RMP Lecture Notes

Reacting Systems

Most Chemical Engineering systems involve some sort of chemical reaction. Including reactions in material balance calculations is not hard, but it does complicate things -- you now have to worry about the "production" and "consumption" terms.

Stoichiometry describes the proportions in which chemical species combine.

is a stoichiometric equation for the combustion of methane -- it tells you the relative number of molecules or moles involved: "1 mole methane combines with 2 moles oxygen to make 1 mole carbon dioxide and 2 moles water".

All stoichiometric equations can be represented generically as:

The numbers which quantify the amounts (a,b,c,d, nu) are called stoichiometric coefficients. An even more general form that is often used in reaction studies is: Generic

where the stoichiometric coefficients for reactants are defined as negative, those for products as positive.

Valid stoichiometric equations are balanced -- the number of atoms of each species are the same on both sides (atoms cannot be created or destroyed!). For methane combustion:

The stoichiometric ratio of two components is the ratio of the stoichiometric coefficients in the balanced equation.

You have probably used these in simple problems. For instance, if you are asked "how many kilograms of oxygen are needed to produce 10 kgmoles of CO₂?" Stoich Ratio Example

If the exact amounts needed for a balanced reaction are present, we say we have stoichiometric proportions or stoichiometric amounts. So if I have a sample with 1 mole methane and 1 mole oxygen, they are not in stoichiometric amounts.

If a reaction "proceeds to completion" and if all reactants are present in stoichiometric amounts, all reactants are consumed. WARNING: In this class, most problems will not go to completion, so do not assume they do unless there are good indicators in the problem statement.

So let's consider some cases where the feed to a reactor is not in stoichiometric amounts. Many (if not most) reactions take place sort of slowly, consequently they do not proceed to completion. Hence, there are usually reactants left unconsumed.

What if you had 1 mole CH₄ and 3 moles O₂ and the reaction went to completion? You'd have 1 mole of CO₂, 2 moles of water, and 1 mole of left over oxygen.

In this case, oxygen is said to be an excess reactant or "in excess". Often, we indicate amount in excess as a fraction or percentage:

Now consider the similar case where you have a reaction

and started with 1 mole A, 5 moles B, and 5 moles C. What would you get if the reaction went to completion? 1 mole D, 2 moles E, and excess B and C. The amount produced is limited by the available A, so A is said to be the limiting reactant.

A reactant is limiting if it is present in less than stoichiometric amounts with respect to all other reactants. You can also think of it as the reactant that is used up first (although this isn't necessarily strictly true).

Conversion

We've argued that reactions don't routinely proceed to completion, and defined the ideas of excess and limiting reactants as a way of keeping track. Another very important measure is conversion:

EXAMPLE: Antimony production

Himmelblau (1974) Example 1.25, p. 47 Antimony is obtained by heating stibnite ore (Sb₂S₃) with Iron, and drawing off the molten product.

0.600 kg of stibnite and 0.250 kg of iron are heated to give 0.200 kg of metallic antimony. Calculate (a) the limiting reactant, (b) the percentage excess reactant, and (c) the percent conversion.

A key part of understanding the problem is to make sure the equation is correct, so balance it to obtain

Reacting problems should normally be workied in mole units, so calculate the mols of each reactant

and use the stoichiometric ratio to see which reactant is present in less than the stoichiometric amount find limiting

There isn't enough iron present for all the stibnite to react, so iron is the limiting reactant.

Since iron is limiting, stibnite is excess. First calculate how much stibnite is required to use up all the iron (the stoichiometric amount for the excess calculation)

and use this to determine the percentage excess excess

To calculate the conversion, we first have to calculate the amount of stibnite actually consumed (which will be the same as the stibnite fed only if the reaction goes to completion). It's probably easiest to do this working backward from the antimony produced.

The conversion is the ratio of moles reacted to moles fed, so

Multiple Pass Systems

How should we define conversion for recycle or bypass systems?

Two definitions are needed: (1) the overall conversion, defined for the whole system

and (2) the single pass conversion, defined for the reactor by itself

References:

Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2nd Edition, John Wiley, 1986, pp. 118-24, 134-35.
Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2005 3rd Edition, 2005, p. 116-18, 120-21, 135-38.
Himmelblau, D.M., Basic Principles and Calculations in Chemical Engineering, 6th Edition, Prentice-Hall, 1996, pp. 212-14.

R.M. Price
Original: 6/14/94
Modified: 9/23/96; 1/6/2005