The following chemical reactions take place in a liquid-phase batch reactor of constant volume V.

A → 2B r1 [mol A consumed/ (L∙s)] = 0.100CA

B → C r2 [mol C generated/(L∙s) = 0.200C2B where the concentrations CA and CB are in mol/L. The reactor is initially charged with pure A at a concentration of 1.00mol/L.

(a) Write expressions for (i) the rate of generation of B in the first reaction and (ii) the rate of consumption of B in the second reaction. (If this takes you more than about 10 seconds, you’re missing the point.)

(b) Write mole balances on A, B, and C, convert them into expressions for dCA/dt, dCB/dt, and dCC/dt, and provide boundary conditions.

(c) Without doing any calculations, sketch on a single graph the plots you would expect to obtain of CA versus t, CB versus t, and CC versus t. Clearly show the function values at t = 0 and t → ∞ and the curvature (concave up, concave down, or linear) in the vicinity of t = 0. Briefly explain your reasoning.

(d) Solve the equations derived in part (b) using a differential equation-solving program. On a single graph, show plots of CA versus t, CB versus t, and CC versus t from t = 0 to t = 50 s. Verify that your predictions in part (c) were correct. If they were not, change them and revise your explanation.