Chem 113A Homework #1;Due: Tues. 10/14/14;1. A sample of propane (C3H8) placed in a closed vessel together with an amount of O2 that is 3.00 times;the amount needed to completely oxidize the propane to CO2 and H2O at constant temperature.;Calculate the mole fraction of each component in the resulting mixture after oxidation assuming that;the H2O is present as a gas.;2. Liquid N2 has a density of 875.4 kg m3 at its normal boiling point. What volume does a balloon;occupy at 18.5C and a pressure of 1.00 atm if 2.00 x 103 L of liquid N2 is injected into it?;3. A gas sample is known to be a mixture of ethane and butane. A bulb of 200.0 cm3 capacity is filled;with the gas to a pressure of;at 20.0C. If the weight of the gas in the bulb is 0.3846;g, what is the mole percent of butane in the mixture;4. The total pressure of a mixture of oxygen and hydrogen is 1.00 atm. The mixture is ignited and the;water is removed. The remaining gas is pure hydrogen and exerts a pressure of 0.400 atm when;measured at the same values of T and V as the original mixture. What was the composition of the;original mixture in mole percent?;5. Calculate the pressure exerted by Ar for a molar volume 1.42 L at 300 K using the van der Waals;equation of state. The van der Waals parameters a and b for Ar are1.355 bar dm6 mol2 and 0.0320;dm3 mol1, respectively. Is the attractive or repulsive portion of the potential dominant under these;conditions?;6. The equation of state of a certain gas is given by p = RT/Vm + (a+bT)/Vm2, where a and b are;constants. Find (Vm/T)p.;7. 3.00 moles of an ideal gas at 27.0 C expands isothermally from an initial volume of 20.0 dm3 to a;final volume of 60.0 dm3. Calculate w for this process a) for expansion against a constant external;pressure of;and b) for a reversible expansion.;8. An ideal gas described by Ti = 300 K, Pi = 1.00 bar, and Vi = 10.0 L is heated at constant volume until;P = 10.0 bar. It then undergoes a reversible isothermal expansion until P = 1.00 bar. It is then restored;to its original state by the extraction of heat at constant pressure. Depict this closed-cycle process in a;P-V diagram. Calculate w for each step and for the total process. What values for w would you;calculate if the cycle were traversed in the opposite direction?;9. A pellet of Zn of mass 10.0 g is dropped into a flask containing dilute H2SO4 at a pressure of P = 1.00;bar and temperature T = 298 K. What is the reaction that occurs? Calculate w for the process.;10. 1 mol of an ideal gas for which;is heated from an initial temperature of 0C;to a final temperature of 275C at constant volume. Calculate q, w, U, and H for this process.;11. Calculate U and H for the transformation of 1 mole of an ideal gas from 27.0C and 1.00 atm to;327C and 17.0 atm if;in units of.;12. One mole of N2 in a state defined by Ti = 300 K and Vi = 2.50 L undergoes an isothermal reversible;expansion until Vf = 23.0 L. Calculate w assuming the gas is ideal.;13. An average human produces about 10 MJ of heat each day through metabolic activity. If a human;body were an isolated system of mass 65 kg with the heat capacity of water, what temperature rise;would the body experience? Human bodies are actually open systems, and the main mechanism of;heat loss is through the evaporation of water. What mass of water should be evaporated each day to;maintain constant temperature?;14. Suppose that a 10 kg mass of iron at 20 C is dropped from a height of 100 meters. What is the;kinetic energy of the mass just before it hits the ground? What is its speed? What would the final;temperature of the iron if all its kinetic energy is transformed into internal energy? Take the molar;heat capacity of iron to be;and the gravitational acceleration constant to be.;15. Calculate the work involved in the reversible isothermal expansion of one mole of CH4(g) from a;volume of;to;at 300 K. In this problem assume methane is a van der;Waals gas.;16. Calculate the minimum work required to compress 5.00 moles of an ideal gas isothermally at 300 K;from a volume of;to.;17. Consider the Peng-Robinson equation of state;where and are the gas-specific parameters. Derive and expression for the reversible isothermal;work of expansion for a Peng-Robinson gas.;18. One mole of ethane at 25 C and one atm is heated to 1200 C at constant pressure. Assuming ideal;behavior, calculate the values of;and;given that the molar heat capacity of ethane is;given by;19. Repeat the calculation performed in problem 18 for a constant-volume transformation instead of;constant pressure.;20. Compare the pressures calculated using the ideal gas law, the van der Waals equation, the PengRobinson equation of state (see problem 17), and the Redlich-Kwong equation of state (see below);for propane at 400K and a density of;with the value of 400 bar measured;experimentally. The Peng-Robinson parameters for propane are;and. The Redlich-Kwong equation of state is given by;where;and;for propane.
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