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