THE GASEOUS STATE
KINETIC MOLECULAR THEORY (KMT) OF GASES POSTULATES
The Kinetic Molecular Theory of gases is a model that explains some of the behavior of gases. This is one of the most useful theories in chemistry which is based on six basic postulates or hypotheses about gas particles:
Gases are composed of tiny particles (atoms or molecules)
These particles are so small when compared to the distances between them, that their volume is negligible (assumed to be zero)
These particles are in constant random motion, moving in straight lines and colliding with the inside walls of the container.
Gas particles are assumed to have negligible attractive or repulsive forces between each other.
Gas particles may collide with each other in an elastic way, causing the total kinetic energy of the colliding particles not to change (Remain the same).
The Kelvin temperature (Kº) is directly proportional to the average kinetic energy of the gas particles.
Various scientific laws describe the relationship between four of the important physical properties of gases:
Volume
Pressure
Temperature
Amount (moles)
These are mathematical statements that describe the relationship between two of the variables while keeping the other two constant.
Boyle´s law :
Relation between pressure and volume
( P and V )
Charles' law :
Relation between volume and temperature
( V and T )
Gay Lusaac's law :
Relation between pressure and temperature
( P and T )
Combined gas law
All variables are changed ( P V and T )
Caption: : The volume of a gas is inversely related to the pressure when the temperature is constant
Slide 5
BOYLE´S LAW P1 x V1 = P2 x V2
Not to miss in Boyle´s law :
1. Just pressure and volume are allowed to change. ( T° and moles of gas which can change its volume remain constant ).
2. Volume and pressure are inversely proportional : If the pressure applied to a gas is doubled, its volume will be halved as pressure increased by a factor of two, then the volume decreases by a factor of two. These two variables move and change in precise opposite directions.
BOYLE'S LAW APPLIES TO ALL GASES OR MIXTURES OF GASES ,
for a given quantity of gas at constant temeperature.
Example exercises :
1. A tire with a volume of 11.4L reads 44psi of pressure on the tire gauge. What is the new tire pressure if you compress the tire and its new volume to 10.6L?
2. A syringe is filled with air to 60mL at 1 atmosphere. Then the syringe is sealed and compressed to 20mL. What is its final pressure?
3. A fixed quantity of Oxygen gas O2 is held at a constant temperature and occupies 545mL at 1250mmHg. What is the volume it will take at 1650mmHg?
Caption: : The volume of a gas is directly proportional to the temperature at constant pressure
Slide 7
CHARLE'S LAW V1/ T1 = V2/ T2
Not to miss in Charles law :
1. Just temperature and volume are allowed to change. ( Pressure and moles of gas remain constant ).
2. Volume si directly proportional to the temperature ( expressed in K°) : If the Kelvin temperature of a gas is doubled, so does it´s volume. If th Kelvin temperature is cut by half, the volume of the gas will do as well.
CHARLES´ LAW APPLIES TO ALL GASES OR MIXTURES OF GASES ,
for a given quantity of gas at constant pressure.
1. A hot air balloon has a volume of 2.8L at 100°C, what is the new volume if the air cools to 80°C?
2. At 0°C a gas occupies 22L. How hot must the gas be ( in Celsius ) to reach a volume of 25L?
3. A balloon is filled with 1.5L of air at 20°C and then it is placed in a freezer until it reaches a temperature of 5°C. What is the final volume?
Caption: : The pressure of a gas is directly proportional to the temperature at constant volume
Caption: : Gay Lusaac´s law
GAY LUSSAC´S P1/ T1 = P2/ T2
Slide 9
GAY LUSSAC´S P1/ T1 = P2/ T2
Not to miss in Gay Lussac's law :
1. Just temperature and pressure are allowed to change. ( Volume and moles of gas remain constant ).
2. Pressure is directly proportional to the temperature ( expressed in K°) : If the Kelvin temperature of a gas increases its pressure does as well.
GAY LUSSAC'S LAW APPLIES TO ALL GASES OR MIXTURES OF GASES
contained in a fixed volume, at contant amount of them.
1. A canister of Nitrogen gas has a pressure of 2000psi at 20°C. What will the pressure be if the temperature is increased to 25°C?
2. At 10°C a gas exerts 0.95atm of pressure. At what temperature (in Celsius °C) will it exert a pressure of 0.75 amt?
3. A flask filled with Carbon Dioxide gas is heated from 10°C to 40°C. The starting pressure was 98kPa, what is the final pressure?
1atm = 760mmHg= 760torr = 1.013 x 105 Pa = 101.3 KPa = 0.068psi
Caption: : The gas laws Teacher´s PET synthesis 4:48min
Slide 11
THE COMBINED GAS LAW
Expression that combines all three gas laws into one equation and which is used whenever all the conditions (except for the amount of gas) change. It´s an equation that applies to every gas or mixture of gases if all 5 variables are known and one needs to find the sixth.
V1 x P1 / T1 = V2 x P2 / T2
If a gas originally occupying 6.75 L at 19.21 ºC and 762.5 torr is compressed to give a pressure of 1.26 atm at 26.35 ºC, what would the new volume be? Answer V2 = 5,48L
Exercise ( Solve it yourself!)
If 60L of Carbon Dioxide CO2 are at environmental conditions of temperature and pressure of 20ºC and 560mm Hg respectively, what will the new volume be at 0ºC and 1 atm of pressure?