Problem Set #5 Assigned: January 19, 2024 Due: January 22, 2024 at 2:30 pm Upload your answers to the Canvas website. PDF files are preferred, but Microsoft Word, or image files will be accepted. Please check to make sure that your submission is legible. 1. Use the Maxwell-Boltzmann distribution to estimate the fraction of molecules of N2 which have speeds in the range of 200 m/s to 210 m/s at 400 K. Approach: The Maxwell-Boltzmann equation, 1B.4 in your textbook, is difficult to integrate. However, over very small ranges the area under the curve can be estimated by a simple rectangle (see below). This is done by multiplying the value of the function in the middle of the range by the width of the range. See the chemist’s toolbox on p. 14 of your textbook for additional information on integration. https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_5%3A_Integration/5.1%3A_Approximating_Areas 2. Provide a molecular explanation for the dependence of the mean free path of a molecule on temperature, pressure, and the size of the gas molecule. 3. Determine the relative mean speed of N2 and H2 molecules in a mixed gas at 25 °C. 4. Calculate the most probably speed, the mean speed, and the mean relative speed of CO2 in a gas at 20 °C. 5. Find the collision frequency of H2 molecules in a gas at 1.00 atm and 25 °C. 1 f u du 41T HIT re R 8.314J mol K T 400k 2002210 205ms dv 210 200 10 m s M 28.0134 103 kg mol 1 qu fluidu 4T 41T 28 2055 e 2 1.552.109 flu dv 6.868 10 341 4 95 0.838 205 µ 10 3 As the temperature increases the number of collisions decrease and the mean free path 2 increases which shows us that the mean free path is directly proportional to the temperature. When the pressure increases the distance between the molecules decreases resulting in an increase In the Number of collisions and a decrease In the mean free path telling us that pressure is inversely proportional to the mean free path. When the size of the molecules increases the number of collisions increases and the mean free path decreases. MAMB 3 Vre M matm T 298.15 µ 1 88 g not y mean 4 N 1.88 103 kgmol 1476298.15 3.14 1.88 103 mean 1832.8 m s Vre 1.83 Vmp Vmp E FE 8.31471293157 44.01 Vmp 10.52 ms 1.83Kms 2 59 Kms Vre Vmean E Vrel 11.88 K mean Vmean mean Vrel 11.88 m s 16.8 Kms 5 2 ovreip KT P 1 00 atm 101kPa Z T 298 15 Vre re ii 2 79 14 951 a 5 25 108 a