Consider a sample of nitrogen gas in a 1L container at roomtemperature (25C), ha

Question

Consider a sample of nitrogen gas in a 1L container at roomtemperature (25C), having pressure P=1atm. Keeping the volumeconstant, the temperature is increased to 1000K. What is the meanfree path (in nanometers)? I understand that when the temperature is increased, thepressure will also change and therefore need to be calculated inorder to get the final answer... Consider a sample of nitrogen gas in a 1L container at roomtemperature (25C), having pressure P=1atm. Keeping the volumeconstant, the temperature is increased to 1000K. What is the meanfree path (in nanometers)? I understand that when the temperature is increased, thepressure will also change and therefore need to be calculated inorder to get the final answer...

Explanation / Answer

Mean free path , = RT / 2 d2NA P Where R = ideal gas constant = 8.314 J / mol K            T= Temperature = 25 o C = 25 + 273 = 298 K            d= density of Nitrogen = 1.251 g / L            P= pressure of the gas = 1 atm = 101 300 Pa          NA = Avagadro number = 6.0230 * 10 23 Plug the values we get = 59.136 * 10^-23 m Since Volume is kept constant T / ' = T / T' T' = 1000K ' = T' / T        =  ( 59.136 *10^-23 * 1000 ) / 298        = 198.446 * 10^-23m        = 198.446 * 10^-14nm Plug the values we get = 59.136 * 10^-23 m Since Volume is kept constant T / ' = T / T' T' = 1000K ' = T' / T        =  ( 59.136 *10^-23 * 1000 ) / 298        = 198.446 * 10^-23m        = 198.446 * 10^-14nm

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