1. The Maxwell-Boltzmann distribution of speeds is 3 mv² v²e¯2kT т f (v) = 47 a) Calculate the fraction of CO2 molecules at 300K between 100 and 105 m/s. b) Repeat for 600 and 605 m/s. c) Repeat a) and b) at T=1000K.
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- A specially constructed velocity-selector accepts a beam of molecules from an oven at a temperature T but blocks the passage of molecules with a speed greater than the mean. What is the mean speed of the emerging beam, relative to the initial value? Treat the system as one-dimensional.The best laboratory vacuum pump can generate a vacuum of about 1 nTorr. At 25 °C and assuming that air consists of N2 molecules with a collision diameter of 395 pm, calculate at this pressure (i) the mean speed of the molecules, (ii) the mean free path, (iii) the collision frequency in the gas.Given the van der Waals constants for ethane gas as a = 5.562 L2bar/mol2, b = 0.06380L/mol, for 10.0 mol of ethane at 300 K and under 30 bar, [9]i. Calculate the second virial coefficient B at this temperature.ii. What does this imply about the nature of the interactions between themolecules at this temperature?iii. Calculate the compression factor (Z) from the first two terms of the virialequation of state.iv. Estimate the molar volume from Z
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- For an ideal gas obeying the ideal gas law, P = nRT/V , where R is the gas constant. Write the total differential dz and evaluate the partial derivativesIn general, the compressibility factor Z tends to be larger than 1 at very high pressures (greater than 350 bar for methane.) Which Van der Waals' factor seems to be responsible for this behavior.--- a or b? ExplainAt 300K, the virial coefficients (B) of N2 and CH4 are -4.2cm^3 mol^-1 and -15cm^3 mol ^-1, respectively. Which gas behaves more ideally at this temperature?