Book edition 1st

Author(s) Daniel V. Schroeder

Pages 356 pages

ISBN 9780201380279

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Short Answer

Calculate the rms speed of a nitrogen molecule at room temperature.

Root mean square speed is 515.9m/s.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step1: Given information

Gas is Nitrogen.

Temp = room temp = 25^oC= 298 K

Step2: Explanation

The root mean square velocity is calculated as

$v = \sqrt{\frac{3 k T}{m}} . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)$

where

T = temperature

k = Boltzmann constant

m = mass

Mass of Nitrogen is calculated as

$m = 28 u = 28 \times 1.6 \times 10^{- 27} kg = 4.65 \times 10^{- 26} kg$

Boltzmann constant is $= 1.38 \times 10^{- 23} m^{2} {kgs}^{- 2} K^{- 1}$

Substitute the values in equation (1), we get

$v = \sqrt{\frac{3 \times (1.38 \times 10^{- 23} m^{2} k g s^{- 2} K^{- 1}) \times (298 K)}{4.65 \times 10^{- 26} k g}} v = 515.9 {ms}^{- 1}$

Root mean square speed is 515.9m/s.

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Step by Step Solution

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Step2: Explanation

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