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Integral Method

Guess

AAA Ckr Insert to design

equation AA r

dt

dC

AAA Ck

dt

dC

AAA Ckr

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Integral Method

Integrate and

linearize AoACktC lnln

Obtain

Experimental Data

EXPERIMENTAL DATA

Time CA

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Integral Method

Fit Data

time, t

lnCA

Check goodness

of fit

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Integral Method

Fractional Conversion

Fraction of any reactant that is converted to

another form.

Another form of reporting the extent of

reaction

Simplifies analysis in some particularsituations

Denoted as XA

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Integral Method

Ao

AAoA

N

NNX

Ao

A

N

N

1

V

V1

1

Ao

A

C

C1

Ao

AA

dN

dNdX

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Integral Method

Empirical Reactions of nth Order

When the reaction mechanism is unknown,

we often attempt to fit the data with an nth-

order rate equation of the form:

n

AA

A kCdt

dCr

ktnCC nAon

A 111

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Integral Method

General Strategy:

1. Guess a value of n

2. Fit experimental data to linearized plot

3. If fit is good, determine the value of kA from the

slope

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Integral Method

Notes:

1. Equation is not valid for n = 1

2. For n > 1, complete conversion (CA=0) is

theoretically at t = .

3. For n < 1, complete conversion (CA=0) can be

predicted at some finite time, equal to:

A

n

Ao

kn

Ct

1

1

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Integral Method

n nth order integrated/ linearizedequation

time(t) for CA = 0 of for XA= 1

n1

2 Not defined

3 Not defined

222 AoAA CtkC

AoAACtkC

11 AoAA CtkC

22 2 AoAA CtkC

AAo kCt 22

AAokCt

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Integral Method

1. Half-life method

2. Fractional life method

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Integral Method

Half-Life

For an nth order reaction not equal to 1:

Linearizing:

n

Ao

A

n

Cknt

1

1

21

'1

15.0

A

n

Aokn

Cnt'1

15.0lnln1ln

1

21

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Integral Method

Run:

CAo

t1/2

1

CAo1

(t1/2)1

2

CAo2

(t1/2)2

3

CAo3

(t1/2)3

4

CAo4

(t1/2)4

CAo

CAo1/2

t1/2

lnt1/2

ln CA

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Integral Method

Fractional Life Method

Concentration of reactant drops to a certain

fractional value F = CA

/CAo

.

n

Ao

A

n

F C

kn

Ft

1

1

'1

1

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Integral Method

Variations of the method

Method of excess

Where: = kACBo (B, others in large excesses)

BAAA CCkdt

dC

AA

A

Ckdt

dC

Ak

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Integral Method

Analysis of total pressure data

Applicability:

Exact stoichiometry is known

Only one equation is involved in the reaction

n

aPP ToTAoA

n

rPP ToTRoR