gas laws ab.notebook
December 03, 2013
Gas
The Kinetic Theory of Gases
(A model of how gases behave.)
The assumptions of this theoretical model are:
1. All gases are composed of individual particles that are in continuous, random motion.
2. The collisions that occur between gas particles may result in a transfer of energy from one particle to another, but the net amount of energy in a given system remains the same­­otherwise, the temperature would go up as time passes. (Gases posses kinetic energy) Total Kinetic energy remains the same as long as Temp. and Vol. don’t change.
3. The volume of individual gas particles is insignificant compared to the volume of space in which they move.
4. No forces of attraction are considered to exist between gas particles.
If a gas were to behave exactly like above and conform to all of the assumptions, it would be an "ideal" gas.
1
gas laws ab.notebook
December 03, 2013
These 2 assumptions do not operate in the real world?
­ Real gas particles may be small, but they do have a volume.
­ Gas particles do have some forces of attraction between them­­otherwise you could never liquefy or solidify them.
These 2 deviations become important under high pressure and low temperature when the particles are close together.
How do I get a real gas to act like an ideal one?
Increase the temperature and decrease the pressure enables gases to
follow the kinetic molecular theory (ideal gas law).
This increases the volume and the individual particles of the gas move far apart and exert less attraction between each other.
­ Hydrogen and Helium are the closest to ideal behavior.
2
gas laws ab.notebook
December 03, 2013
The Combined Gas Law
Rather than having to remember each individual law, you can memorize just one formula,
and based on the variables needed, use those and get rid of what’s not needed by using the combined gas law.
3
gas laws ab.notebook
December 03, 2013
Boyle’s Law
(Temperature is constant.)
­ measures how the Volume of a gas varies with its Pressure.
With temperature at a steady 25° C and a set amount of particles:
http://preparatorychemistry.com/Bishop_Gay_Lussac_frames.htm
Based on Boyle’s findings, what can be said about the relationship between Pressure and Volume?
At a constant temperature, as pressure increases, volume
decreases. (Inverse Relationship)
The product of pressure and volume is constant under these conditions. ( P x V = k )
4
gas laws ab.notebook
December 03, 2013
5
gas laws ab.notebook
December 03, 2013
Charles’s Law:
­ (Pressure is constant.)
­ Investigates the relationship between the temperature (in Kelvins) and volume of an ideally behaving gas.
What 2 conclusions can we draw based on the graph:
1. The volume of the gas increases / decreases with Increasing / decreasing temperature. (Direct Relationship)
2. The change in volume with change in temperature is regular: Theoretically, the gases volume should become 0 at 0 K,
but all real gases change to liquids before that temperature is reached.
http://preparatorychemistry.com/Bishop_Gay_Lussac_frames.htm
6
gas laws ab.notebook
December 03, 2013
7
gas laws ab.notebook
December 03, 2013
8
gas laws ab.notebook
December 03, 2013
Gay­Lussac's Law
This law was first stated by the Frenchman Joseph Gay­Lussac (1778 to 1850). According to Gay­Lussac’s law, for a given amount of gas held at constant volume, the pressure is proportional to the absolute temperature. http://preparatorychemistry.com/Bishop_Gay_Lussac_frames.htm
9
gas laws ab.notebook
December 03, 2013
10
gas laws ab.notebook
December 03, 2013
11
gas laws ab.notebook
December 03, 2013
Dalton’s Law of Partial Pressure
­ states that the sum of the partial pressures equals the total pressure exerted.
Imagine a container with a mixture of three ideally behaving gasses, A, B and C. The gases exert a combined pressure on the walls of the container (P total). Each individual gas is a partial pressure. Therefore, Ptotal = P1 + P2 + P3 …
12
gas laws ab.notebook
December 03, 2013
13
gas laws ab.notebook
December 03, 2013
Sample Problem
The total pressure of the three gas components in the mixture described above is 550 torr.
If Pa = 200 torr and Pb = 75 torr, what is the partial pressure of gas C. P total = P1 + P2 + P3 …
550 torr = 275 torr + Pc (Now just subtract and solve for Pc)
550 torr = 200 torr + 75 torr + P
c Pc = 275 torr Sample Problem
Three gases in a tank have respective partial pressures of 0.20
atmosphere, 0.35 atmosphere, 0.15 atmosphere.
What is the total gas pressure inside the tank?
Ptotal = P1 + P2 + P3 …
Ptotal = 0.20 atm + 0.35 atm + 0.15 atm
Ptotal = 1.30 atm
14
gas laws ab.notebook
December 03, 2013
Diffusion and Graham’s Law
What is diffusion?
Diffusion — the tendency of molecules and ions to move toward areas of lower concentration until the concentration is uniform throughout the system.
Scotsman Thomas Graham did work in the 1840’s on effusion — the rate at which a gas escapes through a tiny hole in a container.
He noticed that gases with small molecular masses effuse faster
than those with a high molecular mass. From his observation, he developed Graham’
law: http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gaslaw/micro_effusion.html
http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/animations/Effusion2.html
The rate of effusion of a gas is inversely proportional to the square root of its mass.
.
This relationship was later found to be true for diffusion as well
This relationship is can be understood when considering mass and speed of a moving body and the force the body exerts when it strikes a stationary object.
2
• We know that Kinetic energy = 1/2 mv
If two bodies of unequal mass have the same kinetic energy, which moves faster?
The lighter one!
Thus, for two gases at the same temperature, the one with lower molecular mass will diffuse faster.
Graham’s Law can be written
where A and B are two gases.
15
gas laws ab.notebook
December 03, 2013
16
gas laws ab.notebook
December 03, 2013
If equal amounts of helium and argon are placed in a porous container and allowed to escape, which gas will escape faster and how much faster?
Always Heavier Gas on top
=3.16 X faster
Set rate1 = He = x and rate2 = Ar = 1. The weight of He = 4.00 and Ar = 39.95. By Graham's Law, x / 1 = square root (39.95 / 4.00) = 3.16 times as fast. 17
gas laws ab.notebook
December 03, 2013
Question 1:
Two porous containers are filled with hydrogen and neon respectively. Under identical conditions, 2/3 of the hydrogen escapes in 6 hours. How long will it take for half the neon to escape?
Question 2:
If the density of hydrogen is 0.090 g/L and its rate of diffusion is 6 times that of chlorine, what is the density of chlorine?
18
gas laws ab.notebook
December 03, 2013
Question 1: Solution
rate 1 = H2 = x rate 2 = Ne = 1. The weight of H2 = 2.02 Ne = 20.18. By Graham's Law, x / 1 = square root (20.18 / 2.02) = 3.16 times as fast. 0.67 / 3.16 = 0.211 amount of Ne leaving in 6 hours. Therefore 0.211 / 6 = 0.50 / x. x = 14.2 hours 19
gas laws ab.notebook
December 03, 2013
Question 2: Solution
Set rate 1 = H2 = 6
rate 2 = Cl2 = 1. The weight of H2 = 2.02 and Cl= x. By Graham's Law, 6 / 1 = square root (x / 2.02) = 72.72 (molec. wt. of Cl 2) 72.72 g / 22.414 L = 3.24 g/L. (22.414 is molar volume.) 20
gas laws ab.notebook
December 03, 2013
Avogadro's law is stated mathematically as:
Avogadro's Law proposed by Amedeo Avogadro
States that under equal conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules. Where:
V is the volume of the gas. n is the amount of substance of the gas. k is a proportionality constant. The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that:
Where:
p is the pressure of the gas T is the temperature in kelvin of the gas http://proton.csudh.edu/lecture_help/avogadroslaw.html
21
gas laws ab.notebook
December 03, 2013
Ideal Gas Law An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic & in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.
An ideal gas can be characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them may be deduced from kinetic theory and is called the
22
gas laws ab.notebook
December 03, 2013
n = number of moles R = universal gas constant = 8.314472 L·kPa ·K−1·mol−1
or
R = universal gas constant 0.0820574587 L·atm·K−1·mol−1
1
How do they differ?
23
gas laws ab.notebook
December 03, 2013
At high pressures, how does the volume of a real gas compare with the volume of an ideal gas under the same conditions?
V of a real gas > V of an ideal gas because V of gas molecules is significant when P is high.
Ideal Gas Equation assumes that the individual gas molecules have no volume. 24
gas laws ab.notebook
December 03, 2013
Useful variations of PV=nRT
25
gas laws ab.notebook
December 03, 2013
26