The change in concentration of a reactant or product per unit time.
When a reaction occurs, the concentration of the reactant decreases as the concentration of the product increases. This is why the reaction rate of the reactants is negative while the reaction rate of the products is positive.
Influences
Reactant Concentration
A higher concentration (more reactants) increases the frequency of collisions between particles.
A lower concentration (less reactants) decreases the frequency of collisions between particles.
Temperature
An increased temperature causes the particles to move faster and have more kinetic energy, causing more collisions.
A decreased temperature causes the particles to move slower and have less kinetic energy, causing less collisions.
Surface Area
A larger surface area increases reaction speed because it exposes more of the reactant to collisions, resulting in more collisions.
A smaller surface area decreases reaction speed because it exposes less of the reactant to collisions, resulting in fewer collisions.
Catalyst
A substance that increases the rate of reaction without being consumed or permanently altered in the process. It provides an alternative way for the reaction, which lowers the activation energy needed for the reaction. This will be fully covered in 5.11.
Pressure (Similar to concentration)
Increasing the pressure increases the frequency of collisions between particles since there would be more particles in a given volume.
Decreasing the pressure decreases the frequency of collisions between particles since there would be fewer particles in a given volume.
Calculating Rates
Average Rate is the rate of change (slope) over a set interval.
Instantaneous Rate is the slope of a line tangent, a straight line that touches the curve at one point without crossing it, to the function at any given point.
Calculating with Stoichiometry
If in reaction A + 2B -> 5C, reactant A decreased by 0.5M in 5 seconds, find the rate of reaction of A, B, and C during this time interval.
The rate of reaction would be
The rate of reaction of B would be the rate of A multiplied by 2 because the coefficient of B is double that of A.
-0.1 M/s • 2 = -0.2 M/s
The rate of reaction of C would be the positive rate of A multiplied by 5 because the coefficient of C is five times that of A. 0.1 M/s • 5 = 0.5 M/s
5.2 Introduction to Rate Law
Rate Law
Rate law is an equation of the relationship between the rate of the chemical reaction and the concentrations of the reactants.
Rate = k[A]x[B]y
Rate in M/s
k = rate constant
A and B = Concentration of the reactants (M)
x and y = rate orders
Rate Constant (k)
k is the rate constant, a proportionality factor that is specific to a given reaction at a particular temperature. k can be calculated from the rate law expression once the order is determined.
k is not affected by reactant concentrations, only by temperature and catalysts
The units of k depend on the overall order of the reaction. It can be calculated with the formula: Where n is the order
Overall Reaction Order
The sum of the order of each reactant in the rate law (x+y)
Initial Rate Method
Early on, the rate will only depend on the amount of reactants present.
Differential Rate Law (The Rate Law)
Describes the rate as a function of concentration
The differential rate law is k[A]n
k is the rate constant
n is the order
Zeroth Order
Rate Law = k[A]0 or k
The rate of the reaction is independent of the concentration of A
Unit of k: M1t-1 or M/t where t is a unit of time
First Order
Rate Law = k[A]1
The rate of the reaction is directly proportional to the concentration of A
Unit of k: M0t-1 = t-1
Second Order
Rate Law = k[A]2
The rate is proportional to the square of the concentration of A
Unit of k: M-1t-1 or 1/Mt
5.3 Concentration Changes Over Time
Integrated Rate Law (IRL)
Describes the concentration as a function of time.
[A]0 represents the initial concentration of A
[A]f represents the final concentration of A
Zeroth Order
t1/2 = [A]0 /2k
IRL: [A]t = -kt + [A]0
First Order
t1/2 = ln2/k or 0.693/k, meaning it’s a constant value that is independent of the initial concentration
IRL: ln[A]t = -kt + ln[A]0
All radioactive decay is always in the first order.
Second Order
t1/2 = 1/k[A]0
IRL: 1/[A]t = kt + 1/[A]0
Kinetic Equations given on the AP Equation Sheet
You are given Zeroth, First, and Second Order IRL equations along with First Order’s half-life.
Trends
The higher the order, the faster the reactant is being consumed.
The higher the k (rate constant) value, the smaller the half-life
The IRL equation lines up with y=mx+b
Straight-Line Plot
Since the slope is k, you can solve for k using two points and simple algebra: (y2-y1)/(x2-x1)
Rate of Decomposition Plot/Rate vs Concentration Source: MSJ Chem
5.4 Elementary Reactions
Elementary Reactions
A reaction that occurs in a single step. Rate laws of Elementary Reactions are proportionally represented by stoichiometry, where the coefficients match the rate law. Keep in mind this ONLY works for Elementary Reactions.
Molecularity
Number of molecules involved in an elementary reaction.
Notice in the graph below that the molecularity directly corresponds to the Rate law of the Elementary Steps.
Termolecular (3) is very rare since three separate molecules would have to collide in a very specific way at a specific energy level, which is highly unlikely.
5.5 Collision Model
Collision Model
Molecules must collide to react, but only a small percentage of collisions produce a reaction because of activation energy. The collision must overcome the activation energy (Ea).
Molecular Orientation
The orientation of reactants that collide must allow the formation of new bonds.
In the image below, Cl2 is formed in the reaction. For it to be formed, the NOCl molecules must collide with the Cls facing each other. Source: lhs.sau88.net
Trends
Reactions with a higher activation energy = slower reaction rate
Reactions with a lower activation energy = faster reaction rate
Higher temperature = Molecules have a faster movement speed and a higher kinetic energy, increasing the number of collisions resulting in a faster reaction rate.
Maxwell-Boltzmann Distribution
This graph shows the relationship between temperature and average kinetic energy.
The distribution allows for a qualitative estimate of the fraction of collisions with sufficient energy to lead to a reaction and how the amount of collisions depends on temperature.
EA = activation energy
5.6 Reaction Energy Profile
Reaction Energy Profile
Collisions must have enough energy to produce the reaction (equal to or more than Ea)
Energy Profile Diagram (Potential Energy Diagram)
The peak is called the transition state or the activated complex. This is the point where bonds are partially formed.
∆H = Change in enthalpy (amount of energy absorbed or released in the reaction)
The Arrhenius Equation
A complicated empirical equation describes how the rate constant of a chemical reaction changes with temperature.
You will not be used to calculating with it.
5.7 Introduction to Rate Mechanisms
Reaction Mechanism
Elementary Reaction
Intermediate (Reaction Intermediate)
An intermediate is a temporary species that forms during a reaction, existing as a product in one elementary step and as a reactant in a subsequent (later) elementary step. It is consumed before the reaction finishes and does not appear in the final product(s).
Catalyst
Catalysts help speed up a reaction by lowering the activation energy. They appear in the first elementary step as reactants and as products in the final step. They are not consumed in the overall reaction.
Example:
Intermediate(s): NO3 because it appears as a product of the first equation and as a reactant for the second equation.
Catalyst: NO2 because it appears as a reactant in the first equation and as a product in the second equation.
k1 & k2: The rate constants of the individual elementary steps.
5.8 Reaction Mechanism and Rate Law
Rate-Determining Step
The slowest step (assuming it is the first step) determines the rate of the mechanism.
In a multistep reaction, it is the slowest elementary step since it determins the rate of reaction. The rate law in a reaction mechanism would be the slowest elementary step.
Example:
NO2 (g) + NO2 (g) → NO3 (g) + NO (g) Slow
NO3 (g) + CO (g) → NO2 (g) + CO2 (g) Fast
The rate law would be k[NO2]2 because the slow step is first, which means the overall rate law depends on that slow step. Since there are two NO2 molecules, the molecularity would be two.
5.9 Steady-State Approximation
Steady-state approximation
If the second step is the rate-determining step, the first reaction must be fast and reversible. The rate of consumption of the intermediate would be balanced, causing the intermediate's concentration to remain approximately constant.
Example:
Notice that the slow elementary step is not the first step. Instead, the first step is a faster equilibrium step.
Intermediates: NOBr2
Catalyst: None
Reaction Rate: k'[NO]2[Br2] because there are two NO molecules and a single Br2. The rate constant is primed (') to show that it is not the rate constant of either elementary step but rather the rate law of the overall reaction.
5.10 Multistep Reaction Energy Profile
The slowest (rate-determining) step in a mechanism will have the highest activation energy and therefore a higher bump/peak on the graph.
Each step will have its own activation energy and bump. An endothermic elementary step will end higher (first bump in the graph), while an exothermic elementary step will end lower (last bump in the graph).
5.11 Catalysis
Catalysts
A substance that speeds up a reaction without being consumed or chemically altered in the end.
It lowers the activation energy of a reaction and will be present at the beginning and end of a reaction.
