If the most probable speed of ( CO ₂ ) at (27^ C ) is (400 ~ms ⁻¹ ). The root mean square velocity of ( CO ₂ ) at the same temperature in ( ms ⁻¹ ) is approximately

Step-by-step solution

Given, Temperature ((T) ) is same for most probable velocity ( (v_ mp )) and for root mean square velocity ( [v_ rms ] ) Also, ( aligned & v_ ( mp ) =400 ~ms ⁻¹ & v_ ( mp ) = 2 R T M and & v_ ( mp ) = 2 R T M or, v_ ( mp ) ^2= 2 R T M aligned ) or (M= 2 R T v_ ( mp ) ^2 = 2 R T (400)^2 )...(i) Similarly ( M= 3 R T v_ ( rms ) ^2 [ v_ rms = 3 R T M ] )...(ii) On comparing (i) and (ii), we have ( 2 R T (400)^2 = 3 R T v_ ( rms ) ^2 ) or (v_ ( rms ) ^2= 3 2 (400)^2 ) ( aligned v_ (rms) & =1.2247 400 & =489.89 490.00 ~m