Kinetic Theory

JEE Main level, single correct, medium

44 of 168

Question 44 of 168

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

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Answer: (B) The velocity of atomic oxygen doubles

The RMS velocity of a gas is given by, vRMS=3RTM{v}_{RMS}=\sqrt{\dfrac{3RT}{M}}
When O2{O}_{2} dissociates into OO its molecular mass becomes M2\dfrac{M}{2}. Therefore,
Ratio of RMS speed, v1v2=T1T2×M2M1\dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{{T}_{1}}{{T}_{2}}\times \dfrac{{M}_{2}}{{M}_{1}}}⇒v1v2=T2T×M/2M\Rightarrow \dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{T}{2T}\times \dfrac{M/2}{M}}⇒v2v1=2\Rightarrow \dfrac{{v}_{2}}{{v}_{1}}=2

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