ChE 452 Lecture 02

Basic Concepts

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Stoichiometry

Invented by Lavoisier Molecules react in fixed proportions

1 A + 2B 3C+ 4D Stoichiometric Coefficent, n

Number of molecules produced when reaction goes once

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3311 ,

Example

2CO + O2 2CO2

CO + ½ O2 CO2

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Answer

Answer

Reaction Rate

Priestley Total Moles/hr

Van’t Hoff Moles/hr/volume

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Priestley’s Experiment

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Changing the amount of powder did not change the rate of weight loss

Van’t Hoff’s Experiments

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2N2O5 4NO2 + O2

Reaction rate scaled as the volume of the reactor

Special poisoned walls

Reaction Rate

production rate (Moles/hr) reactor volume (liter)

• rA called the Rate of production of A

• rA has dimensions moles/lit-hr

• rA is positive for a product, negative for a reactant

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A

r

r

Heterogeneous Reactions Scale As Surface Area

production rate (Moles/hr) surface area (cm2)• RA is also called the Rate of

production of A• RA has dimensions moles/cm2 –hr

• RA is positive for a product, negative for a reactant

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AR

The Rate Of A Reaction

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r riA

A1

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.

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Variations In RateWith 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

1012 or more) The presence of catalysts (factors of

1012 or more)

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General Effect Of Concentration

Rate for homogeneous reactions goes up with concentration

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1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+51E-8

1E-6

1E-4

1E-2

1E+0

1E+2

Pressure, Torr

Rat

e, T

orr/

sec

Slope=2

Slope=1

Figure 2.3 The rate of CH3NC isomerization to CH3CN as a function of

the CH3CN pressure

Rate Of Heterogeneous Reactions Often Shows A

Maximum

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1012

1013

10-6

Ra

te, M

ole

cule

s/cm

-se

c2

1011

10-7

10-8

10-6

CO pressure, torr10

-710

-8

O pressure, torr2

390 K

410 K415 K

450 K450 K

440 K440 K

425 K

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

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Typical Rate Laws For Simple A C Reactions:

rA = -k (CA) First order

rA = -k (CA)2 Second order

rA = -k (CA)3 Third order

rA = -k (CA)n nth order

n is the orderk is the rate constant

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Rate Equations ForA + B C

rA = -k (CA)n(CB)m

nth order in A, mth order in Boverall (m+n)th order

rA = -k(CA)(CB)2

First order in A, second order in B, third

order overall.

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(2.13)

Notation

k1, k2 rate constants

K1, K2 equilibrium constants

CA=[A] concentration of species A

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Discussion Problem 1

What is the order of reaction?

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CA

Moles/Liter

rateMoles/Lit/

Min

CA

Moles/Liter

rateMoles/Lit/

Min

0.25 0.13 1 0.5

0.5 0.25 2 1.0

Answer

Discussion Problem 2

What is the order of the reaction?

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CA

moles/liter

CB

moles/liter

ratemoles/

liter-min

CA

moles/liter

CB

moles/liter

ratemoles/

liter-min

1 0.25 0.031 0.25 1 0.13

1 0.5 0.13 0.5 1 0.25

1 1 .5 1 1 0.5

1 2 2.0 2 1 1.0

Answer

More Complex Rate Equations

• Very few real reactions have simple reaction orders over a wide range of conditions:

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[Sugar])K(1

Sugar E..ColiKkr

2

21ecoli

(2.18)

More Complex Rate Equations

CH3NC CH3CN

No industrially important reaction is first order over a wide range of

conditions. 25

1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+51E-8

1E-6

1E-4

1E-2

1E+0

1E+2

Pressure, Torr

Rat

e, T

orr/

sec

Slope=2

Slope=1

Figure 2.3 The rate of CH3NC isomerization to CH3CN as a function of

the CH3CN pressure

Rate Equation Not Simply Related To Stoichiometry

]Br[[HBr]

K + 1

]Br][H[k = r

2

2

221

HBr

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HBr2BrH 22

(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.

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Not All Reactions Have Rate Equations

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500 700 900300

1012

1014

Rat

e, M

olec

ule

s/cm

-se

c2

1011

1013

Temperature, K

Figure 2.22 2CO+O22 CO2

On ruthenium

0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time, seconds

Con

cent

ratio

n

Figure 2.23 Belousov-Zhabotinskii Reaction

Summary For Today

Table 2.1 Summary of key definitions

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Stoichiometric coefficient

The amount of product produced when the reaction goes once. The stoichiometric coefficient is positive for a product and negative for a reactant.

rA1 The net rate of production of a species A. rA is positive for a product and negative for a reactant.

Rate of reaction 1, r1 for any species participating in reaction1.

Homogeneous reaction

A reaction which happens throughout the reacting phase.

Heterogeneous reaction

A reaction which happens near the boundary of a reacting phase.

Summary For Today

Table 2.4 The key definitions from Section 2.3.

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Rate equation The rate as a function of the concentration of the reactants.

Order The exponent n in the rate equation.

First order reaction A reaction whose rate is proportional to the reactant concentration to the first power (i.e. n = 1 in eqn. (2.11)).

Second order reaction A reaction whose rate is proportional to the reactant concentration to the second order.

Overall order The 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.

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Class Question

What did you learn new today?

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