Chemical Kinetics

CHEMICAL KINETICS

Reaction Rate- the change in concentration of one of the reactants or products divided by the time interval over with the change occurs (the change in concentration over the change in time).

There are four factors that we can use to influence the rate of a reaction:

1. Concentration- molecules must collide to react. The more frequently molecules collide, the more rapid the reaction, so the more molecules the better.
2. PhysicalState- molecules must mix to collide. Molecules that are in the same physical state will collide easier than those that are not. The more contact out of phase molecules make, the faster the reaction. For instance, if you are reacting a solid and a gas, it helps to grind the solid up as fine as you can. This increases surface area and reaction rate.
3. Temperature- molecules must collide with enough energy to react. More reactions will occur at a given time if the temperature is raised, because an increase in temperature generally means an increase in energy.
4. Catalysts- a catalyst will lower the activation energy required for a reaction, increasing the rate.

The rate equation is given by:

R = Reactant

P = Product

The brackets are used to denote concentrations.

In kinetics, the convention is that the rate is always positive. The placement of the (-) sign in front of the reactant denotes the concentration of the reactant is being consumed and assures a positive rate, since the final concentration is less than the initial one and the difference should always be negative.

The units for rate are commonly mol/L*s, but longer units of time can be used for slower rates.

Unique Average Rate- If there are coefficients in front of the reactants or products, they must be taken into account. This average rate does not take into account the fact that the rate changes over the course of the experiment.

aA + bB  cC + dD

By dividing the concentration of a species by it’s coefficient, we are able to divide the total amount of reactant or product by the number of moles present.

In a plot of concentration vs. time, the slope of the straight line joining any two points on the curve will give the average rate over that period.

Instantaneous Rate- the best approximation of a rate at a single instant. This is gained by drawing a tangent to the plot of concentration vs. time.

For most reactions, the rate decreases as the reaction proceeds.

In general, when reaction rate is mentioned, the instantaneous rate is meant.

Initial Rate- the instantaneous change in concentration the instant the reaction begins.

The initial rate is important because at the start of the reaction, the concentration of products is negligible. This keeps us from having to incorporate the back reaction into the rate law, greatly simplifying our life.

Rate Law- an expression for the instantaneous reaction rate in terms of the concentration of a species at any instant. The rate law expresses the rate as a function of reactant concentrations, product concentrations and temperature.

Rate laws involve a proportionality or rate constant, denoted k.

The rate constant for a given reaction is constant at a constant temperature. Rate constants change with changing reaction conditions.

Reaction Orders- the order of a reaction describes how the reaction behaves with respect to the concentration of the reactants or products. They appear as the exponents in the above rate equation (m and n).

First Order Reaction- the rate is proportional to the first power of the concentration (concentration raised to 1). A plot of ln [A] vs. time gives a straight line, with the slope = -k.

Second Order Reaction- the rate is proportional to the second power of the concentration (concentration squared). A plot of 1/[A] vs. time gives a straight line, with the slope = k.

Zero Order Reaction- the rate is independent of concentration (common in metal catalyzed and biochemical reactions). A plot of [A] vs. time gives a straight line, with the slope = -k.

In general, the order of a reaction cannot be determined from the reaction stoichiometry in the chemical equation. Reaction orders are empirical and must be determined experimentally.

Examples of the effect of concentration on reactions.

First Order
[A] = 1 M
rate = [1]1 = 1
[A] = 2M
rate = [2]1 = 2
[A] = 3M
rate = [3]1 = 3 / Second Order
[A] = 1 M
rate = [1]2= 1
[A] = 2M
rate = [2]2 = 4
[A] = 3M
rate = [3]2 = 9 / Zero Order
[A] = 1 M
rate = [1]0 = 0
[A] = 2M
rate = [2]0 = 0
[A] = 3M
rate = [3]0 = 0

Overall Order- reaction rates may rely on more than one reactant or product. The overall order describes the sum of the individual orders

Rate = k[A]m[B]n

This reaction is mth order with respect to A and nth order with respect to B. The overall order is given by m+n.

A negative reaction order implies that the concentration appears in the denominator of the rate law. Increasing the concentration of this species generally slows the reaction.

Integrated Rate Law- gives the concentration of reactants or products at any time after the start of the reaction.

Zero Order Integrated Rate Law:

A plot of [A]t vs. t gives a straight line with slope = -k and b = [A]0.

First Order Integrated Rate Law:

A plot of ln[A]t vs. t gives a straight line with slope = -k and b = ln[A]0.

Second Order Integrated Rate Law:

A plot of 1/[A]t vs. t gives a straight line with slope = k and b = 1/[A]0.

Half-life- t1/2- the time needed for the concentration to reach one-half its initial value.

First Order Half-life:

In a first order reaction, the half-life is independent on the initial concentration of the reactant, meaning that the time it takes to decrease the concentration by ½ doesn't depend on how much you had to begin with.

Reactions with large rate constants have short half-lives.

Second Order Half-life: as a second order reaction proceeds, the half-life increases. t1/2 is proportional to initial reactant concentration.

Summary of reaction orders and equations

Zero Order / First Order / Second Order
Rate Law / rate = k / rate = k[A] / rate = k[A]2
Units for k / mol/(L*s) / 1/s / l(mol*s)
Int. Rate Law / / /
Linear Plot / [A] vs. t / ln[A] vs. t / 1/[A] vs. t
Slope, Intercept / -k, [A] / -k, ln[A] / k, 1/[A]
t1/2 / [A]/2k / ln2/k / 1/k[A]

Effects of Temperature on Rate- temperature effects the rate by effecting the rate constant.

Instantaneous and integrated rate laws only summarize a reactions’dependence on concentration, not on temperature. They don’t take into account any dependence on temperature. The Arrehenius Equation does:

A = preexponential factor

Ea = Activation Energy

Activation Energy (Ea)-the minimum energy which molecules must have to successfully react, or the energy required to activate the molecules into a state from which a reactant bond may be changed to a product bond.

Reactions that give a straight line when ln k is plotted against 1/T are said to show Arrhenius behavior.

The higher the activation energy, the stronger the temperature dependence of the rate constant.

There are two models used to describe the kinetics that molecules undergo during a reaction:

1. Collision Theory- views the reaction rate as the result of particles colliding with a certain frequency and minimum energy.

2. TransitionState Theory- offers close up view of how the energy of a collision converts reactant to product.

A model of how chemical reactions occur at the molecular level should account for the temperature dependence of the rate constant, as well as reveal the significance of the Arrhenius parameters A and Ea.

Collision Theory

In this theory it is assumed that gas-phase molecules act as billiard balls; if they collide at low speeds they will simply bounce apart, but if they collide at higher speeds, they will smash into pieces. This minimum energy it takes for a collision to result in a chemical reaction is known as the Ea.

The number of collisions of gaseous molecules per unit time determines the upper limit of how fast a reaction may occur. These collisions depend on a number of factors:

1. Concentration- concentrations must be multiplied in the rate law. This is proven by the fact that if there are two molecules there are four ways for them to combine, and if there are three molecules, there are six ways for them to combine, not five.

2. Temperature- this is very important for the Ea. Increasing the temperature increases the number of molecules present in the reaction vessel with the correct Ea, thus increasing the rate.

In an exothermic reaction, the reaction collision Ea is bigger than the product Ea. The reverse is true for an endothermic reaction.

3. Molecular structure- Even if molecules can overcome the Ea, their molecular structure must be correct for them to actually react (the orientation must be correct). Molecules must be facing a certain way in order for the correct molecules to react.

Collision Cross-section- the area that a molecule presents as a target during a collision. The bigger the collision cross-section, the bigger the rate. This is why bigger molecules are more likely to collide and react than smaller molecules. Steric Requirement- a dependence on direction of a reaction

Though it is known that temperature effects the rate of a reaction, an increase in temperature of 10 C only increases the rate by a factor of 1.02. A is a measure of the rate at which molecules collide.

In summary, according to the collision theory, molecules will reaction only if they have the proper Ea when they collide, as well as the proper orientation.

TransitionState Theory

This theory applies to reactions of both gases and molecules in solutions. It improves on the collision theory by suggesting a way of calculating the rate constant even if optimum orientation cannot be met.

Two molecules approach and distort as they meet, where an activated complex is formed (the two molecules are held near each other and finally knocked into one another by the surrounding solvent molecules). In an activated complex, the new bonds are lengthened and weakened, but newer bonds are only partially formed.

Reaction profile- a plot representing the energy changes that occur during a reaction. It includes a peak that relates the Ea of the activated complex to the energy of the reactants.

If the reactants meet with a high enough Ea, they will form the activated complex and climb over the hill.

If the products have less potential energy than the reactants (C is below A), the H0rxn is ___ and the reaction is __thermic. If the products have more potential energy than the reactants (C is above A), the H0rxn is ___ and the reaction is __thermic.

Not all reactions occur in one simple step. A lot of reactions involve individual elementary reactions- the individual steps a reaction must go through before reaching the product. To determine which set of elementary reactions are correct, you look at the reaction mechanism- a sequence of elementary reactions describing the changes that we believe take place as reactants transform into products. Several different mechanisms might be proposed for a given reaction, and rates are used to determine which mechanism most likely is correct.

Reaction intermediate- a species that plays a role in a reaction but does not appear in the chemical equation for the overall reaction. Elementary steps generally involve the formation and consumption of some species that does not show up in the final balanced chemical equation. These intermediates should cancel out of the rate law.

2 NO2 + F2 2 NO2F

i. NO2 + F2 = NO2F + F (slow)

ii. NO2 + F = NO2F (fast)

In this reaction, the overall balanced chemical equation can be broken into two elementary steps. In this reaction you can see the intermediate (F) is formed in the (i) but consumed in (ii), so it does not show up in the final equation. Also, you can see that the first step is the slow step, so this determines the rate of the reaction.

Rate Determining Step- the slowest elementary step in a series of reactions. It is so much slower than the others that it governs the overall rate of the reaction. For example, if your travels to work include riding on a slow-moving ferry, then the portion of your trip which determines how long it will take you to get to work is the ferry part, since it is the slowest part of your trip.

Molecularity- the number of reactant molecules involved in a specified elementary reaction.

Unimolecular reaction- only one reactant molecule participates.

Bimolecular reaction- two species come together to react.

A valid reaction mechanism must be consistent with (1) the balanced chemical equation for the reaction and (2) experimental data. The molecularity of a reaction implies a specific rate law:

Unimolecular- first order rate law

rate = k[A]

Bimolecular- second order rate law

rate = k[A][B] or rate = k[A][A]

Termolecular- third order rate law

rate = k[A][B][C], rate = k[A]2[B], rate = k[A]3

To construct an overall rate law for a mechanism, first write rate laws for individual elementary steps and then combine them into an overall rate law. Remember, intermediates do not appear in the overall rate law.

Steady State Approximation- setting the rate of any intermediate equal to 0. This can be done because we are assuming that the intermediate is being consumed as quickly as it is being produced. Therefore, it’s concentration remains small and generally constant throughout the reaction.

Catalysis

A catalyst is a species that increases the rate of a reaction without being consumed in the reaction. A catalyst increases the rate by lowering the activation energy of the transition complex. Both the forward and reverse rates are increased by a catalyst.

Generally, only a small amount of catalyst is needed, since they can perform t same task over and over again. When a catalyst is rendered inactive, either by contamination or by the binding of a competing species, the catalyst ispoisonedand not useful anymore.

Homogeneous catalysts- the catalyst is in the same phase as the reactants (i.e., if the reactants are gas-phase, then so is the catalyst). In this case, the catalyst must appear in the rate law, even though it is not being consumed in the reaction.

Heterogeneous catalysts- the catalyst is in a different phase than the reactants (i.e., gaseous H2 over Pt rod). In this case, the gas must adsorb, or attach, to the surface of the catalyst for reaction to occur.

Enzymes-biological catalysts. Generally, the enzyme must be the correct shape to fit into its substrate.