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1.) The lowest pressure achievable in a laboratory setting is on the order of 1 x...

1.) The lowest pressure achievable in a laboratory setting is on the order of 1 x 10-15 torr. At 25.0 °C, calculate the number of molecules per L for an ideal gas at a.) 1.00 atm  b.) 1 x 10-15 torr. Assume the gas in question is nitrogen with a collision cross section of 3.75 . Calculate the mean free path and collision frequency at each pressure.

2.) A certain gas obeys the van der Waals equation with a = 0.50 m6 Pa mol-2. Its volume is found to be 5.00 x 10-4 m3 mol-1 at 273 K and 3.0 MPa. Calculate the van der Waals constant b. What is the compression factor under these conditions?

3.) Starting with the Maxwell distribution of Energies (equation 3.12), find an expression for Erms (root mean square energy). Use a gamma function or integration by parts for full credit.  Use of integral tables is allowed but will result in a deduction.

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