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The speed of molecules is a measure of their average kinetic energy. (a) What is root mean square speed? (b) Give the equation for root mean square speed. (c) Calculate the following:(i) Root mean square speed of methane molecule at 27°C. (ii) Most probable speed of nitrogen molecule at 25°C |
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Answer» (a) It is the square root of the mean of the squares of speeds of various molecules of the gas at a given temperature. (b) Urms = \(\sqrt{\frac{u_1^2+u_2^2+...+u_n^2}{n}}\) OR Urms = \(\frac{\sqrt{3RT}}{M}\) OR Urms = \(\sqrt{\frac{3pV}{M}}\) (c) (i) Urms = \(\sqrt{\frac{3\times8.314\,JK^{-1}mol^{-1}\times\,300K}{16\,g\,mol^{-1}}}\) =21.63 ms-1 (ii) Ump = \(\sqrt{\frac{2RT}{M}}\) Ump = \(\sqrt{\frac{2\times8.314\,JK^{-1}mol^{-1}\times\,298K}{14\,g\,mol^{-1}}}\) = 18.81 ms-1 |
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