Translational Energy of Molecules and Vrms

[1st1]

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!

 

[ehild]

The answer is certainly rounded.

ehild

 

[1st1]

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.

 

[ehild]

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

 

[1st1]

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