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Question
1. (A) A radioactive metal atom decays by emitting an alpha particle. The alpha particles are collected as an ideal gas. The volume of the gas collected was 12.05 mL at 765 mmHg and 23°C. How many atoms decayed during the period of the experiment?
(B) You vaporize a liquid substance at 100°C and 755 mmHg. The volume of 0.548 g of vapor is 237 mL. What is the molecular weight of the substance?
2. Starting out on a trip into the mountains, you inflate the tires in your car to a recommended pressure of 3.21x105 Pa on a day when the temperature is –5.0°C. You drive to the beach, where the temperature is 28.0°C. Assume that the volume of the tire has been increased by 3%. What is the final pressure in the tires? The manufacturer of the tire recommends that you not exceed the recommended pressure by more than 10%. Has the limit been exceeded?
3. (A) One good way to treat nonideal gases is the Redlich-Kwong equation of state,
P = RT /(V-b) - a/√T(V(V+b))
where a and b are constants that depend the identity of the gas (i.e., they can be found from critical constants similar to what is done for the van der Waals equation of state, but the formulas are different). Determine the formula for the following partial derivative of the Redlich-Kwong equation of state,
(∂P/∂Vm)T
(B) Five moles of methane are confined to a container with volume 20L at 300K. Estimate the pressure using the ideal gas equation of state. Give your answer in atm.
(C) Estimate the pressure in B using the van der Waals equation of state. Give your answer in atm.
(D) Estimate the pressure in B using the Redlich-Kwong equation of state given the Redlich-Kwong constants for methane are a = 3.2 Pa m^{6}mol^{2}K^{½} and b = 2.96 × 10^{-5} m^{3}mol^{-1}. Give your answer in atm.
4. Calculate the values of the van der Waals parameters a and b for carbon monoxide using the critical constants: T_{C} = 134 K; P_{C} = 3.546 MP_{a}; V_{C} = 0.099 L/mol.
Summary
These questions belong to Chemical Engineering and they deal with radioactive decay to alpha particles, standard tire inflation and effect on temperature changes, Redlich-Kwong equation state for partial derivative and calculating van der Waals parameters for carbon monoxide. Each of these questions has been answered in the solution along with calculations.
Note: The solution is in handwritten format.
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