gas laws ab.notebook 1 December 03, 2013 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 toall of the assumptions, it would be an "ideal" gas. Gas
Transcript
gas laws ab.notebook
1
December 03, 2013
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.
Gas
gas laws ab.notebook
2
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.
gas laws ab.notebook
3
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.
gas laws ab.notebook
4
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:
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 )
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.
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 …
gas laws ab.notebook
13
December 03, 2013
gas laws ab.notebook
14
December 03, 2013
Sample ProblemThe 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 + Pc Pc = 275 torr
Sample ProblemThree 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
gas laws ab.notebook
15
December 03, 2013
Diffusion and Graham’s LawWhat 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 fasterthan those with a high molecular mass. From his observation, he developed Graham’s
law:
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.
• We know that Kinetic energy = 1/2 mv2
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 writtenwhere A and B are two gases.
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?
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.
=3.16 X faster
Always Heavier Gas on top
gas laws ab.notebook
18
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?
gas laws ab.notebook
19
December 03, 2013
Question 1: Solution
rate1 = H2 = x rate2 = 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.
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.)
gas laws ab.notebook
21
December 03, 2013
Avogadro's law is stated mathematically as:
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
Avogadro's Law proposed by Amedeo AvogadroStates that under equal conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules.
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
gas laws ab.notebook
23
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−11
How do they differ?
gas laws ab.notebook
24
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.
