ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY Lecturer: Miss Anis Atikah Ahmad Email: anisatikah@unimap.edu.my Tel: +604 976 3245

Outline PART 1: Rate Laws PART 2: Stoichiometry Relative Rates of Reaction Reaction Order & Rate Law Reaction Rate Constant, k PART 2: Stoichiometry Batch System Stoichiometric Table Flow System Stoichiometric Table Calculation for Concentration in terms of Conversion

1. Relative Rates of Reaction Reaction Stoichiometry EXAMPLE If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s), what is the rate of formation of NO?

1. Relative Rates of Reaction If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s), what is the rate of formation of NO?

1. Relative Rates of Reaction EXERCISE The Reaction: is carried out in a reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm3/s, what are the rates of B and C?

1. Relative Rates of Reaction The relative rates are Given, the rate of disappearance of A, -rA, is 10mol/dm3/s Thus, solving the rates of B & C; r A= -10 mol/dm3/s

2. Reaction Order & Rate Law Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration. The reaction rate (rate of disappearance) depends on temperature and composition. It can be written as the product of reaction rate constant, kA and a function of concentrations (activities) of the reactants involved in the reaction:

2. Reaction Order & Rate Law Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration. For reaction in which the stoichiometric coefficient is 1 for ALL species: we shall delete the subscript on the specific reaction rate, (e.g.; A in kA) to let

2.1 Power Law Models & Elementary Rate Laws The rxn is 𝛂 order wrt reactant A AND The rxn is 𝛃 order wrt reactant B The overall order of the reaction, n;

2.1 Power Law Models & Elementary Rate Laws The unit of the specific reaction, k, will vary with the order of reaction. Products Zero order (n=0) First order (n=1) Second order (n=2) Third order (n=3)

2.1 Power Law Models & Elementary Rate Laws Elementary reaction: a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state. Elementary rate law: The rxn is said to follow the elementary rate law if the stoichiometic coefficients are IDENTICAL to the reaction order of each species. Products Unimolecular reaction Products Bimolecular reaction Non-elementary rxn But follows the elementary rate law!

Examples of Reaction Rate Laws

Examples of Reaction Rate Laws

Examples of Reaction Rate Laws

2.2 Non-Elementary Rate Laws Non-elementary rate laws: reactions that do not follow simple rate laws (power rate laws). Example 1: Homogeneous Rxn The kinetic rate law is: Rxn order: first order wrt to CO, three-halves order wrt Cl2, five-halves order overall. Gas phase synthesis of phosgene

2.2 Non-Elementary Rate Laws Gas-solid catalyzed rxn: Hydrodemethylation of toluene (T) Example 2: Heterogeneous Rxn The rate of disappearance of toluene per mass of catalyst is: where KB & KT is the adsorption constants. In terms of partial pressure rather than concentrations

Thermodynamic Equilibrium Relationship 2.3 Reversible Reactions ⇌ For reversible rxn, all rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium. Thermodynamic Equilibrium Relationship

⇌ ⇌ ⇌ 2.3 Reversible Reactions The rate of disappearance of benzene; EXAMPLE: combination rxn of 2 mol of benzene to form 1 mol H2 and 1 mol diphenyl. kB ⇌ k-B kB ⇌ symbolically; k-B The rate of disappearance of benzene; OR The reverse rxn btween diphenyl & hydrogen; k-B ⇌ The rate of formation of benzene (in reverse direction);

2.3 Reversible Reactions The net rate of formation of benzene is; Multiplying both sides by -1, we obtain the rate law of disappearance of benzene, -rB

2.3 Reversible Reactions Replacing the ratio of the reverse & forward rate law constant by equilibrium constants; where Concentration equilibrium constant

3. The Reaction Rate Constant Arrhenius equation A= preexponential factor or frequency factor E= activation energy, J/mol or cal/mol R=gas constant = 8.314 J/mol-K = 1.987 cal/mol-K T= absolute temperature, K -no of collision -probability that the collision will result in a reaction

3. The Reaction Rate Constant Activation energy is a measure of the minimum energy that the reacting molecules must have in order for the reaction to occur (energy required to reach transition state). Transition state - no of collision that result in a rxn Energy barier -total no of collision probability that - the collision will result in a rxn Reactants Products

3. The Reaction Rate Constant Taking a natural logarithm; The larger the activation energy, the more temperature sensitive k and thus the reaction rate. E ⬆, k ⬆, -r = ⬆

4. Batch Systems Stoichiometric Table Purpose of developing stoichiometric table: To determine the no of moles of each species remaining at a conversion of X.

4. Batch Systems Stoichiometric Table refers to moles of species reacted or formed Components of stoichiometric table: Species Initially (mol) Change (mol) Remaining (mol) A B C D I Totals

4. Batch Systems Stoichiometric Table aA + bB  cC + dD Recall from Chapter 2: Factorizing; moles of A reacted moles of A remaining in the reactor at a conversion of X

4. Batch Systems Stoichiometric Table Moles B reacted, NB Moles B reacted Moles A reacted Moles A reacted Moles C formed, NC Moles D formed, ND

4. Batch Systems Stoichiometric Table moles B remaining in the system, NB moles of B reacted moles of B initially in the system NC moles of C formed ND moles of D formed

4. Batch Systems Stoichiometric Table Species Initially (mol) Change (mol) Remaining (mol) A B C D I - Totals

4. Batch Systems Stoichiometric Table Total no of moles per mole of A reacted can be calculated as: where Change in the total number of moles per mole of A reacted

4. Batch Systems Stoichiometric Table Can we express concentration of each species?? Species Initially Change Remaining Concentration A B C D I Totals

4. Batch Systems Stoichiometric Table Concentration of each species in terms of conversion can be expressed as: Recall from stoichiometric table Remaining (mol) A B C D

4. Batch Systems Stoichiometric Table

4. Batch Systems Stoichiometric Table

4. Batch Systems Stoichiometric Table Species Initially Change Remaining Concentration A B C D I -

4. Batch Systems Stoichiometric Table Species Initially Change Remaining Concentration A B C D I -

4. Batch Systems Stoichiometric Table EXAMPLE Given the saponification for the formation of soap from aqueous caustic soda & glyceryl stearate is: Letting X the conversion of sodium hydroxide, set up a stoichiometric table expressing the concentration of each species in terms of its initial concentration and the conversion.

4. Batch Systems Stoichiometric Table EXAMPLE We know that this is a liquid-phase reaction. Therefore, V=V0

4. Batch Systems Stoichiometric Table EXAMPLE Species Initially Change Remaining Concentration A B C D I - Total

5. Flow Systems Stoichiometric Table Purpose of developing stoichiometric table: To determine the effluent flow rate of each species at a conversion of X.

5. Flow Systems Stoichiometric Table Components of stoichiometric table: Species Feed rate to reactor (mol/time) Change within the reactor (mol/time) Effluent rate from reactor (mol/time) A B C D I Totals

5. Flow Systems Stoichiometric Table Species Feed rate to reactor (mol/time) Change within the reactor (mol/time) Effluent rate from reactor (mol/time) Concentration (mol/L) A B C D I - Totals

QUIZ 5 Given a liquid phase reaction: A+ 2B  C + D The initial concentration of A and B are 1.8 kmol/m3 and 6.6 kmol/m3 respectively. Construct a stoichiometric table for a flow system considering A as the basis of calculation.

Answer For Quiz 5 A+ 2B  C + D Given: From stoichiometry, we know that, Since C & D are products.

Answer for quiz 5 A B C D Totals Species Feed rate to reactor (mol/time) Change within the reactor (mol/time) Effluent rate from reactor (mol/time) A B C D Totals

Answer for quiz 5 Substituting the numerical values; A B C D Totals Species Feed rate to reactor (mol/time) Change within the reactor (mol/time) Effluent rate from reactor (mol/time) A B C D Totals

6. Concentration in terms of conversion 1. For liquid phase: Batch System:

6. Concentration in terms of conversion 1. For liquid phase: Flow System -

6. Concentration in terms of conversion 2. For gas phase: Batch System Need to substitute V from gas law equation From equation of state; At any time t, At initial condition (t=0) T= temperature, K P= total pressure, atm (1 atm= 101.3 kPa) Z= compressibility factor R= gas constant = 0.08206 dm3-atm/mol-K (1) (2)

6. Concentration in terms of conversion 2. For gas phase: Batch System Dividing (1) by (2); (1) (2) Recall from stoichiometric table (4) (3) Dividing (4) by NT0 ;

6. Concentration in terms of conversion 2. For gas phase: Batch System Applies for both batch and flow systems Will be substitute in (3) Rearranging; At complete conversion (for irreversible rxn): X=1, NT=NTf

6. Concentration in terms of conversion 2. For gas phase: Batch System Substituting the expression for NT/NT0 in (3), (3) If the compressibility factor are not change significantly during rxn, Z0⩳Z (5)

6. Concentration in terms of conversion 2. For gas phase: Flow System Need to substitute υ from gas law equation From gas law, at any point in the reactor, At the entrance of reactor; (1) (2) Dividing (1) by (2) (3)

6. Concentration in terms of conversion 2. For gas phase: Flow System Substituting for FT; Recall from stoichiometric table (4)

6. Concentration in terms of conversion 2. For gas phase: Flow System Substituting υ & Fj; Need to substitute υ from gas law equation (5) (4) Stoichiometric coefficient (d/a, c/a, -b/a, -a)

6. Concentration in terms of conversion 2. For gas phase: Flow System Concentration for each species: aA + bB  cC + dD

Summary Relative rate of reaction: Power Law Model:

Summary Elementary rate law: The rxn that in which its stoichiometic coefficients are IDENTICAL to the reaction order of each species. Non-elementary rate laws: The reactions that do not follow simple rate laws (power rate laws) in which its stoichiometic coefficients are NOT IDENTICAL to the reaction order of each species. Reversible reaction: All rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium. Power Law Model:

Summary E ⬆, k ⬆, -r ⬆ Reaction Rate Constant, k The larger the activation energy, the more sensitive k is, (towards the change in temperature)

Summary Stoichiometric Table for Batch Systems A B C D I - Species Initially Change Remaining A B C D I -

Summary Stoichiometric Table for Flow Systems A B C D I - Totals Species Feed rate to reactor (mol/time) Change within the reactor (mol/time) Effluent rate from reactor (mol/time) A B C D I - Totals

Summary Expression of V and υ in calculating the concentration of each species: Batch systems Liquid phase: Gas phase: Flow systems

Quiz 6 Derive a concentration for each species for the isothermal gas phase reaction below, neglecting the pressure drop: A + B  C