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A straight glass tube has two inlets X and Y at the two ends. The length of the tube is 200 cm. HCl gas through inlet X and NH_3gas through inlet Y are allowed to enter the tube at the same time. White fumes first appear at a point Pinside the tube. Find the distance of P from X.

Answer» <html><body><p></p>Solution :This <a href="https://interviewquestions.tuteehub.com/tag/problem-25530" style="font-weight:bold;" target="_blank" title="Click to know more about PROBLEM">PROBLEM</a> can easily be understood with the help of the following figure. <br/> White fumes appear at point P due to the formation of `NH_4Cl`according to the equation <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/NTN_HCS_ISC_CHE_XI_P1_C05_SLV_032_S01.png" width="80%"/> <br/> `NH_3 (g) + HCl(g) to NH_4 CI(g)` <br/>At point P, HCl gas and `NH_3` gas meet together and react to form fumes of `NH_4 <a href="https://interviewquestions.tuteehub.com/tag/cl-408888" style="font-weight:bold;" target="_blank" title="Click to know more about CL">CL</a>`. <a href="https://interviewquestions.tuteehub.com/tag/suppose-656311" style="font-weight:bold;" target="_blank" title="Click to know more about SUPPOSE">SUPPOSE</a> the distance of point P from the inlet X is x cm.<br/> `:.`The distance travelled by HCl gas = x cm and, the distance travelled by `NH_3 " gas " = (200 - x) cm`. The time <a href="https://interviewquestions.tuteehub.com/tag/taken-659096" style="font-weight:bold;" target="_blank" title="Click to know more about TAKEN">TAKEN</a> by HCl gas to reach point P will be the same as the time taken by `NH_3` to reach point P. Let this time be equal to t.<br/> Rate of diffusion of HCl gas <br/> `(r_1) = (" distance travelled ")/("time") =X/t` <br/>Rate of diffusion of `NH_3 " gas " (r_2) (200-x)/t`<br/><a href="https://interviewquestions.tuteehub.com/tag/molecular-562994" style="font-weight:bold;" target="_blank" title="Click to know more about MOLECULAR">MOLECULAR</a> mass of `HCl (M_1) = 36.5` <br/> Molecular mass of `NH_3 (M_2) = 17` <br/>According to Graham.s law of diffusion, <br/>`r_1/r_1 =sqrt(M_2/M_1)` <br/> `:.(x//t)/((200 - x)//t)= sqrt(17/(36.5))` <br/> or `x/(200-x) = 0.6825 " or " x = 81.13 cm`<br/>Hence, white fumes appear at a distance of 81.13 cm from the inlet X.</body></html>


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