Chemical Reaction Engineering Asynchronous Video Series Chapter 7, Part 1: PSSH Enzyme Kinetics H....

Chemical Reaction Engineering

Asynchronous Video Series

Chapter 7, Part 1:

PSSH

Enzyme Kinetics

H. Scott Fogler, Ph.D.

Active Intermediates/Free Radicals


Mechanism:

€

r1NO 3* = k1CNOCO2


Mechanism:

€

r2NO 3* = −k 2CNO 3

*

€

r1NO 3* = k1CNOCO2


Mechanism:

€

rNO2= k3CNO 3

* CNO

€

r2NO 3* = −k 2CNO 3

*

€

r1NO 3* = k1CNOCO2


Mechanism:

€

r2NO 3* = −k 2CNO 3

*

€

r1NO 3* = k1CNOCO2

€

rNO2= k3CNO 3

* CNO

€

r3NO2

Pseudo Steady State Hypothesis (PSSH)A* is an active intermediate that is highly reactive. It disappears as fast as it is formed.

€

rA*net

=0


€

rNO3

* =r1NO3

* +r2NO3

* +r3 NO3

*

€

rA*net

=0


€

rNO3

* =r1NO3

* +r2NO3

* +r3 NO3

*

€

rA*net

=0

€

r1NO3

* =k1 NO( ) O 2( )

r2NO3

* = −k 2 NO 3*

( )


€

rNO3

* =r1NO3

* +r2NO3

* +r3 NO3

*

€

rA*net

=0

€

r3NO3

* = −r3 NO2

2= −

k 3

2NO 3

*( ) NO( )

€

r3NO 3

*

−1 =r3NO 2

2

€

r1NO3

* =k1 NO( ) O 2( )

r2NO3

* = −k 2 NO 3*

( )


€

rNO3

* =r1NO3

* +r2NO3

* +r3 NO3

*

€

rA*net

=0

€

r3NO3

* = −r3 NO2

2= −

k 3

2NO 3

*( ) NO( )

€

r3NO 3

*

−1 =r3NO 2

2

€

k1 NO[ ] O 2[ ]− k 2 NO3*

( ) −k 3

2NO 3( ) NO( ) = 0

€

r1NO3

* =k1 NO( ) O 2( )

r2NO3

* = −k 2 NO 3*

( )

Pseudo Steady State Hypothesis (PSSH)

Enzymes: Michaelis-Menten Kinetics

Urea DecompositionA given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.


Rate Laws:

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( )


€

rE•S = r1E•S + r2E•S + r3E•S

Rate Laws:

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( )


€

rE•S = r1E•S + r2E•S + r3E•S

Rate Laws:

€

=k1 E( ) S( ) − k 2 E • S( ) − k 3 E • S( ) W( )If

€

E • S( ) =k1 E( ) S( )

k2

+ k3

€

rE•S ≈ 0

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( )

Urea Decomposition

€

E T( ) = E( ) + E • S( )

€

= E( ) +k1

k 2 + k 3

⎛

⎝ ⎜ ⎞

⎠ ⎟ E( ) S( )

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( ) =k1 k 3 E( ) S( )

k2

+ k3

Urea Decomposition

€

E T( ) = E( ) + E • S( )

€

= E( ) +k1

k 2 + k 3

⎛

⎝ ⎜ ⎞

⎠ ⎟ E( ) S( )

€

E( ) =k 2 + k 3

k1

⎛

⎝ ⎜ ⎞

⎠ ⎟E T

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( ) =k1 k 3 E( ) S( )

k2

+ k3

Urea Decomposition

€

rP =k 3 E T

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

E T( ) = E( ) + E • S( )

€

= E( ) +k1

k 2 + k 3

⎛

⎝ ⎜ ⎞

⎠ ⎟ E( ) S( )

€

E( ) =k 2 + k 3

k1

⎛

⎝ ⎜ ⎞

⎠ ⎟E T

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( ) =k1 k 3 E( ) S( )

k2

+ k3

Urea Decomposition

€

rP =k 3E TS

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

E T( ) = E( ) + E • S( )

€

= E( ) +k1

k 2 + k 3

⎛

⎝ ⎜ ⎞

⎠ ⎟ E( ) S( )

€

E( ) =k 2 + k 3

k1

⎛

⎝ ⎜ ⎞

⎠ ⎟E T

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( ) =k1 k 3 E( ) S( )

k2

+ k3

Urea Decomposition

VMAX

rP

S

€

VMAX

2

Km

€

E T( ) = E( ) + E • S( )

€

= E( ) +k1

k 2 + k 3

⎛

⎝ ⎜ ⎞

⎠ ⎟ E( ) S( )

€

E( ) =k 2 + k 3

k1

⎛

⎝ ⎜ ⎞

⎠ ⎟E T

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

€

rP = ′ k 3 E • S( ) W( ) = k 3 E • S( ) =k1 k 3 E( ) S( )

k2

+ k3

€

rP =k 3E TS

k 2 + k 3

k1

⎛

⎝ ⎜

⎞

⎠ ⎟ + S

Urea Decomposition

Types of Enzyme Inhibition

Chemical Reaction Engineering Asynchronous Video Series Chapter 7, Part 1: PSSH Enzyme Kinetics H....

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