
surface
Pressure is caused by gas particles slamming into the container’s walls.
•When pressure increases, the number of collisions in a determine time increases
also
VOLUME (V)
• The volume of the gas is the same as the volume of the container. The unit is the Liter (L) = 1000cm3
Units of Pressure:1) atmosphere (atm) 2) Pascal (Pa) 3) millimeters of Mercury (mm Hg)4) Torr5) Pounds per square inch (lb/in2)
1 atm = 101,325 Pa 1 atm= 760 mm Hg = 760 torr
1 atm = 14.70 lb/in2
Bar = 100,000 Pa = 0.9869
Amount of gas
• The mole is the unit for specifying the amount of a sample of matter. You can
relate the number of moles and the mass to the number of
gas particles.
• The pressure exerted by air in the atmosphere is called atmospheric pressure.•VIDEO 1 Weather and air pr
essure•VIDEO 2 What is weather?
Learning CheckA. What is 475 mm Hg expressed in atm? 1) 475 atm 2) 0.625 atm 3) 3.61 x 105 atm
B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?
1) 2.00 mm Hg2) 1520 mm Hg3) 22,300 mm Hg
SolutionA. What is 475 mm Hg expressed in atm?
485 mm Hg x 1 atm = 0.625 atm (B) 760 mm Hg
B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?29.4 psi x 1.00 atm x 760 mmHg = 1.52 x 103 mmHg 14.7 psi 1.00 atm (B)
Enclosed Gases
• If the container is closed, the pressure inside the container may be different from the atmospheric pressure.• Manometer: Instrument to
measure the pressure in a closed container.
• Determining the pressure in the container will depend on the levels of the Hg on the two sides.• Pressure of the gas in the container is
the same as the atmosphere WHEN THE TWO LEVELS ARE EQUALY HIGH• If the level of mercury is LOWER on the
container side, the pressure in the container is higher than atmosphere.
• The difference between pressures in mmHg is simply the difference between the heights of the two columns.• To find the pressure of the gas in the
container you must add or subtract the difference in pressures to the atmospheric pressure, witch you have separately determined by using a barometer.
• If the mercury level in the container is HIGHER that atmospheric side, the pressure in the container is less than the atmospheric pressure.
• WHEN THE GAS PRESSURE IS HIGHER THAN ATMOSPHERE PRESSURE, THE LEVEL OF MERCURY ON THE SIDE OF THE GAS WILL BE LOWER THAN OPEN ENDED SIDE.
Add differences
• WHEN GAS PRESSURE IS LOWER THAN ATMOSPHERIC PRESSURE, THE LEVEL ON THE SIDE OF THE GAS WILL BE HIGHER THAN OPEN ENDED SIDE..
• Subtract differences
• Pcontainer = Height difference – Atmospheric pressure
• Pcontainer = Height difference + Atmospheric pressure
STOP…collaborate and listen
THE GAS LAWS
• Mathematical representation of the observed relationships among the 4 variables
• BOYLE’S LAW : The pressure- volume Famous experiment involved trapping air,
changing its pressure , and measuring its volume.
If the temperature remains unchanged the product of the pressure times the volume have a constant value K.
• PV = K• The pressure and volume of a sample of gas at
constant temperature are inversely proportional to each other.
• IF PRESSURE INCREASES, VOLUME DECREASES
• IF VOLUME INCREASES, PRESSURE DECREASES
• At same temperature the product of the pressure times the volume of a sample is always the same.
Boyle’s Law
MUST BE AT CONSTANT TEMPERATURE!!
P1V1 = P2V21 = trial 1
2 = after (trial 2)
A gas occupies a volume of 0.458 L at a pressure of 1.01 kPa and temperature of 295 Kelvin. Although the temperature
stays the same, the volume is increased to 0.477 L. What is the new pressure?
0.970 kPa
Charles’ Law
• The relationship between volume gas and its temperature while the pressure and the amount of gas were held constant
• VOLUME INCREASES AS TEMPERATURE INCREASES
• V= K2 T• At constant pressure the volume of a fixed
amount of gas is directly proportional to its absolute temperature.
Charles’ Law
MUST BE AT CONSTANT PRESSURE!!
V1T2 = V2T1
1 = before2 = after
What will be the volume of a gas sample at 309 K if its volume at 215 K is 3.42 L? Assume that pressure is constant.
4.92 L
Gay-Lussac’s Law
MUST BE AT CONSTANT VOLUME!!
1 = before2 = after
2
2
1
1
T
P
T
P
A balloon with a pressure of 0.900 atm is heated from
105 K to 155 K. If volume is held constant, what is the new pressure?
1.33 atm
Combined Gas Law
1 = before 2 = after2
22
1
11
T
VP
T
VP
JUST HOLD ONE QUANTITY CONSTANT!!(take it out of the equation)
The gas in a 0.010 L container has a pressure of 1.39 atmospheres. When the gas is transferred to a 0.017 L container at the same
temperature, what is the pressure of the gas?
0.82 atm
The gas inside a 70.8 mL piston has a temperature of 35.0°C. If the temperature is raised to 100.0°C, what is the new volume of the gas?
85.7 mL
An elastic container is inflated to a volume of 18.0 liters at a pressure of 1.26 atm. The container then expands to a new volume at a pressure of
1.05 atm. What is the new volume?
21.6 liters
Avogadro’s Law
The amount- volume relationship
Equal volumes of gas (at same P and T) contain the same amount of particles
• It states that all gases show the same physical behavior
• A gas with a larger volume must consist of a greater number of particles. As long as the pressure and temperature do not change
• If the amount of gas increases the volume increases
• If the amount of gas decreases the volume decreases
1 mole = 6.02 x 1023 particles
Only works at same P and T
V = K n
1 mole = 22.4 L
Ideal Gas LawThe mother of all gas
laws. It includes everything!
PV = nRT
P = pressure (atm)V = volume (L)n = moles (mol)
R = Gas ConstantT = Temperature
(Kelvin)
PV = nRT
KmolLatm0821.0R
MUST USE THESE UNITS!!!
PV = nRT
If the pressure exerted by a gas at 0.00°C in a volume of 0.0010 L is 5.00 atm, how many moles of gas are present?
2.2 x 10-4 moles
Ideal gases don’t really exist…
…real gases do!
Ideal Gas
A gas that is described by the KMT postulates.
Ideal Gas Law works most of the time.
It does NOT work at very low temperatures and very high pressures.
Dalton’s Law of Partial Pressures
The sum of the partial pressures
of the gases is equal to the total
pressure
Dalton’s Law of Partial Pressures
Ptotal = P1 + P2 + P3 + …
A balloon contains O2 and N2 gas. If the partial pressure of the O2 is 0.75 atm and the partial pressure of the N2 is 0.55 atm, what is the total pressure of
the balloon?
1.30 atm
The gas inside a 70.8 mL can contains H2O(g) and CO2(g) and has a total pressure of 760 mm Hg. If the partial pressure of the H2O is 350 mm Hg, what is the partial
pressure of the CO2?
410 mm Hg
STPStandard Temperature and PressureBehavior of gases depend strongly on temperature and pressure .
0°C or 273 K and 1 atm
How many moles of N2 gas are in a 4.5 L balloon at STP?
0.20 moles
A gas at STP is heated to 55°C. What is the new pressure if volume is held constant?
1.2 atm
A gas tank contains CO2 and O2 gas. What is the total pressure in the tank if the partial pressure of CO2 is 0.45 atm and the partial pressure of O2 is 0.55?
1.00 atm