O 12/10/2015 11:00 PM A 86.8/100 O 12/2/2015 12:19 PM Gradebook Print Calculator

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O 12/10/2015 11:00 PM A 86.8/100 O 12/2/2015 12:19 PM Gradebook Print Calculator Periodic Table Question 16 of 17 Map A pling Your research director informs you that the molecules of a sample of gas at 329 K have a root-mean- square (rms) speed of 257 m/s and asks you to calculate the most probable speed and the average speed Also, while you're at it and before lunch, you should calculate the mass of a molecule. Please do So here. Most probable speed Number Average speed: Number Molecular mass: Number kg A Previous ® Give Up & View Solution Check Answer Next Ext O Hint

Explanation / Answer

Here ,

temperature , T = 329 K

rms speed , vrms = 257 m/s

let the molecular mass is m

rms speed = sqrt(3 * R * T/m)

257 = sqrt(3 * 8.314 * 329/m)

solving for m

m = 0.124 Kg/mol

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for most probable speed ,

vmp = sqrt(2 * R* T/m)

vmp = sqrt(2 * 8.314 * 329/.124)

vmp = 210 m/s

the most probable speed is 210 m/s

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for average speed

vavg = sqrt(8*R*T/(m *pi))

vavg = sqrt(8 * 8.314 * 329/(pi*0.124))

vavg = 237 m/s

the average speed of the molecule is 237 m/s

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for the molecular mass ,

as calculated above

the molecular mass is 0.124 Kg/mole

molecular mass = 0.124/(6.022 *10^23) kg

molecular mass = 2.06 *10^-25 Kg

the mass of molecule is 2.06 *10^-25 Kg

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