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Unformatted text preview: ECH 152B Homework #4 Due: Friday February 13, 2010 1) (25 points) Consider the watergasshift reaction: H2(g) + CO2(g) H2O(g) + CO(g) At high temperatures and low to moderate pressures the reacting species form an idealgas mixture. By equation (11.27): G = y i Gi + RT y i ln y i i i When the Gibbs energies of the elements in their standard states are set equal to zero, Gi = G O for each fi species, then: (A) t G = y i G O + RT y i ln y i fi
i i It has been noted that (dG )T,P = 0 is a criterion for equilibrium. Applied to the watergasshift reaction with the understanding that T and P are constant, this equation becomes: dG t = d (nG ) = ndG + Gdn = 0 n dG dn +G = 0 d d Here, however, dn/d=0. The equilibrium criterion therefore becomes: (B) dG = 0 d Once the yi are eliminated in favor of , Equation (A) relates G to . Data for GfiO for the compounds of interest are given in example 13.13. For a temperature of 1,000 K (the reaction is unaffected by P) and for a feed of 1 mol H2 and 1 mol CO2: a. Determine the equilibrium value of by application of Equation (B). b. Plot G vs. , indicating the location of the equilibrium value of determined in part a. 2) (25 points) Reactionequilibrium calculations may be useful for estimation of the compositions of hydrocarbon feedstocks. A particular feedstock, available as a lowpressure gas at 500 K, is identified as "aromatic C8." It could in principle contain the C8H10 isomers: oxylene (OX), mxylene (MX), pxylene (PX), and ethylbenzene (EB). Estimate how much of each species is present, assuming the gas mixture has come to equilibrium at 500 K and low pressure. The following is a set of independent reactions (why?): (I) OX MX (II) (III) OX EB a. Write reactionequilibrium equations for each equation of the set. State clearly any assumptions. b. Solve the set of equations to obtain algebraic expressions for the equilibrium vaporphase mole fractions of the four species in relation to the equilibrium constants, KI, KII, KIII. OX PX ECH 152B Homework #4 Due: Friday February 13, 2010 c. Use the data below to determine numerical values for the equilibrium constants at 500 K. State clearly any assumptions. Species OX(g) MX(g) PX(g) EB(g) Hf,298O (J/mol) 19,000 17,250 17,960 29,920 Gf,298O (J/mol) 122,200 118,900 121,200 130,890 d. Determine numerical values for the mole fractions of the four species. 3) (25 points) Consider the hydrogenation reaction of 1butene to butane by the following reaction: C4H8 + H2 C4H10 For a feed flow ratio of 10 moles H2 to 1 mole C4H8, a reactor temperature of 1000 K, and a reactor pressure of 5 bar, calculate the ratio of butane to 1butene at equilibrium. Assume ideal gas behavior and that hrxn0 is constant. The following data is given: Species C4H8(g) C4H10(g) Hf,298O (J/mol) 130 126,230 Gf,298O (J/mol) 71,340 17,170 4) (25 points) The following is a set of VLE data for the system of methanol(1)/water(2) at 333.15 K (extracted from K. Kurihara et al., J. Chem. Eng. Data, vol. 40, pp. 679684, 1995): P (kPa) 19.953 39.223 42.984 48.852 52.784 56.652 x1 0.0000 0.1686 0.2167 0.3039 0.3581 0.4461 y1 0.0000 0.5714 0.6268 0.6943 0.7345 0.7742 P (kPa) 60.614 63.998 67.924 70.229 72.832 84.562 x1 0.5282 0.6044 0.6804 0.7255 0.7776 1.0000 y1 0.8085 0.8383 0.8733 0.8922 0.9141 1.0000 Basing calculations of equation 12.1, find parameter values for the Margules equation that provide the best fit of GE/RT to the data, and prepare a Pxy diagram that compares the experimental points with curves determined from the correlation. ...
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