Question

two gases nitrogen and oxygen are at the same temperature what is ratio of their mean square speed?​

Answer 1

as we know, v = √{3RT/M}

where v is square mean root speed

T is temperature, M is molecular mass of gas and R is universal gas constant.

given, Two gases nitrogen and oxygen are at the same temperature.

so, T = constant

then, v ∝ 1/√M

⇒v1/v2 = √{M2/M1}

here, molecular mass of nitrogen, M1 = 28g/mol

molecular mass of oxygen, M2 = 32 g/mol

⇒ v1/v2 = √{32/28} = √{8/7} = √8/√7

hence, ratio of RMS speed of nitrogen and oxygen is √8 : √7

Answer 2

$\huge\bold\purple{Answer:-}$

as we know, v = √{3RT/M}

where v is square mean root speed

T is temperature, M is molecular mass of gas and R is universal gas constant.

given, Two gases nitrogen and oxygen are at the same temperature.

so, T = constant

then, v ∝ 1/√M

⇒v1/v2 = √{M2/M1}

here, molecular mass of nitrogen, M1 = 28g/mol

molecular mass of oxygen, M2 = 32 g/mol

⇒ v1/v2 = √{32/28} = √{8/7} = √8/√7

hence, ratio of RMS speed of nitrogen and oxygen is √8 : √7