Air contains approximately 80% N2 molecules (mass 4.65*10-26 kg) and 20% O2 molecules (mass 5.36*10-26 kg). At STP, what is the rms speed of O2 molecules in air?a) 486.5 m/sb) 493.1 m/s c) 459.3 m/s If we don’t distinguish between N2 and O2, what would be the average rms speed of air molecules?a) 486.5 m/s b) 493.1 m/s c) 476.2 m/s

The rms (root-mean-square) speed of O2 molecules in the air can be determined as follows.…

Answered: Air contains approximately 80% N2…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter10: Thermal Physics

Section: Chapter Questions

Problem 10CQ: The air we breathe is largely composed of nitrogen (N2) and oxygen (O2) molecules. The mass of an N2...

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Question

Air contains approximately 80% N₂ molecules (mass 4.65*10^-26kg) and 20% O₂ molecules (mass 5.36*10^-26kg). At STP, what is the rms speed of O₂ molecules in air?

a) 486.5 m/s

b) 493.1 m/s

c) 459.3 m/s

If we don’t distinguish between N₂ and O₂, what would be the average rms speed of air molecules?

a) 486.5 m/s

b) 493.1 m/s

c) 476.2 m/s

Expert Solution

Step 1

The rms (root-mean-square) speed of O₂ molecules in the air can be determined as follows.

$\begin{array}{rcl} v_{r m s, O_{2}} & = & \sqrt{\frac{3 k T}{M_{O_{2}}}} \\ = & \sqrt{\frac{3 (1.38 \times 10^{- 23} m^{2} \cdot k g / s^{2} \cdot K) (273.15 K)}{5.36 \times 10^{- 26} k g}} (A t S T P, T = 273.15 K) \\ = & 459.3 m / s \end{array}$

Therefore, option (c) is correct.

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