# 1. Mole Balances*

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for use, starting with the ones below.

## Topics

1. Chemical Identity
2. Reaction Rate
3. General Mole Balance Equation
4. Mole Balance on Different Reactor Types
5. Self Test Exercises

 Chemical Identity top

A chemical species is said to have reacted when it has lost its chemical identity. The identity of a chemical species is determined by the kind, number, and configuration of that species' atoms.

Three ways a chemical species can lose its chemical identity:

1. decomposition
2. combination
3. isomerization

 Reaction Rate (p.2) top

The reaction rate is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction can be expressed as the rate of disappearance of a reactant or as the rate of appearance of a product. Consider species A:

A B

rA = the rate of formation of species A per unit volume
-rA = the rate of a disappearance of species A per unit volume
rB = the rate of formation of species B per unit volume

Example: A B

If B is being created at a rate of 0.2 moles per decimeter cubed per second, ie, the rate of formation of B is,
rB = 0.2 mole/dm3/s

Then A is disappearing at the same rate:
-rA = 0.2 mole/dm3/s
the rate of formation of A is
rA = -0.2 mole/dm3/s

For a catalytic reaction, we refer to -rA', which is the rate of disappearance of species A on a per mass of catalyst basis.

NOTE: dCA/dt is not the rate of reaction
Is sodium hydroxide reacting?

Consider species j:

• rj is the rate of formation of species j per unit volume [e.g. mol/dm3*s]
• rj is a function of concentration, temperature,pressure, and the type of catalyst (if any)
• rj is independent of the type of reaction system (batch, plug flow, etc.)
• rj is an algebraic equation, not a differential equation

We use an algebraic equation to relate the rate of reaction, -rA, to the concentration of reacting species (e.g., CA) and to the temperature (T) at which the reaction occurs [e.g. -rA = k(T)CA2].

Reaction Video: Sodium with Chlorine

Would you like to see some other rates of reaction?
The Convention for Rates of Reaction

 General Mole Balance Equation (p.6) top

FA0= Entering molar flow rate of A (mol/time)
FA= Exiting molar flow rate of A (mol/time)
GA= Rate of generation(formation) of A (mol/time)
V = Volume (vol e.g. m3)
rA= rate of generation(formation) of A (mole/time•vol)
NA= number of moles of A inside the system Volume V (mols)

How about testing what you've learned?

 Mole Balance on Different Reactor Types (p.25) top

The GMBE applied to the four major reactor types (and the general reaction, A->B):

Reactor Differential Algebraic Integral
Batch
CSTR
PFR
PBR

 Self Test Exercises top

Multiple Choice Questions
Batch Reactor Time
What's wrong with this solution?
Polymath ODE solver tutorial
Polymath NLE solver tutorial
Objective Assessment of Chapter 1

The following movie was made by the students of Professor Alan Lane's chemical reaction engineering class at the University of Alabama Tuscaloosa

* All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .