Reaction Kinetics - Physical Chemistry

Enzymes are biological catalysts that speed up many reactions essential for the human body. Their chemistry is the same as catalysts. They speed up reactions by lowering the activation energy of reactions. This allows reactions to easily overcome the energy barrier and create the necessary products from reactants.

An adiabatic reaction is characterized as a reaction that neither gains nor loses net heat. This means that the process of converting the reactants to products does not alter the heat in the system (reaction) or the surroundings; therefore, both the heat inside and outside the system will be constant.

Individual order of reactants is a variable used to determine the rate of a reaction. Each reactant in the rate-limiting step of a reaction is assigned an order (typically zeroth, 1st, or 2nd). The reaction order is the sum of all individual orders. The rate of a reaction is defined as follows.

Where is the rate of the reaction, and are reactants, is rate constant, and and are individual orders. The reaction order of of this reaction would be . Note that the rate of a reaction depends on the concentration of reactants, rate constant, and the individual orders. It doesn’t depend on the reaction order.

Catalysts are added to a reaction to decrease the activation energy. This will allow for reactants to easily overcome the energy barrier (activation energy) and carry out the reaction; therefore, the reaction will happen quicker and the rate of reaction will increase. Recall that the rate constant quantifies the rate of a reaction. Since rate of reaction and rate constant are directly proportional, addition of catalyst will lower the activation energy, increase the rate of reaction, and, subsequently, increase the rate constant.

It’s important to remember that catalysts only alter the rate of a reaction (speeds up the reaction). They have no effect on thermodynamics/equilibrium (the amount of products produced).

The speed of a reaction is increased when the amount of reactants reaching the activation energy (energy barrier) is increased. This can be done via two ways: increasing temperature or adding a catalyst. Increasing temperature will add kinetic energy to the reactant and increase the amount of reactants reaching the energy barrier. Adding a catalyst will decrease the activation energy and, subsequently, increase the amount of reactants reaching the energy barrier.

Since the temperature is kept relatively constant in the human body (due to homeostasis), the most common way human body increases the speed of a reaction is by using catalysts. Biological catalysts are called enzymes and they are usually named with the suffix -ase. The only molecule that is an enzyme in this question is DNAase, which catalyzes the hydrolysis of phosphodiester bonds in the backbone of DNA.

ATP provides energy for active reactions but it cannot speed up the reaction. Histones are proteins found in nucleus that are involved in DNA packaging. They are irrelevant to this question.

Catalysts are chemicals that function to speed up a reaction. They do not, however, change the amount of products produced (the equilibrium of the reaction). They just make it so that the equilibrium is reached at a faster rate. The main way catalysts decrease reaction rate is by lowering the activation energy. This is the energy peak required to create transition states (molecules that are in between reactants and products). Once past this peak, the transition states convert into the products. Catalysts lower this peak so that it is easier to create transition states.

As mentioned, equilibrium constant will not change because catalysts do not alter the equilibrium of the reaction. Enthalpy (change in heat) of the reaction will also remain constant because it is not altered by the catalyst.

Competitive inhibition decreases enzyme activity by binding to the active site of the enzyme. Recall that active sites are sites on enzymes where the substrates bind. Upon binding to the enzyme, the substrates undergo changes that facilitate and speed up the chemical reaction. A competitive inhibitor binds to this active site and prevents the substrate from binding. With no binding, the substrate will not undergo the necessary changes and, subsequently, the chemical reaction. A key characterisitic of competitive inhibitors is that the bond between the inhibitor and the active site is reversible. This means that the chemical bonds involved here are weak, reversible noncovalent bonds such as hydrogen bonds and van der Waals forces. Covalent bonds are very strong and are usually found in irreversible interactions.

Allosteric inhibitors are molecules that bind to enzymes at their allosteric site(s). In this way, the allosteric inhibiton is very similar to, and is a subset of, another type of enzyme inhibition, noncompetitive inhibition.

Noncompetitive inhibitors bind to enzymes and prevent the formation of the enzyme-substrate complex. These inhibitors bind to a location other than the active site. Upon binding, the inhibitors alter the conformation of the active site and prevent the binding of substrate. They form covalent bonds with the enzyme; therefore, these are irreversible inhibitors and are hard to remove. and are altered by both types of inhibitors (competitive and noncompetitive). Competitive inhibitors alter the whereas the noncompetitive inhibitors alter the .

This implies that competitive inhibition can be overcome by increasing substrate concentration whereas noncompetitive inhibition cannot. Molecularly this makes sense. Competitive inhibitors bind reversibly to the active site and prevent binding of substrate. If we were to drastically increase its concentration, substrate will compete with and remove the competitive inhibitor from the active site. Noncompetitive inhibitors, on the other hand, alter the conformation of the active site, making it hard for substrates to bind to the active site; therefore, the substrate will not be able bind, regardless of the substrate concentration.

Recall that competitive inhibition can be overcome by increasing substrate concentration. Competitive inhibitors alter the Michaelis constant, , but maintain the (maximum reaction rate). Inhibitors act to decrease the reaction rate. To figure out the effect of competitive inhibitors on the Michaelis constant, we need to look at the Michaelis-Menten equation.

where is reaction rate, is maximum reaction rate, is substrate concentration, and is the Michaelis constant. Since reaction rate is inversely proportional to the , competitive inhibitors will increase and, thereby, decrease reaction rate.

To answer this question we need to first figure out the equation for slope and x-intercept of Lineweaver-Burk plot. The Linweaver-Burk plot is a graphical way to plot the Michaelis-Menten equation. It is defined as the reciprocal of Michaelis-Menten equation. Michaelis-Menten equation is as follows.

where is reaction rate, is maximum reaction rate, is substrate concentration, and is the Michaelis constant. Taking the reciprocal of this gives us

The slope, therefore, is . The x-intercept can be found by plugging in zero for the Y value (the reaction rate, ). The x-intercept is .

The question states that the slope is and the x-intercept is . Using the equation for x-intercept we can solve for .

Using the equation for slope we can solve for

Recall that the addition of a noncompetitive inhibitor alters the but not the ; therefore, is still after the addition of noncompetitive inhibitior.

Note that if we were asked to solve for the , we would have had to use the new slope () and the same value ().

Inhibitors are molecules that prevent the action of catalysts. They bind to catalysts and prevent substrate binding, thereby halting the catalytic action. Since catalysts increase the speed of a reaction, addition of an inhibitor will lower the speed of the reaction. This does not mean that the reaction will stop proceeding; it simple means that it will take longer for the reaction to complete (reach equilibrium).

Remember that a catalyst speeds up both the forward and the reverse reaction; therefore, inhibitors will slow down both reactions. As mentioned, inhibitors will only slow down the reaction. The amount of products produced (equilibrium) will not change, although it will take longer for products to form.

There are two main types of inhibitors. Competitive inhibitors bind to the active site of the catalyst and prevent substrate from binding. This phenomenon causes a decreasing in the binding affinity of substrate and catalyst. However, competitive inhibitors can be overcome by adding excess substrates. The substrates will dissociate the competitive inhibitor and carry out the reaction; therefore, the reaction can still be carried out at a faster rate and the maximum rate of reaction is not altered.

Noncompetitive inhibitors bind to the catalyst at an allosteric site. They alter the conformation of the active site and prevent substrate binding. They cannot be overcome by addition of excess substrate; therefore, they lower the maximum rate of reaction.

Michaelis constant, or , is defined as the concentration of substrate at which the reaction rate is half the maximum (). It is a useful measure of how much substrate is needed for reaction to proceed rapidly. A reaction with a high Michaelis constant will need lots of substrate to reach high reaction rates whereas a reaction with low Michaelis constant will need small amounts of substrate to reach high reaction rates.

Reaction rate, according to Michaelis-Menten model is as follows.

where is reaction rate, is maximum reaction rate, is substrate concentration, and is the Michaelis constant. If we analyze the given options, we will observe that the greatest increase in occurs when is doubled (increased by a factor of 2). Increasing substrate concentration by a factor of 2 will have nearly the same effect; however, since is also found in the denominator it will only slightly contribute to an increase in .

Note that the units for is molarity, is molarity, and is . Solving for will give us units of .

To solve this problem we need to use the Michaelis-Menten equation.

where is reaction rate, is maximum reaction rate, is substrate concentration, and is the Michaelis constant. If we plug in the given values we get a reaction rate of

Note that the Michaelis-Menten equation implies that the will never exceed . Regardless of how high the substrate concentration is, the reaction rate will approach but will never equal or exceed it. You can try this by substituting very high values for substrate concentration. The will get very close to 0.2 () but will never equal or exceed it.

The Michaelis-Menten equation is as follows.

Where is reaction rate, is maximum reaction rate, is substrate concentration, and is the Michaelis constant. Since the Michaelis constant, , is in the denominator, the reaction rate is inversely proportional to the Michaelis constant; therefore, increasing the Michaelis constant will decrease the reaction rate.

The half-life is defined as the amount of time it takes to reduce the concentration of a substance (in this case a drug). After one half-life, 50% of the drug will be eliminated and 50% will remain. After the second half-life, half of the remaining drug (25%) will be eliminated; therefore, at the end of second half-life 75% of drug will be eliminated. To solve for this time, we can simply calculate the half-life and multiply it by 2.

To solve this question, we need to know the equation for half-life. It is stated that the reaction follows first-order; therefore, the half-life for a first order reaction is defined as

Where is half-life and is the rate constant. Since we are not given the rate constant we cannot calculate the half-life.

The half-life of a first order reaction is as follows:

Where is half-life and is the rate constant. The half-life only depends on the rate constant. Since rate constant is in the denominator, half-life and rate constant are inversely proportional. This means that half-life increases as rate constant decreases and vice versa. Concentration of reactants does not affect the half-life for a first order reaction.

Rate constant is a unique constant for each reaction that determines the rate of a reaction. It is one of several variables that determines the rate of reaction. As rate constant increases the rate of reaction increases. Rate constant depends on two main factors: temperature and activation energy. The rate constant increases as the temperature is increased. Recall that increasing temperature increases the kinetic energy of the molecules; therefore, an increase in temperature will increase the amount of molecules that reach activation energy. This will increase the rate constant and, subsequently, the rate of the reaction.

Rate constant increases as the activation energy is decreased. Activation energy is the energy hill that reactants must overcome to produce products. If the activation energy is decreased then it will be easier for reactants to overcome the energy hill and convert into products; therefore, decreasing activation energy will increase the rate constant and, subsequently, the rate of the reaction. Recall that catalysts speed up a reaction (increase rate of reaction) by lowering activation energy; therefore, catalysts increase the rate constant.

Condition I is false. The reactant concentration does change over time (can be seen the integrated rate law, which has a term), it just does not depend on the reactant concentration.

Condition II is true. The rate is independent of reactant concentration for 0th order reactions.

Condition III is false. does have an affect on the overall reactant concentration over time (can be seen by in the integrated rate law, which has a term).