Question

Lactic acid (CH,CHOHCOOH), a byproduct of cheese manufacture, can be used to make a variety of chemicals. For example, it may be hydrogenated to produce propanediol (CH,CHOHCH,OH) by the reversible reaction A total of 300 moles of a vapor containing 1:3:2 lactic acid:Hyinert (mole ratios) at a total pressure of S atm (absolute) is charged to a reactor. The temperature is such that ideal gas conditions may be assumed. The equilibrium constant for the reaction, K, is defined as: (PPD)Pw (PLA)PM Where Pro. Pw. Pu and py are the equilibrium partial pressures (in atm) of propanediol, water, lactic acid, and hydrogen, respectively. a) Determine the moles of each species in the feed directly from the problem statement (don't forget the inert component). (4 points) b) Draw a flow chart for this system. (2 points) c) Write mole balances on each species in terms of (4 pts) d) Obtain an estimate for (12 pts) e) Calculate the equilibrium conversion of the limiting reactant and the composition (mole fractions) of the product vapor. (4+4 pts) Answer: Equilibrium conversion: 86%; composition of product stream: yi,-0.027, ?? 0.25, y-0.39

Answer 1

Given: (LA) + 2(H) rightleftarrow (PD) + (W) eta_T = 300 moles. LA: H_2: inert rightwardsdoublearrow 1: 3: 2 P_T = 5 atm K_p = (p_PD)(P_w)/(P_La)(P_H) = 3.2 atm^-1 Moles of each species in feed Moles of La, n_L A = 1/8 times 300 = 50 moles Moles of H_2, n_H = 3/6 times 300 = 150 moles Moles of inerts, n_I = 2/6 times 300 = 100 moles (b) Lactic Acid (50 moles) (c) Mole balance of each species in terms of (zeta) A general material balance is n dot_1 = n dot_i_0 + v_i zeta v_i rightarrow stoichiometric coefficient of ith species n dot_LA = 50 - zeta n dot_H_2 = 150 - 2 zeta n_I = 100 - 0 n_Pd = 0 + zeta & n_H_2_0 = 0 + zeta Total number of moles at equilibrium n_T = 300 - zeta (d) Estimation of (zeta) Given that k = (P_PD)(p_w)/(P(LA)(P_H)^2 = 3.2 in terms of mole fractions k = (y_PD)(y_Pw)/(y_LA)(y_H)^2 = 3.2 times 5