The rms speed of oxygen molecule in a gas is v. If the absolute temperature is doubled and the oxygen molecule dissociate into oxygen atoms, the rms speed will become –

The root mean square (rms) speed of a gas molecule is given by the formula:

v = sqrt(3kT/m)

where:

• v is the rms speed,
• k is Boltzmann's constant,
• T is the absolute temperature, and
• m is the mass of the molecule.

If the absolute temperature is doubled, the formula becomes:

v' = sqrt(3k(2T)/m) = sqrt(2) * sqrt(3kT/m) = sqrt(2) * v

This means that the rms speed of the oxygen molecule will increase by a factor of sqrt(2) if the temperature is doubled.

However, if the oxygen molecule dissociates into oxygen atoms, the mass m in the formula will be halved (since an oxygen molecule O2 consists of two oxygen atoms). Therefore, the rms speed will become:

v'' = sqrt(3k(2T)/(m/2)) = sqrt(4) * sqrt(3kT/m) = 2 * v

So, if both the temperature is doubled and the oxygen molecule dissociates into oxygen atoms, the rms speed will increase by a factor of 2 * sqrt(2) compared to the original speed.