The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon...

The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are

{v}_{H}, {v}_{O}

and

{v}_{C}

respectively, then:

Options

A ${v}_{C} > {v}_{O} > {v}_{H}$
B ${v}_{H} = {v}_{O} > {v}_{C}$
C ${v}_{H} > {v}_{O} > {v}_{C}$
D ${v}_{H} = {v}_{O} = {v}_{C}$

Correct answer

C. ${v}_{H} > {v}_{O} > {v}_{C}$

Step-by-step solution

The formula of root-mean-square speed in terms of absolute temperature and molecular mass of the gas is, ${v}_{RMS} = \sqrt{\dfrac{3RT}{M}} ⇒ {v}_{RMS} ∝ \dfrac{1}{\sqrt{M}}$ , here we know that, ${M}_{{H}_{2}} < {M}_{{O}_{2}} < {M}_{{CO}_{2}}$ $⇒ {v}_{H} > {v}_{O} > {v}_{C}$ .

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