What type of molecule has the highest average speed in a room filled with gases?

AI Thread Summary
In a room filled with gases, the type of molecule with the highest average speed is determined by its molecular mass. The equation 1/2 mv^2 = 3/2 kT indicates that molecular speed varies inversely with the square root of molecular mass. Among the gases listed, water (H2O) has the lowest molar mass at 18 g, making it the fastest. Therefore, water molecules will have the highest average speed compared to oxygen, nitrogen, and carbon dioxide. The conclusion is that lighter molecules move faster in a gas mixture at a constant temperature.
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Homework Statement



The gases in this room include oxygen (molar
mass 32 g), nitrogen (28 g), water (18 g), and
carbon dioxide (44 g). Which type of molecule has
the highest average speed?

A) O2
B) N2
C) H2O
D) CO2
E) They have the same average speed.

Homework Equations



1/2 mv^2 = 3/2 kT

The Attempt at a Solution



Is the answer water because it's mass is the smallest?
 
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The molecular speed of gases at constant temperature varies inversely with the square root of the molecular mass. So the lightest molecule will go the fastest.
 
Thanks for replying. Sorry if it seemed obvious - I'm doing review problems without looking at the answers.
 

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