Which of the following order of root mean square speed of different gases at the same temperature is true?

(U_{r m s})_{H_{2}} > (U_{r m s})_{C H_{4}} > (U_{r m s})_{N H_{3}} > (U_{r m s})_{C O_{2}}

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(U_{r m s})_{H_{2}} < (U_{r m s})_{C H_{4}} < (U_{r m s})_{N H_{3}} < (U_{r m s})_{C O_{2}}

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(U_{r m s})_{H_{2}} < (U_{r m s})_{C H_{4}} > (U_{r m s})_{N H_{3}} > (U_{r m s})_{C O_{2}}

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(U_{r m s})_{H_{2}} > (U_{r m s})_{C H_{4}} < (U_{r m s})_{N H_{3}} < (U_{r m s})_{C O_{2}}

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Solution

The correct option is A $(U_{r m s})_{H_{2}} > (U_{r m s})_{C H_{4}} > (U_{r m s})_{N H_{3}} > (U_{r m s})_{C O_{2}}$
Root mean square velocity (R.M.S.) has the formula : $R . M . S . = \sqrt{\frac{3 R T}{M}}$
M = Molecular mass of the gas molecule
So, $R M S \propto \frac{1}{\sqrt{M}}$ at constant temperature.
$H_{2}$ = 2 g/mol
$C H_{4}$ = 16 g/mol
$N H_{3}$ = 17 g/mol
So, order of RMS values of gases are :
$U_{(R M S) H_{2}} > U_{(R M S) {C H}_{4}} > U_{(R M S) {N H}_{3}} > U_{(R M S) {C O}_{2}}$

Suggest Corrections

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