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

Root mean square velocity of gas is given as

v_rms

where R=gas constant whose value is 8.31 J/mol K.

T=temperature of gas.

M= molar mass of molecule of gas

Given,

Root mean square of oxygen

v_rms

Molar mass of oxygen molecule M=32. So,

When temperature is doubled, oxygen molecule dissociates into oxygen atom.

Molar mass of oxygen atom M’=16

New temperature T’=2T

Then rms speed of oxygen atom becomes

Multiplying and diving above equation by 2 we get,

New rms speed of oxygen will ve 2v.