Question

CALC (a) Explain why in a gas of Nmolecules, the number of molecules having speeds in the finiteintervalto is . (b) If is small, then is approximately constant over the interval and For oxygen gas molar mass at use this approximation to calculate the number of molecules with speeds within of . Express your answer as a multiple of N. (c) Repeat part (b) for speeds within of. (d) Repeat parts (b) and (c) for a temperature of . (e) Repeat parts (b) and (c) for a temperature of. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions

Short answer

(a)The speed of the molecules in the interval is

(b) The number of molecules with the speed of is The number of molecules with the speed of for interval

is

(C)Number 0f molecule at the speed of for thetemperature

For is and is .

(d) number 0f molecule at the speed of for thetemperature

For is and for is

(e)The temperature is low then maxwell boltzmann distribution curve has the sharp peak

Step-by-step solution

About Maxwell Botlzman distribution curve and Determine molecule having speed in finite interval

The Maxwell–Boltzmann distribution concerns the distribution of an amount of energy between identical but distinguishable particles.It represents the probability for the distribution of the states in a system having different energies. A special case is the so-called Maxwell distribution law of molecular velocities.

fraction of particle with speed in certain interval

Number of particles that have speed in that interval is

Therefore the speed of the molecules in the interval is

Step 2:Determine The number of molecules with the speed of

solve for RMS velocity of molecule

Function of the speed is

solve the function

Solve for number of molecules

Therefore ,The number of molecules with the speed of is