Question

The rms speed of oxygen molecules in a gas is V . If the temperature is doubled and the O2 molecule dissociates into oxygen atoms , the rms speed will become

Answer 1

Answer: The rms speed will becomes 2 times.

Explanation:

Given that,

rms speed of oxygen = v

We know that,

The rms speed is defined as:

$V_{rms}=\sqrt{\dfrac{3RT}{M}}$

We have,

The rms speed is

$V_{rms}=\sqrt{\dfrac{3RT}{M}}=v$

Now, Temperature T'= 2 T

The $O_{2}$ molecule dissociates into oxygen atoms.

So. $M'=\dfrac{M}{2}$

The rms speed will be

$V'_{rms}=\sqrt{\dfrac{3RT'}{M'}}=v$

$V'_{rms}=\sqrt{\dfrac{3R\times2T}{\dfrac{M}{2}}}$

$V'_{rms}=2v$

Hence, The rms speed will becomes 2 times.

Answer 2

$\sf \pink{Solution \: in \: Attachment} \: { ⬆}$