1. Mole Balances^*

Topics

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

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.

Reaction Video: Carbon Dioxide and Magnesium

Three ways a chemical species can lose its chemical identity:

1. decomposition
2. combination
3. isomerization  
   

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

r_A = the rate of formation of species A per unit volume
-r_A = the rate of a disappearance of species A per unit volume
r_B = 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,
r_B = 0.2 mole/dm³/s

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

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

Is sodium hydroxide reacting?

Consider species j:

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

We use an algebraic equation to relate the rate of reaction, -r_A, to the concentration of reacting species (e.g., C_A) and to the temperature (T) at which the reaction occurs [e.g. -r_A = k(T)C_A²].

Reaction Video: Sodium with Chlorine

Would you like to see some other rates of reaction?

The Convention for Rates of Reaction

F_A0= Entering molar flow rate of A (mol/time)
F_A= Exiting molar flow rate of A (mol/time)
G_A= Rate of generation(formation) of A (mol/time)
V = Volume (vol e.g. m³)
r_A= rate of generation(formation) of A (mole/time•vol)
N_A= number of moles of A inside the system Volume V (mols)

How about testing what you've learned?

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

Reactor	Differential	Algebraic	Integral
Batch
CSTR
PFR
PBR

Multiple Choice Questions

Batch Reactor Time

What's wrong with this solution?

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Visual Encyclopedia

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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 .

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