 # 1. How many collisions does a single Ar atom make in 1.0 second whe...

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1. How many collisions does a single Ar atom make in 1.0 second when the temperature is 25°C and the pressure is (a) 10 bar, (b) 1 bar and (c) 0.01 bar? [Note that the collision cross-section of argon is 0 = 0.36 nm².] 2. Calculate and compare the root-mean-square speeds and mean free paths of helium and krypton at (a) 10 K, (b) 300K and (c) 1200 K. 3. Calculate and compare the pressures of 10.00 g of carbon dioxide confined in a 3 container of 100 cmi volume at 25.0°C predicted by the perfect gas and van der Waals gas models. Comment on the reason for any difference. 4. A cylinder containing gas for a carbon dioxide laser comprising equal amounts of carbon dioxide, nitrogen and helium. If 1.0 g of carbon dioxide leaks from the cylinder by effusion, what mass of nitrogen and helium escapes? a. Starting at 7,000 kPa total pressure, what would be the final composition of the gas remaining in the cylinder if 50% of nitrogen escapes? 5. A meteorological balloon had a radius of 1.5 m when released at sea level at 20°C ad expanded to a radius of 3.5 m when it rose to its maximum altitude where the temperature was -25°C. What is the pressure inside that balloon at that altitude? a. Estimate the altitude using the barometric equation. 6. The critical parameters for methane, ethane, and propane are given in the table below. Use the data to calculate the compression factor at the critical point for the different gases listed. Comment on any trends you might see in the calculated values and offer an explanation? Pc (atm) Vc (cm³/mol) Tc (K) CH1 45.6 98.7 190.6 C,H6 48.6 260 562.7 C3Hg 41.9 200 369.8 7. The critical constants are related to the van der Waals parameters by Pc =2762.Vc= = a = 8a 3b, , and Tc = For ethane, the values of the critical constants are Pc = 48.20 atm, 27Rb Vc = 148 cm 3mol-¹ , and Tc = 305.4 K. Calculate the van der Waals parameters for ethane and estimate the radius of the molecule.

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