If two gases CH ₄ and SO ₂ , are allowed to enter from the two ends of a 1 ~km long vacuum tube at the same time, where will the gases meet from the CH ₄ end?

Step-by-step solution

M _ CH ₄ =16 ; ( C _ CH ₄ )_ rms = 3 RT 16 = 3 RT 4 ~m / s aligned & M _ SO ₂ =64 ; ( C _ SO ₂ )_ rms = 3 RT 64 = 3 RT 8 ~m / s & ( C _ CH ₄ )_ rms > ( C _ SO ₂ )_ rms aligned Suppose, at time ' t ', both the gas will meet. At time t , CH ₄ molecules travel 3 RT 4 tm and At time SO ₂ molecules travel 3 RT 8 tm . 3 RT t 4 + 3 RT t 8 =1000 or 3 RT t 4 (1+ 1 2 )=1000 or 3 RT t 4 3 2 =1000 or t= 8000 3 3 R T Distance travelled by time ' t ' = 3 RT 4 8000 3 3 RT =667 ~m