Material Balance
No Reactors

Upon studying this section, you should be familiar with the following:


This page encompasses all the basic Mass Balance problems, as well as processes that have recycle and bypass streams, but not for processes that include reactors.

Solution Process:

In general, a typical solution process for these types of mass balance problems are as followed:

  1. read problems statement
  2. re-read and write flow chart
  3. re-write flow chart: if
    a-the first flow chart is messy, or
    b-if the problems presents a unit conversion exercise, that is, if given information is in several unit systems, convert all to a consistent unit system on this re-written flow chart
  4. Draw boundaries on flow chart.
  5. Make a table and write balances next to it
  6. Solve: Fill out table, and if necessary, you may need to do one or more of the following:
    a-solve simultaneous equations
    b-choose a basis if the requesting a ratio for an answer (eg. mass fraction)
    c-scale to get subsequent answers
  7. Is your answer reasonable?


  • The Mass Balance Equation gives In = Out for all boundaries.
  • Remember the rules for drawing boundaries on flow chart, draw a boundary around each of the following:
    • Components (eg. distillation column)
    • Junction Points
    • The Total Process
  • In making a table
    • The top row labels a column for total material in addition to a column for each component (and of course, the far left column labels a row for each stream.
    • We can do either mass or mole balances, which ever is more convenient.
  • Solving simultaneous equations
  • Choosing a Basis
  • Scaling the answer
  • For processes that have Recycle and Bypass streams, the solution process is the same, the only new concept is in drawing the stream correctly on the flow charts (and remember, draw a boundary around each junction point).

Example 1:
Three hundred gallons of a mixture containing 75.0 wt% ethanol (ethyl alcohol) and 25% water (mixture specific gravity = 0.877) and a quantity of a 40.0 wt% ethatnol-60 % water mixture (SG = 0.952) are blended to produce a mixture containing 60.0 wt% ethanol. The object of this problem is to determine V40 (the volume of the 40% mixture).

Goto | Check Answer | See Solution

Example #2:
Here, we are given the flow chart. PLACE "MBINTROEX1" HERE. Determine all unknown stream variables, given that the molar flow rate in stream 1 = 1/5 * molar flow rate of stream 2.
Goto | Flow Chart | Boundries and Unique Equations | Table Setup

Example 3: Problem Statement:

A liquid mixture containing 30.0 mole% benzene (B), 25.0 % toluene (T), and the balance xylene (X) is fed to a distillation column. The bottoms product contains 98.0 mole% X and no B, and 96.0% of the X in the feed is recovered in this stream. The overhead product is fed to a second column. The overhead product from the second column contains 97.0% of the B in the feed to this column. The composition of this stream is 94.0 mole% B and the balance T.

    i. Calculate the percentage of benzene in the process feed that emerges in the overhead product stream from the second column.


    ii. Calculated the percentage of toluene in the process feed that emerges in the bottoms product of the second distillation column.

Recycle Example:

Fresh air containing 4.00 mole% water vapor is to be cooled and dehumidified to a water content of 1.70 mole % H2O. A stream of fresh air is combined with recycle stream of previously dehumidified air and passed through the cooler. The blended stream entering the unit contains 2.30 mole % H2O. In the air conditioner, some of the water in the feed stream is condensed and removed as liquid. A fraction of the dehumidified air leaving the cooler is recycled and the remainder is delivered to a room. Taking 100 mol of dehumidified air delivered to the room as a basis of calculation, calculate the moles of fresh feed, moles of water condensed, and moles of dehumidified air recycled.

Goto | Check Answer | See Solution

Bypass Example:

A steam containing 5.15 wt% chromium, Cr, is contained in the wastewater from a metal finishing plant. The wastewater stream is fed to a treatment unit that removes 95% of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above 4500 kg/h> bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon. Waste water leaves the finishing plant at a rate m-dot = 6000 kg/h. Calculate the flow rate of liquid to the waste lagoon, and the mass fraction of Chromium in this liquid.

Goto | Check Answer | See Solution

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