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Calculate the RMS velocity of chlorine molecules at 15^@C and 75 cm Hg pressure. (Given : density of Hg = 13.596 g cm , g = 980.6 " cm " s^(-2) |
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Answer» Solution :At S.T.P one mole of a GAS occupies 22400 `cm^3`. Let us FIRST convert this volume corresponding to the given conditions. `P_1 = 76 cm Hg`, `V_1 = 22400 cm^3`, `T_1 = 273 K` At given conditions `P_2 = 75 cm Hg`, `V_2` = ?, `T_2 = 15+273 = 288 K` ACCORDING to the gas EQUATION, `(P_1 V_1)/T_1 = (P_2 V_2)/T_2` Hence,`(76 xx 22400)(273) = (75 xx V_2)/(288)` `:. "" V_2 = 23945.8 cm^3` The RMS velocity (u) is given by `u=sqrt((3RT)/M) = sqrt((3PV)/M)`(for one mole of the gas) In the present case, `P = hd g = 75 xx 13.596 xx 980.6 = 9.999 xx 10^@ " dynes " cm^2` `V=23945.8 cm^3 " and " M=71` `:. "" u= sqrt((3xx9.999xx10^5xx23945.8)/71)` `=3.181xx10^4 " cm " s^(-1)` Therefore, the RMS velocity of chlorine molecules at `15^@C` and 75 cm pressure is `3.181xx10^4 " cm " s^(-1)` |
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