Methanol is formed from carbon monoxide and hydrogen in the gas-phase reaction

CO+2H2<=>CH3OH

(A) (B) (C)

The mole fractions of the reactive species at equilibrium satisfy the relation

(Yc/(YaY^2b))(1/P^2)=Ke(T)

Where P is the total pressure (atm), Ke the reaction equilibrium constant (atm^-2), and T the temperature (K). The equilibrium constant Ke equals 10.5 at 373 K, and 2.316x10^-4 at 573K. A semilog plot of Ke (logarithmic scale) versus 1/T (rectangular scale) is appropriately linear between T=300K and T=600K.

a) Derive a formula for Ke(T), and use it to show that Ke(450K)=0.0548 atm^-2.

b)Write expressions for n(sub a),n(sub b), and n(sub c) (gram-moles of each species), and then Ya,Yb,Yc, in terms of na0,nb0,nc0, and xi symbol, the molar extent of reaction. Then derive an equation involving only na0,nb0,nc0,P,T, and xi symbol e, where xi simbol e (mol) is the value of the extent of reaction at equilibrium.

c) suppose you begin with equimolar quantities of CO and H2 and no CH3OH, and the reaction proceeds to equilibrium at 423K and 2.00 atm. Calculate the molar composition of the product (Ya,Yb, and Yc) and the fractional conversion of CO.

d) The conversion of CO and H2 can be enhanced by removing methanol from the reactor while leaving unreacted CO and H2 in the vessel. Review the equations you derived in solving part c and determine any physical constraints on xi associated with na0=nb0=1 mol. Now suppose that 90% of the methanol is removed from the reactor. Estimate the fractional conversion of CO and the total gram moles of methanol produced in the modified operation.

e) Repeat part d but now assume that nb0=2 mol. Explain the significant increase in fractional conversion of CO.

f) Write a set of equations for ya,yb,yc and fa (the fractional conversion of CO) in terms of ya0,yb0, T and P(the reactor temp at equilibrium). Enter the equations in an equation solving program. Check the program by running it for the conditions of part c then use it to determine the effects of fa (increase, decrease, no effect) of separately increasing, (i) the fraction of CH3OH in the feed, (ii) temperature, and (iii) pressure.