Translational Energy of Molecules and Vrms

AI Thread Summary
The discussion focuses on calculating the average (rms) speed of hydrogen molecules in a one-liter container at 200 K and 1 atm. The initial calculation yielded an rms speed of 1579.30 m/s, which was deemed incorrect as the expected answer is 1600 m/s. Participants clarify that the discrepancy is not due to rounding, as the provided multiple-choice options suggest a precise answer. It is recommended to select the closest value in a multiple-choice format. The conversation emphasizes the importance of accuracy in physics calculations, especially in exam settings.
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1. A quantity of molecular hydrogen (H2) gas fills a one liter container at a temperature of 200 K and pressure of 1 atm.

What is the average (rms) speed of the molecules?

Homework Equations



KE_trans = 1/2 M<v^2>
Energy_trans = 3/2kT = 3/2RT
H2 = 2g/mol

The Attempt at a Solution



Assuming 1 mol of H2:
mass = .002kg

1/2 M<v^2> = 3/2RT
(.002kg)<v^2> = 3R(200K)
<v^2> = 2494200m/s
Vrms = sqrt(<v^2>) = 1579.30m/s

Which is wrong.
The correct answer is 1600m/s. (Not a rounding error.)

Can anyone help me?
Thanks!
 
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The answer is certainly rounded.

ehild
 
The reason I don't believe its rounded is because the options are:
(a) 16 m/s
(b) 74 m/s
(c) 274 m/s
(d) 1600 m/s
(e) 4570 m/s

So if it were rounded it would be rounded to 1580 and in my
physics exams they always give you the exact answer or really close to it.
 
You result is correct. Do you need to present your calculation, or just have to choose one value? If it is a multi-choice question mark the closest one.

ehild
 
Yea, its a multiple choice question.
Thanks for your help!
 
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