1.

A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is 27^(@)C. Obtain the ratio of (i) average kinetic energy per molecule, and (ii) root mean square speed v_("rms") of the molecules of the two gases.Atomic mass of argon =39.9 u, Molecular mass of chlorine = 70.9 u.

Answer» <html><body><p></p>Solution :The important point to <a href="https://interviewquestions.tuteehub.com/tag/remember-621937" style="font-weight:bold;" target="_blank" title="Click to know more about REMEMBER">REMEMBER</a> is that the average kinetic energy (per molecule) of any (ideal) <a href="https://interviewquestions.tuteehub.com/tag/gas-1003521" style="font-weight:bold;" target="_blank" title="Click to know more about GAS">GAS</a> (be it monatomic <a href="https://interviewquestions.tuteehub.com/tag/like-1073845" style="font-weight:bold;" target="_blank" title="Click to know more about LIKE">LIKE</a> argon, diatomic like chlorine or polyatomic) is always equal to `(3//2) k_(B)T`. It depends only on temperature, and is independent of the nature of the gas.<br/> (i) <a href="https://interviewquestions.tuteehub.com/tag/since-644476" style="font-weight:bold;" target="_blank" title="Click to know more about SINCE">SINCE</a> argon and chlorine both have the same temperature in the flask, the ratio of average kinetic energy (per molecule) of the two gases is 1:1.<br/>(ii) Now `(1)/(2)v_("rms")^(2)=`average kinetic energy permolecule =`(3//2) k_(B)T` where m is the mass of a molecule of the gas. Therefore, <br/> `(V_("rms")^(2))_(Ar)/(V_("rms")^(2))_(Cl)= (m)_(Cl)/(m)_(Ar)=(M)_(Cl)/(M)_(Ar)=(70.9)/(39.9)= 1.77` <br/> where M denotes the molecular mass of the gas. (For argon, a molecule is just an atom of argon.) Taking square root of both sides,<br/> `(V_("rms"))_(Ar)/(V_("rms"))_(Cl)= 1.33` <br/> You should note that the composition of the mixture by mass is quite irrelevant to the above Calculation . any other propotion by mass of argon and chlorine would give the same answers to (i) and (ii) provided the temperature <a href="https://interviewquestions.tuteehub.com/tag/remains-621920" style="font-weight:bold;" target="_blank" title="Click to know more about REMAINS">REMAINS</a> unaltered.</body></html>


Discussion

No Comment Found

Related InterviewSolutions