What will be the effect on the root mean square velocity of oxygen...

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?

Options

AThe velocity of atomic oxygen remains same
BThe velocity of atomic oxygen doubles
CThe velocity of atomic oxygen becomes half
DThe velocity of atomic oxygen becomes four times

Correct answer

B. The velocity of atomic oxygen doubles

Step-by-step solution

The RMS velocity of a gas is given by, ${v}_{RMS} = \sqrt{\dfrac{3RT}{M}}$

When ${O}_{2}$ ~dissociates into $O$ ~its& molecular mass becomes $\dfrac{M}{2}$ . Therefore,

Ratio of RMS~speed,& $\dfrac{v1}{v2} = \sqrt{\dfrac{T1}{T2} \times \dfrac{M2}{M1}}⇒ \dfrac{v1}{v2} = \sqrt{\dfrac{T}{2T} \times \dfrac{M / 2}{M}}⇒ \dfrac{v2}{v1} = 2$

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