Monday, December 17, 2007
grahams law of effusion
Gases : Graham's Laws of Diffusion and Effusion
Only a few physical properties of gases depends on the identity of the gas.
Diffusion - The rate at which two gases mix.
Effusion - The rate at which a gas escapes through a pinhole into a vacuum. Thomas Graham
Graham's Law of Diffusion
The rate at which gases diffuse is inversely proportional to the square root of their densities.
Since volumes of different gases contain the same number of particles (see Avogadro's Hypothesis), the number of moles per liter at a given T and P is constant. Therefore, the density of a gas is directly proportional to its molar mass (MM).
Graham's Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of either the density or the molar mass of the gas.
The time required for 25-mL samples of different gasses to diffuse through a pinhole into a vacuum.
The Kinetic Molecular Theory and Graham's Law
Since KEavg is dependent only upon T, two different gases at the same temperature must have the same KEavg.
Simplify the equation by multiplying both sides by two:
Rearrange to give the following:
Take the square root of both sides to obtain the following relationship between the ratio of the velocities of the gases and the square root of the ratio of their molar masses:
This equation states that the velocity (rate) at which gas molecules move is inversely proportional to the square root of their molar masses.
Next: "Deviation from Ideal Gas Behavior: Van der Waals Equation"
Only a few physical properties of gases depends on the identity of the gas.
Diffusion - The rate at which two gases mix.
Effusion - The rate at which a gas escapes through a pinhole into a vacuum. Thomas Graham
Graham's Law of Diffusion
The rate at which gases diffuse is inversely proportional to the square root of their densities.
Since volumes of different gases contain the same number of particles (see Avogadro's Hypothesis), the number of moles per liter at a given T and P is constant. Therefore, the density of a gas is directly proportional to its molar mass (MM).
Graham's Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of either the density or the molar mass of the gas.
The time required for 25-mL samples of different gasses to diffuse through a pinhole into a vacuum.
The Kinetic Molecular Theory and Graham's Law
Since KEavg is dependent only upon T, two different gases at the same temperature must have the same KEavg.
Simplify the equation by multiplying both sides by two:
Rearrange to give the following:
Take the square root of both sides to obtain the following relationship between the ratio of the velocities of the gases and the square root of the ratio of their molar masses:
This equation states that the velocity (rate) at which gas molecules move is inversely proportional to the square root of their molar masses.
Next: "Deviation from Ideal Gas Behavior: Van der Waals Equation"
combined gas law
Combined gas law
From Wikipedia, the free encyclopedia
The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other while pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally Gay-Lussac's law introduces a direct proportionality between temperature and pressure at constant volume. The inter-dependence of these variables is shown in the combined gas law, which states that:
“
The ratio between the pressure-volume constant and the temperature of a system remains constant.
”
This can be stated mathematically as
where:
P is the pressure.
V is the volume.
T is the temperature (measured in kelvin).
k is a constant with units of energy divided by temperature.
For comparing the same substance under two different sets of conditions, the law can be written as:
The addition of Avogadro's law to the combined gas law yields the ideal gas law.
Retrieved from "http://en.wikipedia.org/wiki/Combined_gas_law"
From Wikipedia, the free encyclopedia
The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other while pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally Gay-Lussac's law introduces a direct proportionality between temperature and pressure at constant volume. The inter-dependence of these variables is shown in the combined gas law, which states that:
“
The ratio between the pressure-volume constant and the temperature of a system remains constant.
”
This can be stated mathematically as
where:
P is the pressure.
V is the volume.
T is the temperature (measured in kelvin).
k is a constant with units of energy divided by temperature.
For comparing the same substance under two different sets of conditions, the law can be written as:
The addition of Avogadro's law to the combined gas law yields the ideal gas law.
Retrieved from "http://en.wikipedia.org/wiki/Combined_gas_law"
boyle's law
http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html
Animated Boyle's Law
A slide and text version of this slide is also available.
Air is a gas. Gases have various properties which we can observe with our senses, including the gas pressure (p), temperature, mass, and the volume (V) which contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.
In the mid 1600's, Robert Boyle studied the relationship between the pressure p and the volume V of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. The product of pressure and volume is exactly a constant for an ideal gas.
p * V = constant
This relationship between pressure and volume is called Boyle's Law in his honor.
In a scientific manner, we can fix any two of the four primary properties and study the nature of the relationship between the other two by varying one and observing the variation of the other. This slide shows a schematic "gas lab" in which we can illustrate the variation of the various properties. In the lab a theoretical gas is confined in a blue container. The volume of the gas is shown in yellow and is determined by the position of a red piston. The volume can be changed by moving the red piston using the red screw at the top of the piston. The number of moles of the gas is indicated by the number of small black "molecules" in the volume. The moles can be changed by injecting or withdrawing molecules using the pump at the left. There are two probes inserted into the bottom of the container to measure the pressure and the temperature. The pressure can be changed by adding or removing green weights from the top of the red piston, and the temperature can be changed by heating the container with the "torch" at the bottom.
Animated Boyle's Law
A slide and text version of this slide is also available.
Air is a gas. Gases have various properties which we can observe with our senses, including the gas pressure (p), temperature, mass, and the volume (V) which contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.
In the mid 1600's, Robert Boyle studied the relationship between the pressure p and the volume V of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. The product of pressure and volume is exactly a constant for an ideal gas.
p * V = constant
This relationship between pressure and volume is called Boyle's Law in his honor.
In a scientific manner, we can fix any two of the four primary properties and study the nature of the relationship between the other two by varying one and observing the variation of the other. This slide shows a schematic "gas lab" in which we can illustrate the variation of the various properties. In the lab a theoretical gas is confined in a blue container. The volume of the gas is shown in yellow and is determined by the position of a red piston. The volume can be changed by moving the red piston using the red screw at the top of the piston. The number of moles of the gas is indicated by the number of small black "molecules" in the volume. The moles can be changed by injecting or withdrawing molecules using the pump at the left. There are two probes inserted into the bottom of the container to measure the pressure and the temperature. The pressure can be changed by adding or removing green weights from the top of the red piston, and the temperature can be changed by heating the container with the "torch" at the bottom.
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