Reaction Mechanisms

Reaction Mechanisms 授課教師：林佳璋

Active Intermediates and Nonelementary Rate Laws A number of simple power law models, that is, n was integer of 0, 1, or 2 corresponding to a zero-, first-, and second-order reaction. orders are noninteger involving a number of elementary reactions and a least one active intermediate An active intermediate is a high-energy molecule that reacts virtually as fast as it is formed. As a result, it is present in very small concentrations. Active intermediates (e.g., A*) can be formed by collision or interaction with other molecules. The activation occurs when translational kinetic energy is transferred into energy stored in internal degrees of freedom, particularly vibrational degree of freedom.

~An active intermediate is not formed solely as a consequence of the molecule moving at a high velocity (high translational kinetic energy). ~The energy must be absorbed into the chemical bonds where high-amplitude oscillations will lead to bond ruptures, molecular rearrangement, and decomposition. ~In the absence of photochemical effects, the transfer of translational energy to vibrational energy to produce an activate intermediate can occur only as a consequence of molecular collision or interaction. ~Other types of active intermediate that can be formed are free radials (one or more unpaired electrons, e.g., CH3), ionic intermediates (e.g., carbonium ion), and enzyme-substrate complexes. formed the active intermediate shown in the small trough at the top of the energy reaction coordinate diagram reaction to form two ethylene molecules did not proceed directly

Pseudo-Steady-State Hypothesis (PSSH) Because a reactive intermediate reacts virtually as fast as it is formed, the net rate of formation of an active intermediate (e.g., A*) is zero, i.e., Pseudo-Steady-State Hypothesis (PSSH) active intermediate appears in n reactions Consider a gas-phase decomposition of azomethane, AZO, to give ethane and nitrogen: The rate of formation of ethane is first order with respect to AZO at pressures greater than 1 atm (relatively high concentrations) and second order at pressures below 50 mmHg (low concentrations):

~In reaction 1, two AZO molecules collide and the kinetic energy of one AZO molecule is transferred to internal rotational and vibrational energies of the other AZO molecule, and it becomes activated and highly reactive (i.e., AZO*). ~In reaction 2, the activated molecule (AZO*) is deactivated through collision with another AZO by transferring its internal energy to increase the kinetic energy of the molecules with which AZO* collides. ~In reaction 3, this high activated AZO* molecule, which is wildly vibrating, spontaneously decomposes into ethane and nitrogen, Because each of the reaction steps is elementary, the corresponding rate laws for the active intermediate AZO* in reaction (1), (2), and (3) These rate laws are pretty much useless in the design of any reaction system because the concentration of the active intermediate AZO* is not readily measurable.

The rate of formation of product (with k3=k3AZO*) second-order first-order

Consider a reaction The reaction is first order but the reaction is not elementary. The reaction proceeds by first forming an active intermediate, A*, from the collision of the reactant molecule and an inert molecule of M. Either this wildly oscillating active intermediate is deactivated by collision with inert M, or it decomposes to form product.

Searching for a Mechanism reaction mechanism rate law

Example 7-1 Light is given off when a high-intensity ultrasonic wave is applied to water. Thus light results from microsize gas bubbles (0.1 mm) being formed by the ultrasonic wave and then being compressed by it. During the compression stage of the wave the contents of the bubble (e.g., water and whatever else is dissolved in the water, e.g., CS2, O2, N2) are compressed adiabatically. This compression give rise to high temperatures and kinetic energies of the gas molecules, which through molecular collisions generate active intermediates and cause chemical reactions to occur in the bubble. The intensity of the light given off, I, is proportional to the rate of deactivation of an activated water molecule that has been formed in the microbubble. An order-of-magnitude increase in the intensity of sonoluminescence is observed when either carbon disulfide or carbon tetrachloride is added to the water. The intensity of luminescence, I, for the reaction is A similar result exists for CCl4.

However, when an aliphatic alcohol, X, is added to the solution, the intensity decreases with increasing concentration of alcohol. The data are usually reported in terms of a Stern-Volmer plot in which relative intensity is given as a function of alcohol concentration, CX. (See Figure E7-1.1, where I0 is the sonoluminescence intensity in the absence of alcohol and I is the sonoluminescence intensity in the presence of alcohol.) Suggest a mechanism consist with experimental observation. Solution where CX=(X)

From rule 1 of Table 7-1, the denominator suggests that alcohol (X) collides with the active intermediate: The alcohol acts as what is called a scavenger to deactivate the active intermediate. The fact that the addition of CCl4 or CS2 increases the intensity of the luminescence, leads us to postulate (rule 3 of Table 7-1) that the active intermediate was probably formed from CS2: where M is a third body (CS2, H2O, N2, etc.).

Example 7-2 The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is believed to proceed in the following sequence: (a) Use the PSSH to derive a rate law for the rate of formation of ethylene. (b) Compare the PSSH solution in Part (a) to that obtained by solving the complete set of ODE mole balances.

Solution (a) The rate of formation of ethylene (Reaction 3) is

The rate of disappearance of ethane is entering ethane concentration is 0.1 mol/dm3

(b) The initial concentration of ethane is 0.1 mol/dm3 and the temperature is 1000 K.

~FigureE7-2.1 shows the concentration time trajectory for CH3 (i.e., C2). One notes a flat plateau where the PSSH is valid. ~Figure E7-2.2 shows a comparison of the concentration-time trajectory for ethane calculated from the PSSH (CP1) with the ethane trajectory (C1) calculated from solving the mole balance equations. ~Figure E7-2.3 shows a similar comparison for ethylene (CP5) and (C5). One notes that the curves are identical, indicating the validity of PSSH under these conditions. ~Figure E7-2.4 shows a comparison of the concentration-time trajectories for methane (C3) and butane (C8).

Reaction Pathways ~With the increase in computing power, more and more analyses involving free-radial reactions as intermediates are carried out using the coupled sets of differential equations. ~The key in any such analyses is to identify which intermediate reactions are important in the overall sequence in predicting the end products. ~Once the key reactions are identified, one can sketch the pathways in a manner similar to that shown in Figure 7-2.

Reaction pathways find their greater use in metabolic pathways where the various steps are catalyzed by enzymes. The metabolism of alcohol is catalyzed by a different enzyme in each step.

Enzymatic Reaction Fundamentals ~An enzyme is a high-molecular-weight protein or protein-like substance that acts on a substrate (reactant molecule) to transform it chemically at a greatly accelerated rate, usually 103 to 1017 times faster than the uncatalyzed rate. ~Without enzymes, essential biological reactions would not take place at a rate necessary to sustain life. ~Enzymes are usually present in small quantities and are not consumed during the course of the reaction nor do they affect the chemical reaction equilibrium. ~Enzymes provide an alternate pathway for the reaction to occur thereby requiring a lower activation energy. ~One enzyme can usually catalyze only one type of reaction. ~Enzymes usually work under mild conditions: pH 4 to 9 and temperatures 75 to 160F. active intermediate (ES) lower activation energy Figure 7-4 shows the reaction coordinate for the uncatalyzed reaction of a reactant molecule called a substrate (S) to form a product (P) SP

Enzyme-Substrate Complex The key factor that sets enzymatic reaction apart from other catalyzed reactions is the formation of an enzyme-substrate complex, ES. Here substrate binds with a specific active site of the enzyme to form this complex. Figure 7-5 shows the schematic of the enzyme chymotrypsin (MW=25000 Daltons), which catalyzes the hydrolytic cleavage of polypeptide bonds. In many cases the enzyme’s active catalytic sites are found where the various folds or loops interact. For chymotrypsin the catalyst sites are noted by the amino acid numbers 57, 102, and 195 in Figure 7-5. ~Much of the catalytic power is attributed to the binding energy of the substrate to the enzyme through multiple bond with the specific functional groups on the enzyme (amino side chains, metal ions). ~The interactions that stabilize the enzyme-substrate complex are hydrogen bonding and hydrophobic, ionic, and London van der Waals forces. ~If enzyme is exposed to extreme temperatures or pH environments (i.e., both high and low pH values), it may unfold losing its active sites. When this occurs, the enzyme is said to be denatured.

There are two models for substrate-enzyme interactions: the lock and key model and the induced fit model, both of which are shown in the following figure. For many years the lock and key model was preferred because of the sterospecific effects of one enzyme acting on the substrate. However, the induced fit model is the more useful model. In induced fit model both the enzyme molecules and the substrate molecules are distorted. These changes in conformation distort one or more of the substrate bonds, thereby stressing and weakening the bond to make the molecule more susceptible to rearrangement and attachment. There are six classes of enzymes and only six

Mechanisms The catalytic action of urease would cause urea to decompose into ammonia and carbon dioxide. The mechanism of the reaction is believed to proceed by the following sequence of elementary reactions: 1.The enzyme urease (E) reacts with the substrate urea (S) to form an enzyme- substrate complex (ES). 2.This complex (ES) can decompose back to urea (S) and urease (E): 3.Or it can react with water (W) to give the products (P) ammonia and carbon dioxide, and recover the enzyme urease (E).

The net rate of disappearance of the substrate, -rS, is The net rate of formation of the enzyme-substrate complex is using PSSH can’t use this rate law owing to that we can’t measure the unbound enzyme concentration (E)

Michaelis-Menten Equation water is in excess, and the concentration of water is considered constant Michaelis-Menten Equation The parameter kcat (s-1) is also referred to as the turnover number. It is the number of substrate molecules converted to product in a given time on a single-enzyme molecule when the enzyme is saturated with substrate (i.e., all active site on the enzyme are occupied, S>>KM). The constant KM (mol/dm3) is called the Michaelis constant and for simple systems is a measure of the attraction of the enzyme for its substrate, so it’s also called the affinity constant. Km is equal to the substrate concentration at which the rate of reaction is equal to one-half the maximum rate.

Example 7-3 Determine the Michaelis-Menten parameters Vmax and KM for the reaction The rate of reaction is given as a function of urea concentration in this table. Solution

Product-Enzyme Complex In many reactions the enzyme and product complex (EP) is formed directly from the enzyme substrate complex (ES) according to the sequence Applying the PSSH to both (ES) and (EP), we obtain

Batch Reactor Calculations for Enzyme Reactions A mole balance on urea in the batch reactor gives this reaction is liquid phase

Example 7-4 Calculate the time needed to convert 99% of the urea to ammonia and carbon dioxide in a 0.5-dm3 batch reactor. The initial concentration of urea is 0.1 mol/dm3, and the urease concentration is 0.001 g/dm3. The reaction is to be carried out isothermally at the same temperature at which the data in Table E7-3.2 were obtained. Solution

Effect of Temperature If the enzyme structure would remain unchanged as the temperature is increased, the rate would probably follow the Arrhenius temperature dependence. As the temperature increases, the reaction rate increases up to a maximum with increasing temperature and then decreases as the temperature is increased further. As the temperature increases, the enzyme can unfold and/or become denatured and lose it catalytic activity.

Inhibition of Enzyme Reactions ~In addition of temperature and solution pH, another factor that greatly influences the rates of enzyme-catalyzed reactions is the presence of an inhibitor. ~Inhibitors are species that interact with enzymes and render the enzyme ineffective to catalyze its specific reaction. ~The most dramatic consequences of enzyme inhibition are found in living organisms where the inhibition of any particular enzyme involved in a primary metabolic pathway will render the entire pathway inoperative, resulting in either serious damage or death of the organism. The inhibition of a single enzyme, cytochrome oxidase, by cyanide will cause the aerobic oxidation process to stop; death occurs in a very few minutes. ~There are also beneficial inhibitors such as the ones used in the treatment of leukemia and other neoplastic disease. Aspirin inhibits the enzyme that catalyzes the synthesis of postaglandin involved in the pain-producing process.

~The three most common types of reversible inhibition occurring in enzymatic reactions are competitive, uncompetitive, noncompetitive. ~When competitive inhibition occurs, the substrate and inhibitor are usually similar molecules that compete for the same site on the enzyme. ~Uncompetitive inhibition occurs when the inhibitor deactivates the enzyme-substrate complex, sometimes by attaching itself to both the substrate and enzyme molecules of the complex. ~Noncompetitive inhibition occurs with enzymes containing at least two different types of sites. The substrate attaches only to one type of site, and the inhibitor attaches only to the other to render the enzyme inactive.

E+S ES E+P + I EI Competitive Inhibition The rate of formation of product is PSSH

The effect of a competitive inhibition is to increase the “apparent” Michaelis constant, KM’. A consequence of the larger “apparent” Michaelis constant KM’ is that a larger substrate concentration is need for the rate of substrate decomposition to reach half its maximum rate. As the inhibitor (I) concentration is increased the slope increases (i.e., the rate decreases) while the intercept remains fixed.

E+S ES E+P + I ES I Uncompetitive Inhibition The slope remains the same as the inhibition (I) concentration is increase, while the intercept increases.

E+S ES E+P + I + I EI+S ES I Noncompetitive Inhibition Both the slope and intercept increase with increasing inhibitor concentration. In practice, uncompetitive inhibition is observed only for enzymes with two or more substrates, S1 and S2.

1. In competitive inhibition, the slope increases with increasing inhibitor concentration, while the intercept remains fixed. 2. In uncompetitive inhibition, the y-intercept increases with increasing inhibitor concentration while the slope remains fixed. 3. In noncompetitive inhibition, both the y-intercept and slope will increase with increasing inhibitor concentration.

Substrate Inhibition In a number of cases, the substrate itself can act as a inhibitor. In the case of uncompetitive inhibition, the inactive molecules (SES) is formed by the reaction rate increases linearly with increasing substrate concentration rate decreases as the substrate concentration increases

Closure ~The theme running through most of this section is the pseudo- steady-state hypothesis (PSSH) as it applies to gas-phase reactions and enzymatic reactions. ~The student should be able to apply the PSSH to reactions in such problems as P7-7 and P7-12 in order to develop rate laws. ~Reaction pathways were discussed in order to visualize the various interactions of the reacting species. ~After completing this section the student should be able to describe and analyze enzymatic reactions and the different types of inhibition as displayed on a Lineweaver-Burk plot.

Reaction Mechanisms