# Material Balances with Reactors

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

• How to read, set up, and solve a material balance problem on processes that include reactors.

Explanation:

Here, instead of "reinventing the wheel", let's just start with the Solution Process and Notes we established for basic mass balance equations, and make any new notes that apply to reactive systems in red.
I have worked an example for a reactor in which the combustion of two different hydrocarbons take place, click here to see this example.

Solution Process:

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

2. re-read and write flow chart
3. re-write flow chart: if
a-the first flow chart is messy, or
b-if the problem presents a unit conversion exercise, that is, if the 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 and write extents of reaction equations only around reactors, that is, apply this formula for each species, the first written for a single reaction, the second if multiple reactions take place,

ni, leaving the reactor = ni,into the reactor + vi*x

ni, leaving the reactor = ni,into the reactor + Sof all reactions (vi*x)

6. Solve: Fill out table, make use of new reactor interrelations (such as fraction / % excess, fraction / % conversion, selectivity, etc.)
for this reaction, A + B ® C + D, and for the last two relations, consider a second reaction, C + D ® E the formulas would be write as followed

 fraction excess (of A) (moles A Fed - moles A that reacted) = --------------------------------------------------- moles A that reacted fraction conversion (of A) moles A that reacted = --------------------------------------------------- moles A Fed selectivity (of C)(for multiple reactions) moles C that exist after both reactions = --------------------------------------------------- moles C the formed from the first reaction yield (of C)(for multiple reactions) moles C that exist after both reactions = --------------------------------------------------- the moles of A + B + D + E that exist after both reactions
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)

Notes:

• The Mass Balance Equation gives In = Out for all the boundaries, this applies only for non-reactor components and junctions because the number of moles can change going into or out of a reactor. BUT around the reactors, we use extent of reaction equations, which take the In + Generation - Out - Consuption = 0 form of the equation.
• Remember the rules for drawing boundaries on the flow chart: draw a boundary around each of the following:
• Components (eg. distillation column)
• Junction Points
• The Total Process (the compounds that entered this process have rearranged during the reaction to become new compounds, so the compounds that enter the process and what eventually leaves it, are not the same ones).
• In making a table
• The top row labels a column for total material in addition to a column--there is no column for total material in our new table (what entered and what leaves is not the same) 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. With basic material balance problems, we had a choice, now we are dealing with reactions, so we will use MOLE BALANCES exclusively
• Solving simultaneous equations
• Choosing a Basis
• 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:

The reaction between propylene and hydrogen chloride to form propyl chloride is carried out in a continuous reactor. The product stream is analyzed and found to contain 54.9 mole% C3H7Cl and 14.6% HCl. The feed to the reactor contains only propylene and hydrogen chloride. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is 165 mol/s, what is the extent of reaction? (Give its numerical value and its units.)

Example 2:

Methane is burned with air in a continuous steady-state combustion reactor to yield a mixture of carbon monoxide, carbon dioxide, and water. The reactions taking place are

CH4 + 3/2 O2 --> CO + 2H2O
CH4 + 3/2 O2 --> CO2 + 2H2O

The feed to the reactor contains 7.80% CH4, 19.4% O2, and 72.8% N2. The percentage conversion of methane is 90.0%, and the gas leaving the reactor contains 8 mol CO2/mol CO. Calculate the molar composition of the product stream.

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