Kinetics Quiz AP Chemistry Lovrencic
Which conditions will affect the rate of a reaction? Four variables affect the rate of reaction:
1. The concentrations of the reactants 2. The concentration of the catalyst 3. The temperature at which the reaction occurs 4. The surface area of the solid reactant or catalyst
Reaction Mechanism
A balanced chemical equation is a description of the overall result of a chemical reaction. However, what actually happens on a molecular level may be more involved than what is represented by this single equation. For example, the reaction may take place in several steps. That set of steps is called the reaction mechanism.
Catalyst
A catalyst is not consumed in a reaction. Rather, it is present in the beginning, is used in one step, and is produced again in a subsequent step. As a result, the catalyst does not appear in the overall reaction equation. A catalyst increases the reaction rate by providing an alternative reaction path with a lower activation energy. When Ea is reduced, k increases exponentially. This relationship is illustrated on the potential energy diagram for the decomposition of ozone.
Reaction Intermediate
A reaction intermediate is a species produced during a reaction that does not appear in the net equation because it reacts in a subsequent step in the mechanism.
Rate Law and Reaction Mechanism
A reaction mechanism cannot be directly observed. We can, however, determine the rate law by experiment and decide if the reaction mechanism is consistent with that rate law. The rate of a reaction is determined completely by the slowest step, the rate-determining step.
It is also possible to find the order by examining the data qualitatively.
Again choosing experiments 1 and 2, we note that the concentration of NO is doubled and the rate is quadrupled. That means the reaction is second order in NO. Choosing experiments 1 and 3, we note that the concentration of O2 is doubled and the rate is doubled. That means the reaction is first order in O2.
The rate of this reaction can be found by measuring the concentration of O2 at various times.
Alternatively, the concentration of NO2 could be measured. Both of these concentrations increase with time. The rate could also be determined by measuring the concentration of N2O5, which would decrease over time.
The half-life of a reaction, t½, is the time it takes for the reactant concentration to decrease to one-half of its initial value.
By substituting ½[A]0 for [A]t, we solve the integrated rate law for the special case of t = t½.
Catalysis
Catalysis is an increase in the rate of reaction that results from the addition of a catalyst. Enzymes are biological catalysts.
Chemical Kinetics
Chemical kinetics is the study of reaction rates, including how reaction rates change with varying conditions and which molecular events occur during the overall reaction.
Collision Theory
Collision theory assumes that reactant molecules must collide with an energy greater than some minimum value and with the proper orientation.
Elementary Reaction
Each step in the reaction mechanism is called an elementary reaction and is a single molecular event.
Rates are determined experimentally in a variety of ways.
For example, samples can be taken and analyzed from the reaction at several different intervals. Continuously following the reaction is more convenient. This can be done by measuring pressure, as shown on the next slide, or by measuring light absorbance when a color change is part of the reaction.
Certainly, Z will increase with temperature, as the average velocity of the molecules increases with temperature.
However, this factor alone cannot explain the dramatic effect of temperature changes.
Concentration of Catalyst
Hydrogen peroxide, H2O2, decomposes rapidly in the presence of HBr, giving oxygen and water. Some of the HBr is oxidized to give the orange Br2, as can be seen above.
Surface Area of a Solid Reactant or Catalyst
If a reaction involves a solid with a gas or liquid, then the surface area of the solid affects the reaction rate. Because the reaction occurs at the surface of the solid, the rate increases with increasing surface area. For example, a wood fire burns faster if the logs are chopped into smaller pieces. Similarly, the surface area of a solid catalyst is important to the rate of reaction. Right: The photo shows a powder igniting.
Graphs of Reaction Rates Give the Reaction Order
Left: The plot of ln[NO2] versus t is not linear, so the reaction is not first order. Right: The plot of 1/[NO2] versus t is linear, so the reaction is second order in NO2.
Concentrations of Reactants
Often the rate of reaction increases when the concentration of a reactant is increased. In some reactions, however, the rate is unaffected by the concentration of a particular reactant, as long as it is present at some concentration.
For the generic reaction aA + bB +cC → dD + eE the rate law is
Rate = k[A]m[B]n[C]p
2N2O5(g) → 4NO2(g) + O2(g) We can express these changes in concentration as follows. Square brackets mean molarity.
Rate of formation of O2 = ∆[O2]/∆t Rate of formation of NO2 = 1/4 ∆[O2]/∆t Rate of decomposition of N2O5 = -1/2∆[O2]/∆t
For a first-order reaction, a plot of ln[A]t versus t is linear.
The graph crosses the origin (b = 0).
Activation Energy
The minimum energy is called the activation energy, Ea.
These equations give the average rate over the time interval Δt. As Δt decreases and approaches zero, the equations give the instantaneous rate.
The next slides illustrate this relationship graphically for the increase in concentration of O2.
Overall Order
The overall order of a reaction is the sum of the orders of the reactant species from the experimentally determined rate law.
Below is the equation of nitric oxide reacting with oxygen to produce nitrogen dioxide: 2NO(g)+O2→ 2NO2(g) which has an experimentally determined third order rate law: rate of reaction=k[NO]2[O2] Because a termolecular mechanism (a three-body reaction occurring in a single step) is extremely rare, a mechanism with two bimolecular elementary steps can be suggested: 2NO(g)⇌N2O2(g) (Step 1 fast) N2O2(g)+O2(g) → 2NO2(g) (Step 2 slow)
The proposed mechanism has the same stoichiometry as the overall reaction. Step 1 is a reversible process in which equilibrium is reached quickly. Step 2 is therefore the rate-determining step. The relative rate of the Step 2 is k3[N2O2][O2], which does not seem to match with the experimental rate of k[NO]2[O2]. However, N2O2 is actually a reaction intermediate, because it appears in both elementary steps but not in the equation of the overall reaction. Because an intermediate cannot appear in the rate law for the overall reaction, a value equivalent to N2O2 is required. Because Step 1 is a fast, reversible reaction, it can be assumed that: k1[NO]2=k2[N2O2] Therefore, [N2O2]=k1k2[NO]2 Through substitution, k3[N2O2][O2] = k3(k1/k2) [NO]2[O2]. The rate constant is k=k3k1/k2, so the rate of reaction is k[NO]2[O2], matching the experimental rate law. This proposed mechanism fulfills both requirements for a possible mechanism.
Rate Constant and Temperature
The rate constant depends strongly on temperature. How can we explain this relationship?
Integrated rate law
The rate law tells us the relationship between the rate and the concentrations of reactants and catalysts. To find concentrations at various times, we need to use the integrated rate law. The form used depends on the order of reaction in that reactant.
Reaction Order
The reaction order with respect to a specific reactant is the exponent of that species in the experimentally determined rate law.
Rate Law
The reaction rate usually depends on the concentration of one or more reactant. This relationship must be determined by experiment. This information is captured in the rate law, an equation that relates the rate of a reaction to the concentration of a reactant (and catalyst) raised to various powers. The proportionality constant, k, is the rate constant.
Reaction Mechanism
The set of elementary reactions, which when added give the balanced chemical equation, is called the reaction mechanism. Because an elementary reaction is an actual molecular event, the rate of an elementary reaction is proportional to the concentration of each reactant molecule. This means we can write the rate law directly from an elementary reaction.
As Δt gets smaller and approaches zero, the hypotenuse becomes a tangent line at that point.
The slope of the tangent line equals the rate at that point.
rate-determining step (RDS)
The slowest step in the reaction mechanism is called the rate-determining step (RDS). The rate law for the RDS is the rate law for the overall reaction.
For a second-order reaction, a plot of 1/[A]t versus t is linear.
The y-intercept is 1/[A]0.
For a zero-order reaction, a plot of [A]t versus t is linear.
The y-intercept is [A]0.
The reaction rate also depends on p, the proper orientation for the collision.
This factor is independent of temperature.
To find the order in NO, we will first identify two experiments in which the concentration of O2 remains constant. Then, we will divide the rate laws for those two experiments. Finally, we will solve the equation to find the order in NO.
To find the order in O2, we will repeat this procedure, this time choosing experiments in which the concentration of NO remains constant. Once the order in NO and the order in O2 are known, data from any experiment can be substituted into the rate law. The rate law can then be solved for the rate constant k.
Each test tube contains potassium permanganate, KMnO4, and oxalic acid, H2C2O4, at the same concentrations. Permanganate ion oxidizes oxalic acid to CO2 and H2O.
Top: One test tube was placed in a beaker of warm water (40°C); the other was kept at room temperature (20°C). Bottom: After 10 minutes, the test tube at 40°C showed a noticeable reaction, whereas the other did not.
Transition State Theory and Activated Complex
Transition-state theory explains the reaction resulting from the collision of two molecules in terms of an activated complex (transition state), an unstable grouping of atoms that can break up to form products.
Temperature at Which Reaction Occurs
Usually reactions speed up when the temperature increases. It takes less time to boil an egg at sea level than on a mountaintop, where water boils at a lower temperature. Reactions during cooking go faster at higher temperature.
The rate law for a reaction must be determined experimentally.
We will study the initial rates method of determining the rate law. This method measures the initial rate of reaction using various starting concentrations, all measured at the same temperature.
The fraction of molecular collisions having the minimum energy required is given by f:
f=e^(-Ea/RT)=1/e^(Ea/RT) Now we can explain the dramatic impact of temperature. The fraction of collisions having the minimum energy increases exponentially with temperature.
We will now explore the effect of a temperature increase on each of the three requirements for a reaction to occur. The rate constant can be given by the equation
k = Zfp where Z = collision frequency f = fraction of collisions with the minimum energy p = orientation factor
Rate constants for most chemical reactions closely follow an equation in the form
k=Ae^(-Ea/RT) This is called the Arrhenius equation. A is the frequency factor, a constant. A more useful form of the Arrhenius equation is ln(k2/k1)=Ea/R(1/T1 - 1/T2)
Reaction rate
the increase in molar concentration of product of a reaction per unit time or the decrease in molar concentration of reactant per unit time. The unit is usually mol/(L • s) or M/s.
The average rate is
the slope of the hypotenuse of the triangle formed.
Note that the units on the rate constant are specific to the overall order of the reaction.
• For a zero-order reaction, the unit is M/s. • For a first-order reaction, the unit is 1/s or s-1. • For a second-order reaction, the unit is 1/(M s). If you know the rate constant, you can deduce the overall rate of reaction.
