Calculate the root mean square velocity and kinetic energy...

Key Concepts

Root Mean Square Velocity

The root mean square (rms) velocity is a measure of the typical speed of particles in a gas and is calculated using the formula vrms = ?(3kT/m), where k is Boltzmann's constant, T is the absolute temperature, and m is the mass of an individual gas molecule. This concept is essential in the kinetic theory of gases, showing that at a given temperature, lighter molecules move faster than heavier ones.

Average Kinetic Energy

In an ideal gas, the average kinetic energy per molecule is given by (3/2)kT. This energy is solely dependent on the temperature and is independent of the mass of the gas molecules. Therefore, at the same temperature, all gases have the same average kinetic energy, even though their individual molecular speeds vary.

Molecular Mass and Its Impact

Molecular mass plays a critical role in determining the speed of gas molecules. Since the rms velocity is inversely proportional to the square root of the molecular mass, lighter molecules will exhibit higher speeds compared to heavier ones at a fixed temperature. This relationship is fundamental when comparing different gases under identical thermal conditions.

Graham's Law of Effusion

Graham’s Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molecular mass. This means that lighter gases effuse faster than heavier gases. This concept is crucial in understanding how gases escape through small openings and is directly tied to the kinetic energy and rms speed of the gas molecules.

Transcript

00:01 Question number 84.

00:05 Calculate the root mean square velocity and kinetic energy of co, co2, so2 at 728, 298, kyivine.

00:19 Let me calculate their molecular weight force.

00:25 1212, 28 gram per growth.

00:29 I may need to compare to kilogram.

00:32 To cover this to kilogram i have to divide by 1000 that will give me 0 .08 kilogram per more then i do for co2 that's 12 plus 16 pounds and that is 44 gram per more and that is 0 .04 4 .44 and that is 0 .04 4 kilogram per more for so for so3 32 plus multiplied by 3 and that gives 80 gram and that is 0 .0 80 gram more and that is 0 .0 .0 .0 philogram now i've read the formula for the okay for velocity i want to write the formula for root news square velocity urms a cost square root of 3rt divided by m m is the molar mass and the r is the gas constant so i will that's why i want i will use this value of r which is eight point three one four two per more and our temperature has been given to the 298 so let me calculate for a couple of hominocide so u .r .m .s.

02:37 It is square root of three times 28 .314314 multiplied by 298 divided by molecular molecular malamal 0 .08 because i want to have the units in metapacillac.

03:13 That is why i use all this one.

03:16 Joe, we know one joe is, one joe is, kilogram meter square per second square.

03:31 So the unit of everything will be meter per seconds.

03:35 And let me use my calculator.

03:39 Square root of 3 multiplied by 8 .314 times 298 divide by 0 .02bate and that is 515 515 .2 meter per second so let me calculate for co2 urms will be just similar just like these 3 times 8 .314 times 298 divided by 0 .04 and that is three times 8 .314.

04:39 298 divided by 0 .0.

04:44 That gives 411.

04:49 411 .01...

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