ChE 452 Lecture 02 Basic Concepts 1

Stoichiometry Invented by Lavoisier Molecules react in fixed proportions  1 A +  2 B   3 C+  4 D Stoichiometric Coefficent,  n  Number of molecules produced when reaction goes once 2

Example 2CO + O 2  2CO 2 CO + ½ O 2  CO 2 3 Answer

Solution 1 2CO + O 2  2CO 2 4 ß CO = -2, ß O 2 = -1, ß CO 2 = 2

Solution 2 CO + ½ O 2  CO 2 5 ß CO = -1, ß O 2 = -1/2, ß CO 2 = 1

Reaction Rate Priestley Total Moles/hr Van’t Hoff Moles/hr/volume 6

Priestley’s Experiment 7 Changing the amount of powder did not change the rate of weight loss

Van’t Hoff’s Experiments 8 2N 2 O 5  4NO 2 + O 2 Reaction rate scaled as the volume of the reactor Special poisoned walls

Reaction Rate production rate (Moles/hr) reactor volume (liter) r A called the Rate of production of A r A has dimensions moles/lit-hr r A is positive for a product, negative for a reactant 9

Heterogeneous Reactions Scale As Surface Area production rate (Moles/hr) surface area (cm 2 ) R A is also called the Rate of production of A R A has dimensions moles/cm 2 –hr R A is positive for a product, negative for a reactant 10

The Rate Of A Reaction 11

Heterogeneous vs. Homogeneous Reactions Homogeneous Reaction A reaction which happens throughout the reacting phase. Heterogeneous reaction A reaction which happens near the boundary of a reacting phase. 12

Variations In Rate With Conditions Rates vary with: Concentrations of all species (reactants, products, inerts) (factors of 2-100) Temperature (factors of 100 or more) The presence of solvents (factors of or more) The presence of catalysts (factors of or more) 13

General Effect Of Concentration Rate for homogeneous reactions goes up with concentration 14 Figure 2.3 The rate of CH 3 NC isomerization to CH 3 CN as a function of the CH 3 CN pressure

Rate Of Heterogeneous Reactions Often Shows A Maximum 15 Figure 2.15 The influence of the CO pressure on the rate of CO oxidation on Rh(111). Data of Schwartz, Schmidt, and Fisher.

Rate Equations Rate as a function of the concentration of all of the species in the reactor 16

Typical Rate Laws For Simple A  C Reactions: r A = -k (C A )First order r A = -k (C A ) 2 Second order r A = -k (C A ) 3 Third order r A = -k (C A ) n nth order n is the order k is the rate constant 17

Rate Equations For A + B  C r A = -k (C A ) n (C B ) m nth order in A, mth order in B overall (m+n)th order r A = -k(C A )(C B ) 2 First order in A, second order in B, third order overall. 18 (2.13)

Notation k 1, k 2 rate constants K 1, K 2 equilibrium constants C A =[A] concentration of species A 19

Discussion Problem 1 What is the order of reaction? 20 C A Moles/Liter rate Moles/Lit/Min C A Moles/Liter rate Moles/Lit/Min Answer

Discussion Problem 1 Answer What is the order of reaction? Answer: rate doubles as concentration doubles  first order in A 21 C A Moles/Liter rate Moles/Lit/Min C A Moles/Liter rate Moles/Lit/Min

Discussion Problem 2 What is the order of the reaction? 22 C A moles/liter C B moles/liter rate moles/liter -min C A moles/liter C B moles/liter rate moles/liter- min Answer

Discussion Problem 2 Answer Answer: Rate goes up by 4 times when B doubles  Second order in B Rate goes up by 2 times when A doubles  First order in A Overall order = = 3 23 C A moles/liter C B moles/liter rate moles/liter -min C A moles/liter C B moles/liter rate moles/liter- min

More Complex Rate Equations Very few real reactions have simple reaction orders over a wide range of conditions: 24 (2.18)

More Complex Rate Equations CH 3 NC  CH 3 CN No industrially important reaction is first order over a wide range of conditions. 25 Figure 2.3 The rate of CH 3 NC isomerization to CH 3 CN as a function of the CH 3 CN pressure

Rate Equation Not Simply Related To Stoichiometry 26 (2.21)

ChBE424 Assumed First Or Second Order Reactions Why does this work? Usually reactors run under a limited range of conditions – fitting rate to a line or parabola often good enough Rate changes with temperature or catalysts much larger than changes with concentration. 27

Not All Reactions Have Rate Equations 28 Figure CO+O 2  2 CO 2 On ruthenium Figure 2.23 Belousov-Zhabotinskii Reaction

Summary For Today Table 2.1 Summary of key definitions 29 Stoichiometric coefficientThe amount of product produced when the reaction goes once. The stoichiometric coefficient is positive for a product and negative for a reactant. r A1 The net rate of production of a species A. r A is positive for a product and negative for a reactant. Rate of reaction 1, r 1 for any species participating in reaction1. Homogeneous reactionA reaction which happens throughout the reacting phase. Heterogeneous reactionA reaction which happens near the boundary of a reacting phase.

Summary For Today Table 2.4 The key definitions from Section Rate equationThe rate as a function of the concentration of the reactants. OrderThe exponent n in the rate equation. First order reactionA reaction whose rate is proportional to the reactant concentration to the first power (i.e. n = 1 in eqn. (2.11)). Second order reactionA reaction whose rate is proportional to the reactant concentration to the second order. Overall orderThe sum of the orders for each of the reactants.

Summary For Today Real reactions rarely follow simple rate laws over wide ranges of conditions. Simple rate laws OK if the range of conditions small Some reactions do not have a rate law. 31

Class Question What did you learn new today? 32