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 y_C/(y_A.y_B^2 ) 1/P^2 =K_e (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 573 K. A semilog plot of Ke (logarithmic scale) versus 1/T (rectangular scale) is approximately linear between T = 300 K and T =600 K.

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

(b) Write expressions for nA; nB, and nC (moles of each species), and then yA; yB,and yC, in terms of nA0; nB0; nC0, and , the extent of reaction. Then derive an equation involving only nA0; nB0; nC0, P, T, and e ,where e is 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 423 K and 2.00 atm. Calculate the molar composition of the product (yA, yB, and yC) and the fractional conversion of CO.