|Sep27-06, 10:26 AM||#1|
A physics student measures molecular speeds in a laboratory apparatus and concludes that the distribution of speeds is such that:
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
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.
|Sep27-06, 10:41 AM||#2|
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
First get rid of the square root by squareing both sides:
(rms speed)2= 3RT/M.
Now isolate T by multiplying both sides of the equation by M and dividing both sides by 3R:
T= M(rms speed)2/3R.
|Similar Threads for: Molecule Speed|
|RMS Speed of a Gas Molecule||Introductory Physics Homework||0|
|What is this molecule?||Chemistry||4|
|compound and molecule?||Biology, Chemistry & Other Homework||3|
|is h_2 consider a molecule?||Biology, Chemistry & Other Homework||2|
|Gas Molecule||Introductory Physics Homework||2|