Deduce (a) Charle's law (b) Graham's law of diffusion from Kinetic gas equation.
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(a) Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:
An animation demonstrating the relationship between volume and temperature
Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant kB =
R
/
NA
=
n R
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N
(in each law, properties circled are variable and properties not circled are held constant)
When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.[1]
This relationship of direct proportion can be written as:
v equation t
where:
V is the volume of the gas,
T is the temperature of the gas (measured in kelvins),
and k is a non-zero constant.
This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:
The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.
(b) Faster-moving molecules can escape more readily through small holes or pores in containers. Such an escape is called effusion. They can also mix more rapidly with other gases by diffusion. Such processes are usually carried out at constant temperature, and so the relative rates of diffusion or effusion of two gases A and B depend only on the molar masses MA and MB:
This result is known as Graham’s law of diffusion after Thomas Graham (1805 to 1869), a Scottish chemist, who discovered it by observing effusion of gases through a thin plug of plaster of paris. Graham's law of diffusion states that the ratio of the diffusion rate of two gases is the same as the ratio of the square root of the molar mass of the gases.
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