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HW2ques and soln

# HW2ques and soln - Chem 331 Homework#2(Due Fri Sept 7th...

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Unformatted text preview: Chem 331, Homework #2 (Due Fri., Sept. 7th, 2007 at beginning of class) Topics: heat, work, lst law of thermodynamics, enthalpy (1) (a) Calculate q, w, AU, and AH for the reversible isothermal expansion at 300 K of 5.00 mol of an ideal gas from 500 to 1500 cm3. (b) What would AU and w be if the expansion connects the same initial and ﬁnal states as in (a) but is done by having the ideal gas expand into vacuum? (c) Likewise, if the gas expands against a constant pressure of 10 bar, how much work is done by the gas? (2) 1.5 moles of an ideal gas, for which 5, = 3R/2, initially at 200°C and 1.00 x 106 Pa undergoes a two-stage transformation. For each of the stages described below, calculate the ﬁnal pressure, as well as q, w, AU, and AH. Also calculate c], w, AU, and AH for the complete (overall) process. (a) The gas is expanded isothermally and reversibly until the volume doubles. (b) Beginning at'the end of the lst stage, the temperature is raised to 800°C at constant volume. (3) The heat capacities of a gas may be represented by (7P = or+,BT+yT2 +5T3 For N2, at: 28.883 J K“ mol-1, B= —1.57 x 10'3 J K‘2 mol-1, y= 0.808 x 10‘5 J K3 mol—1, and 8: —2.871 x 10'9 J K4 mol'l. How much heat is required to heat a mole of N2 from 200 to 1000 K? (4) (a) Derive the equation for the work of reversible isothermal expansion of a van der Waals gas from V1 to V2. (b) One mole of CH4 expands reversibly from 1.00 to 50.0 L at 25°C. Calculate the work in joules assuming (1) the gas is ideal and (2) the gas obeys the van der Waals equation of state. For CH4(g), a = 2.283 L2 bar mol-1 and b = 0.04278 L mol'l. (5) Liquid water is vaporized at 100°C and 1.013 bar. The heat of vaporization is 40.69 kJ mol'l. What are the values of (a) wrev per mole, (b) q per mole, (c) A17 , and ((1) AH ? (6) Two moles of He gas with CV = 3W2 essentially independent of temperature expands reversibly from 24.6 L and 300 K to 49.2 L. Calculate the ﬁnal pressure and temperature if the expansion is (a) isothermal (b) adiabatic (7) A nearly 'flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Assume the initial pressure and temperature of the air before it is put into the tire to be P,- = 1.00 bar and T,- = 298 K. The ﬁnal volume of the air in the tire is Vf= 1.00 L and the ﬁnal pressure is Pf= 5.00 bar. Calculate the ﬁnal temperature of the air in the tire. Assume that C, =5R/2. (8) For a certain ideal gas, CV = 2.5R at all temperatures. Calculate q, w, AU, and AH when 2.00 mol of this gas undergoes each of the following processes: (a) a reversible isobaric expansion from (1.00 atm, 20.0 dm3) to (1.00 atm, 40.0 dm3) (b) a reversible isochoric' change of state from (1.00 atm, 40.0 dm3) to (0.500 atm, 40.0 drug) (0) a reversible isothermal compression from (0.500 atm, 40.0 dm3) to (1.00 atm, 20.0 dm3). Also calculate q, w, AU, and AH for the cycle that consists of steps (a), (b), and (c). #4) 5d; 2*2. 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HW2ques and soln - Chem 331 Homework#2(Due Fri Sept 7th...

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