Mole Balance and Stoichiometry Theory

What is the general mole balance for any species j?

\text{Accumulation} = \text{In} - \text{Out} + \text{Generation}

What is the steady-state mole balance?

0 = \text{In} - \text{Out} + \text{Generation}

For which reactor types is the mole balance valid?

Batch reactors, CSTRs, and PFRs under steady or unsteady state

What is the general reaction used for stoichiometric analysis?

aA + bB \rightarrow cC + dD

What is the definition of extent of reaction?

\xi measures the progress of reaction based on stoichiometry

What are the initial moles for a general reaction?

n{A,0}, \; n{B,0}, \; n{C,0}=0, \; n{D,0}=0

How are mole changes written using extent of reaction?

\Delta nA = -a\xi \Delta nB = -b\xi
\Delta nC = +c\xi \Delta nD = +d\xi

How are final moles written in terms of extent of reaction?

nA = n{A,0} - a\xi
nB = n{B,0} - b\xi
nC = c\xi

nD = d\xi

How is the limiting reactant identified?

\min\left(\frac{n{A,0}}{a}, \frac{n{B,0}}{b}\right)

What does the limiting reactant determine?

Maximum possible conversion

For which species is conversion defined?

The limiting reactant

What is the definition of conversion of A?

XA = \frac{n{A,0} - nA}{n{A,0}}

How is extent of reaction related to conversion?

\xi = \frac{n{A,0} XA}{a}

a is the stoichiometric coefficient of limiting reactant A

Why is conversion preferred as a variable?

X_A \text{ is dimensionless and reactor-independent}

How are moles of limiting reactant written in terms of conversion?

nA = n{A,0}(1 - X_A)

How are moles of non-limiting reactant B written in terms of conversion?

nB = n{B,0} - \frac{b}{a} n{A,0} XA

How are moles of product C written in terms of conversion?

nC = n{C,0} + \frac{c}{a} n{A,0} XA

How are molar flowrates written for flow reactors?

FA = F{A,0}(1 - XA) FB = F{B,0} - \frac{b}{a}F{A,0}X_A

What is the key stoichiometric principle for all species?

\text{All quantities are written relative to the limiting reactant}

How is concentration written for liquid-phase reactions with constant volume?

CA = C{A,0}(1 - X_A)

Why is this concentration expression valid in liquids?

V = \text{constant}

Why do gas-phase concentrations require correction?

V \neq \text{constant}

What causes volume change in gas-phase reactions?

Change in moles, temperature, or pressure

What is the gas-phase concentration expression with volume change?

CA = C{A,0}\frac{1 - XA}{1 + \varepsilon XA}

What does the expansion factor ε represent?

\varepsilon = \frac{V{X=1} - V{X=0}}{V_{X=0}}

Why do gas-phase concentrations not vary linearly with conversion?

V = V(X_A)

Why must stoichiometry be done before kinetics?

-rA = f(CA), \quad CA = f(XA)

What is the correct order of reactor problem solving?

Stoichiometry → Concentrations → Rate law → Reactor design equation

What is a common stoichiometric error to avoid?

Forgetting to divide by the stoichiometric coefficient of the limiting reactant

What notation mistake commonly causes errors?

Mixing batch moles 𝑛𝑖 with flowrates 𝐹𝑖

One-sentence exam definition of stoichiometry and mole balances

Stoichiometry and mole balances allow all species amounts, concentrations, and flowrates to be written in terms of conversion, forming the foundation of reactor design calculations