1. Lecture 6. Strategy for Solving Material Balance Problems

2. 1.Read and understand the problem statement. 2.Draw a sketch of the process and specify the system boundary. 3.Place labels (symbols, numbers and units) on the diagram for all of the known flows, materials and compositions. 4.Obtain any data you need to solve the problem, but are missing. 5.Choose a basis : by mass or by time 6.Determine the number of unknowns. 7.Determine the number of independent equations and carry out a degrees of freedom analysis. – Degrees of freedom (N D ) = number of unknowns – number of independent equations – N D = 0 -> a solution exists – N D > 0 -> more independent equations required – N D in general no solution exists unless some constraints are eliminated or some additional unknowns are included in the problWrite down the equations to be solved in terms of the knowns and unknowns. 8.Write down the equations to be solved in terms of the knowns and unknowns. 9.Solve the equations and calculate the quantities asked for in the problem. 10.Check your answer(s).

5. Examples Lecture 6 (E7.2, DMH) A continuous mixer mixes NaOH with H 2 O to produce an aqueous solution of NaOH. Determine the composition and flow rate of the product, if the flow rate of NaOH is 1000 kg/hr, and the ratio of the flow rate of the H 2 O to the product solution is 0.9. (see DMH, p. 170-185)

6. (P3 and P4, DMH) How may values of the concentrations and flow rates in the process shown in Figure SAT7.2P3, p. 189 are unknown? The streams contain two components, 1 and 2. How many material balances are needed to solve this problem? Is the number the same as the number of unknown variables? Explain. Ans. F, D, P, w D2, w P1 Three unknowns exist. Because only two independent material balances can be written for the problem, one value of F, D or P must be specified to obtain a solution. Note that specifying values of w D2 or w P1 will not help.

8. Problems 7.1, 7.11