conservation of mass (review) 1 living with the lab if chemical reactions occur, new system components may be generated... while others are consumed accumulation of mass in the system © 2011 David Hall

batch & rate problems 2 living with the lab BATCH - start with nothing in system & end with nothing in system RATE – continuous flow of inputs and outputs 1.steady state – the amount or type of mass in the system does not change with time 2.non steady state – the amount or type of mass in the system changes with time

3 living with the lab 1.Draw a picture of the system. Sometimes it’s not easy to determine the boundaries of your system. (a large river flowing into the ocean for example... where does river end and ocean begin?) 2.Label all inputs and outputs, listing all known quantities & concentrations and assigning variables to the unknowns. This key step is where errors usually occur. 3.Think about the problem a little bit... determine if the process is a rate or batch problem. Are components generated or consumed? Revise (1) and (2) if needed. 4.Write conservation of mass (or weight) for each component and for the entire system. Modify the diagram as new information is uncovered. 5.Solve for the unknowns. 6.Reflect on your solution. Do the concentrations or quantities make sense? problem solving tips WARNING avoid trying to just solve these problems in your head... use the systematic approach above

paper machine problem A paper mill has equipment that uses heat, chemicals, and mechanical forces to break wood chips down into wood fibers that are used to make paper. The wood fibers and other ingredients are mixed with water to form “stock,” a wet mixture that contains 99.5% water and 0.5% dry material. The stock is first discharged onto a moving “wire” that is made of woven brass or bonze cloth that may be traveling at 2,000 feet per minute. The moving wire passes over several rolls were water is drained or sucked from the forming sheet. When the wire passes over the final roll, which is called the “couch roll,” it contains 82% water. The paper is then transferred to a traveling woolen felt where it passes through several presses, reducing the water content to 72%. The paper, which can then support its own weight, passes into the long dryer section where the paper winds around a large number of heated drums. When the paper exits the dryer section, the final concentration of water is 3% by weight. Class Problem: If 1000 lbs. of paper is produced each minute, then find the rates of water removed from the wire, felt and dryer sections as well as the total rate of water and solids that enter the system at the wire section. 4 living with the lab

paper machine problem 5 living with the lab wirefeltdryer stock water paper water headbox (stock dumped on moving wire) wire felt dryer section

solution 6 living with the lab wirefeltdryer water paper water label all known concentrations stock assign variables to unknown mass flow rates label any know mass flow rates solve for unknown flow rates: (1) dryer (2) felt (3) wire (4) overall