A physics student measures molecular speeds in a laboratory apparatus and concludes that the distribution of speeds is such that:(adsbygoogle = window.adsbygoogle || []).push({});

10% have a speed of 200 m/s

10% gave a speed of 250m/s

15% have a speed of 500m/s

30% have a speed of 650m/s

20% have a speed of 900m/s

15% have a speed of 1300 m/s

Calculate

a) the average speed

b) the rms speed

c)the most probable speed

Assuming that the apparatus contains and ideal gas with the molecular mass m = 50 x 10^-3 kg/mol, and the above distribution of speeds

d) determine the temperature of the gas in the apparatus

a) The precentages throw me off in this problem. I know that to find the average speed, I need to add up all the speeds^2 and divide by the total number of molecules.

[(1 x 200m/s) + (1 x 250m/s) + (1.5 x 500 m/s)+ (3.0 x 650 m/s) + (2 x 900m/s) + (1.5 x 1300m/s)]/10

b) [(1 x 200m/s)^2 + (1 x 250m/s)^2 + (1.5 x 500 m/s)^2 + (3.0 x 650 m/s)^2 + (2 x 900m/s)^2 + (1.5 x 1300m/s)^2]/10

=1.15x 10^6 m^2/s^2

The rms speed = sqrt(1.15x 10^6 m^2/s^2)

c) I really don't know what the most probable speed is or how to go about calculating it please help!!

d)I know that the rms speed = sqrt(3RT/M)

I'm not too good at math ( if you didn't already realize by now) so I'm not sure how to set the equation to solve for T.

T^2 = sqrt((Vrms^2(M))/3RT)

Any help is much appreciated. Thanks in advance.

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# Homework Help: Molecule Speed

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