Consider Argon (40 g/mol, d = 188 pm) at 0°C, 550 mm Hg: a) What is the collision frequency/ b) What is the collision density? c) What is the mean free path?
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- Hydrogen gas is cooled to 100 K, while the pressure is reduced to 0.1 Pa. a) Determine the mean free path A and the average frequency of collision. b) What are the rms speed and the average kinetic energy of a molecule? c) What is the momentum flux of the gas on the container? d) What are the most probable free path, the most probable speed, and the most probable velocity?3. Solid molecular hydrogen. For H₂ one finds from measurements on the gas that the Lennard-Jones parameters are & = 50×10-¹6 erg_and o = 2.96 Å. Find the cohesive energy in kJ per mole of H₂; do the calculation for an fcc structure. Treat each H₂ molecule as a sphere. The observed value of the cohesive energy is 0.751 kJ/mol., much less than we calculated, so that quantum corrections must be very important.a) Estimate the average spacing between the molecules of 1 mol of an ideal gas at a pressure of 1atm and a temperature of 300 K. b) 1 mol of liquid water occupies a volume of 18 cm. Estimate the spacing between molecules. c) Use your result from part (a) to estimate the diameter of a water molecule. d) Estimate the factor by which water expands when it boils
- In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle per cubic meter. If the collision diameter is 2.5 x 1010 m, calculate the mean free path 2. The temperature of interstellar space is 2.7 K. 2.a) Calculate the mean free path in meters of a nitrogen molecule (with a mass m=4.68×10¬26 kg) located in Earth's atmosphere at sea level. Assume a temperature of T=300 K and a number density of particles of 1019 cm-3. b) Assuming that the collision cross-section of the molecule is o = 2x10-10 frequency v in Hertz and the time between collisions t in seconds. m, compute the collisionProblem II There is a piece of 10 mm thick a-iron plate. This plate initially has hydrogen uniformly distributed inside with an initial concentration Co. Assume that there is no hydrogen in the air. The plate is left in the air and the hydrogen concentration varies with the time as follows: 4Co C(x, t) = (-9n²Dt\ 12 3nx sin еxp where / is the thickness of the plate. If we would like to remove 95% of the hydrogen from the plate, how long will it take when the plate is at 25 °C? The pre-exponential and activation energy for hydrogen in a-iron are 0.1 mm/s and 13,400 J/mol, respectively.
- Q2/ for a monoatomic ideal gas, the partition function is: Z = e-N %3D h2B calculate F, S, P and U.Fi Calculate the van der Waals second viral coefficient (B) using Zydw at 299.6 K, where Zydw is given as 1 where Pc= 119.9 atm, Vm.c= 122.2 cm3/mol and T= 325.2 K. a Zvdw =1+|b- RT O a. 0.22 O b. -3.22 O c. -2.01 O d. -0.18The average translational kinetic energy of O2 molecules (relative molar mass 32) at a particular temperature is 0.048eV. The translational kinetic energy of N2 molecules (relative molar mass) in eV at the same temperature is? a) 0.0015 b) 0.003 c) 0.048 d) 0.768
- 2. For T = 300 K, calculate the pressure (in bars) at which the mean free path of a hydrogen molecule will be each of the lengths given here. For H₂, o = 2.30 x 10-1⁹ m². (a) 100 μm (b) 1.00 mm (c) 1.00 m LLa. Find the average translational kinetic energy of nitrogen molecules at room temperature, in eV. b. Find the average translational kinetic energy of a 1 microgram dust particle at room temperature, in eV. c. Find the mean speed of nitrogen molecules in thermal equilibrium, at room temperature. d. Find the mean speed of a 1 microgram dust particle in thermal equilibrium, at room temperature.1. For nitrogen at 283 K find, a) The most probable speed ✔m/s b) The average speed m/s c) The rms speed m/s The molar mass of nitrogen is 14.0 g/mol and R= 8.31 kg/(mol K) Hint: You need to convert quantities into SI units.