Process Tech 3, Lect 1-4

Why is reaction engineering important?

It is essential for designing and operating reactors safely and efficiently,

and for predicting and controlling reactor productivity.

What main information is needed for reaction engineering?

• Reaction chemistry/biochemistry
• Material and energy flows in/out of the reactor
• Contacting pattern inside the reactor

What role does the reactor play in a chemical process?

It is the centre where materials are chemically transformed into desired products or energy.

The rest of the process

• prepares,

• separates,

• and purifies materials

before and after the reactor.

Give an example of an industrial gas-phase reaction with equilibrium limitations.

N₂ + 3H₂ → 2NH₃

(ammonia synthesis, catalytic, high T & P)

Give an example of a combustion reaction in gas phase.

2C₄H₁₀ + 7O₂ → 2C₄H₂O₃ + 8H₂O

(gas phase, high T, catalytic)

Give an example of a biochemical process involving hydrolysis and fermentation.

Cellulose

(C₆H₁₀O₅)ₙ + H₂O → C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂

What are the main common types of reactors?

• Batch Reactor (BR)
• Mixed Flow Reactor (MFR) / Continuous Stirred Tank Reactor (CSTR)
• Tubular Flow Reactor / Plug Flow Reactor (PFR)

How can reactors be classified based on operation?

• Homogeneous: reactants & products in the same phase (l or g)
• Heterogeneous: reactants & products in different phases (g–l, g–s, l–l, l–s, g–l–s)

Are catalysts commonly used in industry?

Yes, most industrial reactions are carried out in the presence of catalysts.

What is the general form of a single reaction?

aA + bB → cC + dD

or

aA + bB ⇌ cC + dD

Why must stoichiometric coefficients be included in reaction equations?

To ensure the reaction equation is balanced in terms of atoms and mass.

Why might a reactant mixture not match stoichiometric ratios?

Because not all reactants react completely;

some may be limiting or equilibrium-limited,

leading to lower conversion.

What are the main categories of multiple reactions?

• Parallel (e.g. A → D and B → U)
• Series (e.g. A → D → U)
• Combined series/parallel (A → D → U with side paths)

Why is it important to consider all possible reactions in reactor design?

Because side or secondary reactions can affect

• conversion,

• selectivity,

• and yield of desired products.

What does thermodynamics allow us to predict in reaction engineering?

• Energy released/absorbed (enthalpy)
• Maximum yield in equilibrium-limited reactions
• Equilibrium distribution of components between phases
• Effect of T, P, and inerts on equilibrium and enthalpy

In CH4415, which types of reactions are the focus?

Homogeneous (single-phase) reactions

What is a mole?

Exactly 6.022 × 10²³ entities;

number of atoms in 12 g of ¹²C

How do you convert between moles and mass?

By using molecular mass (g/mol or kg/kmol)

What do stoichiometric coefficients represent?

The ratios of molecules consumed/produced and conservation of atoms in a balanced equation

Give an example of balancing a stoichiometric reaction.

N₂ + 3H₂ → 2NH₃

Why might conversion and yield differ from stoichiometric ratios?

Because the feed composition may not match stoichiometry,

Limiting reactants or equilibrium limitations reduce conversion

What is Hess’s Law for enthalpy of reaction?

ΔHᵣ° = Σ(nᵢ ΔHf,ᵢ°)products − Σ(nⱼ ΔHf,ⱼ°)reactants

What does the superscript “°” mean in thermodynamics?

Standard state:

pure compound at 1 bar and specified temperature

What are ΔHᵣ° and ΔHf° called?

ΔHᵣ°: reaction heat (enthalpy of reaction)
ΔHf°: heat of formation

What sign of ΔHᵣ° indicates an exothermic reaction?

ΔHᵣ° < 0

What sign of ΔHᵣ° indicates an endothermic reaction?

ΔHᵣ° > 0

How is enthalpy of reaction at any temperature calculated?

Kirchhoff’s equation:
ΔHᵣ,ᵀ° = ΔHᵣ,298° + ∫₂₉₈ᵀ ΔCₚ dT

What is ΔCₚ?

Difference in molar heat capacities between products and reactants:
ΔCₚ = Σ(nᵢCₚ,ᵢ)products − Σ(nⱼCₚ,ⱼ)reactants

What is the general heat capacity form used?

Cₚ = α + βT + γT²

If each species has Cₚ,ᵢ = αᵢ + βᵢT + γᵢT², how is ΔCₚ expressed?

ΔCₚ = Δα + ΔβT + ΔγT²

What is the integrated Kirchhoff relation with Δα, Δβ, Δγ?

ΔHᵣ,ᵀ° = ΔHᵣ,298° + Δα(T − 298) + (Δβ/2)(T² − 298²) + (Δγ/3)(T³ − 298³)

For which conditions is the enthalpy derivation valid?

Isothermal reactions at 1 bar pressure

When is ΔHᵣ independent of pressure?

For gas-phase reactions where Δn (change in moles) = 0

(e.g. A + B → C + D)

When does ΔHᵣ vary with pressure?

For gas-phase reactions where Δn ≠ 0

(e.g. A → 2B)

Why must phases be specified when calculating ΔHᵣ?

Because enthalpy depends on state

(must include ΔH_vap if phase change occurs)

What is the key property of enthalpy as a thermodynamic function?

It is a state variable:

depends only on state (T, P, phase),

not the path taken

What happens to the reaction quotient as t → ∞?

It approaches a constant value, which is the equilibrium constant K.

Does a reaction stop at equilibrium?

No, the forward and reverse reaction rates are equal at equilibrium.

Can a catalyst change the equilibrium constant K?

No, it only affects the rate at which equilibrium is reached.

Write the general form of the equilibrium constant for a gas-phase reaction aA + bB ⇌ cC + dD.

Kp = (pC^c · pD^d) / (pA^a · pB^b)

What is the relationship between Kc and Kp for ideal gases?

Kp = Kc (RT)^Δn,

where Δn = (c + d) − (a + b)

What is the relationship between Kp for the forward and reverse reactions?

Kp,_rev = 1 / Kp,_fwd

How is equilibrium conversion of a reactant A defined?

XA = (nA,0 − nA) / nA,0 = 1 − [A]/[A]0

How does the magnitude of Ke affect conversion?

Higher Ke ⇒ lower Ae ⇒ higher XA (greater conversion).

What does the van ’t Hoff equation describe?

Temperature dependence of Ke:
d(ln Ke)/dT = ΔHr° / (RT²)

What is the integrated form of the van ’t Hoff equation?

ln(Ke,T2 / Ke,T1) = −ΔHr°/R (1/T2 − 1/T1)

How is Ke related to Gibbs free energy change?

ΔGr° = −RT ln Ke ⇒ Ke = exp(−ΔGr° / RT)

How is ΔGr° calculated from formation data?

ΔGr° = Σ(ni ΔGf,i°)products − Σ(nj ΔGf,j°)reactants

What is the relationship between ΔGr°, ΔHr°, and ΔSr°?

ΔGr° = ΔHr° − TΔSr°

How is ΔSr° calculated?

ΔSr° = Σ(ni Sf,i°)products − Σ(nj Sf,j°)reactants

What is the expression for ln Ke in terms of ΔHr° and ΔSr°?

ln Ke = −ΔHr°/(RT) + ΔSr°/R

When can ΔHr° and ΔSr° values at 298 K be used directly?

When their temperature dependence is weak

How can ΔSr,T° be estimated at higher temperatures?

ΔSr,T° = ΔSr,298° + ∫₂₉₈ᵀ (ΔCp/T) dT = ΔSr,298° + Δα ln(T/298) + Δβ(T − 298) + (Δγ/2)(T² − 298²)

How are equilibrium constants modified for non-ideal systems?

Replace concentrations/pressures with activities or fugacities:
ai = γi[i],

fi = γiPi,

where γi are activity/fugacity coefficients

What is the corrected equilibrium constant in non-ideal systems?

K′ = ΦKe,

where Φ accounts for non-ideality via γi values

Why are reaction kinetics important in reactor design?

They determine

• reactor type,

• size,

• heating/cooling needs,

• efficiency,

• and safety.

Faster rates mean smaller reactors and better process economics.

Define the generation rate of a component i (gi).

It is the rate of formation of component i. Negative for reactants (consumed),

positive for products (formed).

For the reaction aA + bB → cC + dD, how are generation rates related?

−gA/a = −gB/b = gC/c = gD/d

Give the stoichiometric relation example for N₂ + 3H₂ → 2NH₃ when 5 mol N₂ reacts in 1 s.

−gN₂ = 5 mol/s
−gH₂ = 15 mol/s
gNH₃ = 10 mol/s
All give 5 mol/s when divided by stoichiometric coefficients.

How is the reaction rate defined?

−rA = (−gA)/V,

with units mol/(m³·s)

How is reaction rate measured in liquid and gas systems?

• Liquid:

via concentration change d[A]/dt (batch)

or Ain − Aout (continuous)

• Gas:

via pressure change dPA/dt

or PA,in − PA,out

How is reaction rate expressed for heterogeneous reactions?

Per unit volume,

mass,

or surface area of the solid/catalyst.

What factors affect reaction rate?

Temperature,

reactant/product concentrations,

and the presence of a catalyst.

What is the general rate law for a reaction aA + bB → cC + dD?

−rA = k[A]^α [B]^β [C]^γ [D]^δ

What is the Arrhenius equation?

k = A₀ exp(−Ea/RT)

where

A₀ = pre-exponential factor,

Ea = activation energy

What determines the magnitude of the temperature effect on reaction rate?

Activation energy (Ea).

A larger Ea means a stronger effect of temperature.

Give an example of the temperature effect using Ea.

For Ea = 80 kJ/mol, raising T from 323 K to 343 K increases rate ×5.7.
For Ea = 160 kJ/mol, same increase multiplies rate ×32.

How do catalysts affect reactions?

They alter the pathway, lowering Ea, changing A₀ and sometimes orders.

They speed up desired reactions, increase selectivity, or suppress side reactions.

What are reaction orders (α, β, γ, δ)?

Exponents in the rate law showing dependence on concentrations of A, B, C, D. Can be positive, zero, negative, fractional, or integer (<3).

Determined experimentally.

For elementary reactions, what law applies?

Law of mass action:

reaction orders equal stoichiometric coefficients.

Example:

aA + bB → products,

rate = k[A]^a [B]^b

Give examples of elementary reaction rate laws.

A → C + D : −rA = k[A]
2A → C + D : −rA = k[A]²
A + B → C + D : −rA = k[A][B]
A + 2B → C + 3D : −rA = k[A][B]²

What is the rate law for a reversible elementary reaction aA + bB ⇌ cC + dD?

−rA = kf [A]^a [B]^b − kr [C]^c [D]^d

Why do gas-phase reactions sometimes involve volume change?

Because number of gas molecules changes, affecting concentration at constant T, P

(e.g. N₂ + 3H₂ → 2NH₃, Δn = −2).

Define the expansion factor εi.

εi = (VXi=1 − VXi=0) / VXi=0,

describes volume change relative to conversion of species i.

What is the relation between concentration and conversion for reactions with volume change?

[i] = [i]0 (1 − Xi) / (1 + εiXi)
Xi = ( [i]0 − [i] ) / ( [i]0 + εi[i] )

For a constant volume reaction, what is εi?

εi = 0,

so [i] = [i]0(1 − Xi).