Question

If for two gases of molecular masses MA and MB at
temperatures TA and TB, TA MB = TB MA, then which of the
following properties has the same magnitude for both the
gases
(a) Pressure (b) Density
(c) Molar K.E. (d) rms velocity

Answer 1

If for two gases of molecular masses MA and MB at

temperatures TA and TB, TA MB = TB MA, then which of the

following properties has the same magnitude for both the

gases

(a) Pressure

(b) Density

(c) Molar K.E.

(d) rms velocity

Answer 2

Property which has the same magnitude for both the gases is :

• If for two gases of molecular masses MA and MB at temperatures TA and TB, TA.MB = TB.MA

• Given : TA/TB = MA/MB

• We know that Vrms = √3RT/M

• For A, VrmsA = √3RTA/MA ..... (1)

• For B, VrmsB = √3RTB/MB ..... (2)

• Dividing (1) by (2)

• VrmsA/VrmsB = (√3RTA/MA)/(√3RTB/MB)

= √(TA/TB)×(MB/MA)

• substituting TA/TB = MB/MA

VrmsA/VrmsB = √(MA/MB)×(MB/MA)

= 1

• VrmsA = VrmsB

• Hence, rms velocity is the property which has the same magnitude for both the gases