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Interpretation:
The highest root-mean-square speed has to be predicted
Concept introduction:
Average kinetic energy: Average kinetic energy of the gas molecules is proportional to the temperature of the gas in kelvins.
- Average kinetic energy of a molecule is given by,
¯KE = 12m¯u2= CT
Where, m is the mas of molecule
u is the speed
C is proportionality constant
T is absolute temperature
According to the equation, the absolute temperature of a gas is a measure of the average kinetic energy of the molecules. Higher the temperature, the molecules are highly energetic. Thus, random molecular motion is referred to as thermal motion.
Root-Mean-Square speed:
One of the results of the kinetic theory of gases is that the total kinetic energy of a mole of any gas equals 32RT. The average kinetic energy of one molecule is 12m¯u2.
So,
¯KE =32RTNA (12m¯u2) = 32RT
Where,
NA is
m is mass of a single molecule.
As known, NA m = M
Where,
M is molar mass.
This equation can be arranged to give,
√¯u2= urms = √3RTM
Taking the square root of both sides gives,
√¯u2= urms = √3RTM −−−−−(1)
The unit of each term in the equation (1) is,
Where, R is proportionality constant called gas constant (J/mol.K)
M is molar mass (Kg/mole)
T is temperature (K)
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Chapter 5 Solutions
General Chemistry
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