1.

A gas bulb of 1 litre capacity contains 2.0 xx 10^(21) molecules of nitrogen exerting a pressure of 7.57 xx 10^3 Nm^(-2) . Calculate the root mean square speed and the temperature of gas molecules. If the ratio of most probable speed to the root mean square speed is 0.82, calculate the most probable speed for the molecules at this temperature.

Answer» <html><body><p><br/></p>Solution :Number of moles of <a href="https://interviewquestions.tuteehub.com/tag/nitrogen-1118291" style="font-weight:bold;" target="_blank" title="Click to know more about NITROGEN">NITROGEN</a> = `("number of molecules")/(6.023 xx 10^(23))` <br/> `= (2.0 xx 10^(11))/(6.023 xx 10^(23)) = 3.32 xx 10^(-3)` <br/> According to the gas equation PV = <a href="https://interviewquestions.tuteehub.com/tag/nrt-1109890" style="font-weight:bold;" target="_blank" title="Click to know more about NRT">NRT</a><br/> In the <a href="https://interviewquestions.tuteehub.com/tag/present-1163722" style="font-weight:bold;" target="_blank" title="Click to know more about PRESENT">PRESENT</a> case, `P = 7.57 xx 10^3 N m^(-2), <a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a> = 1` <br/> `L = 10^(-3) m^(3)`, <br/> `R = 8.314 J K^(-1) mol^(-1)` T = ?<br/> Substituting the values, we have <br/> `7.57 xx 10^3 xx 10^(-3) = 3.32 xx 10^(-3) xx 8.314 <a href="https://interviewquestions.tuteehub.com/tag/xxt-3292708" style="font-weight:bold;" target="_blank" title="Click to know more about XXT">XXT</a>` <br/> `:. "" T= 274.2 K` <br/> RMS speed is given by <br/>`u = sqrt((3RT)/M)= sqrt((3 xx 8.314 xx 274.2)/(28 xx 10^(-3)))= 494.2 m s^(-1)` <br/> (Molar mass of `N_2 " in kg " = 28 xx 10^(-3)`) <br/> `:. " Most probable speed " = 0.82 xx RMS` speed <br/> `:. " Most probable speed of " N_2` under given conditions <br/> `= 0.82 xx 494.2 = 405.2 m s^(-1)`</body></html>


Discussion

No Comment Found

Related InterviewSolutions