Chemistry Assignment

1. (25 points) Determine by suitable calculation whether or not each of the following processes are spontaneous: a) isothermal compression of helium (ideal gas) at 25 oC from 1 atm to 5 atm. b) water condensing at 100 oC and 1.0 atm. c) the reaction of 1.0 M solutions of Ba2+ and SO42- at 25 oC and 1.0 atm. 2. (25 points) The enthalpy (J/mol) of a binary liquid mixture of species 1 and 2 at 25 oC and 1.0 atm is given by H = 400x1 + 600x2 + x1x2(40 x1 +20x2) where xi is the mole fraction of species i. a) What are the enthalpies (J/mol) of pure species 1 and 2 at the given conditions? b) Derive and sketch the curve of H versus x1 for of an ideal solution of species 1 and 2. c) Sketch the curve of H versus x1 for a real solution of species 1 and 2 (use the given equation. d) How do your answers to parts b) and c) compare (is the ideal solution assumption in part b) reasonable)? e) Derive an expression for the partial molar enthalpy of component 1, H1, (J/mol) for a real mixture of species 1 and 2 (i.e., from the given expression for H of the solution). 3. (25 points) Using the following compressibility factor data for CO2 at 150 oC: P (bar) Z 10 0.985 20 0.970 40 0.942 60 0.913 80 0.885 100 0.869 200 0.765 300 0.762 400 0.824 500 0.910 a) Prepare a linear fit of Z versus P for the first four points (up to 60 bar) and determine a value B’ (atm-1) for CO2 at 150 oC in the two-term virial equation. b) Use your answer from part b) in the two-term virial equation to prepare a plot of the fugacity coefficient, ?, versus pressure (from 1 to 500 bar) for CO2 at 150 oC. c) prepare a plot of (Z-1)/P versus P for CO2 at 150 oC. d) Use your plot in part c) to obtain a relation for ln ? versus P and prepare a plot of the fugacity coefficient, ?, versus pressure (from 1 to 500 bar) for CO2 at 150 oC. e) How do your answers from parts b) and d) compare? Give reasons for any agreement or disagreement. 4. (25 points) Given the reaction CO(g) + H2O(g) ? CO2(g) + H2(g) Occurring at 1250 K and 1atm. The intial mixture contains 1 mol of CO2 and 1 mol of H2O. The reaction mixture can be considered to be an ideal gas. a) Calculate the equilibrium constant for the reaction. b) Determine the equilibrium mole fractions of all species.