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Q.

The rms speed of oxygen molecules (O2) at a certain temperature T (degree absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, what is its rms speed in atomic form?

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a

vOrms=4vO2rms

b

vOrms=vO2rms

c

vOrms=2vO2rms

d

vOrms=0.5vO2rms

answer is C.

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Detailed Solution

The rms speed is given by v=3RTMw.When the temperature is doubled, the new temperature T’ = 2T and oxygen (O2) dissociates into atomic oxygen, then molecular weight M'w=Mw2Therefore, v'=3RT'M'w=3R2TMw2=43RTMw ⇒v'=23RTMw=2v Hence, vOrms=2vO2rms

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The rms speed of oxygen molecules (O2) at a certain temperature T (degree absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, what is its rms speed in atomic form?