Chemistry: Chemical Kinetics and Equilibrium Flashcards
Chemical Kinetics
The study of the rates (or speed) of reactions.
Reaction Rate
The change of concentration of reactant or finished product with respect to time.
Mechanism
The mechanism of a chemical reaction is the actual series of steps through which it occurs. Knowing the accepted mechanism of a reaction often helps to explain the reaction’s rate, position of equilibrium, and thermodynamic characteristics.
Consider this reaction: A2 + 2B –> 2AB
Suppose this equation actually takes place in two steps.
Step 1: A2 + B –> A2B (slow)
Step 2: A2B + B –> 2AB (fast)
Note that these two steps add up to the overall (net) reaction. A2B is the intermediate.
Intermediate
Molecule that does not appear in the overall reaction because it’s neither a reactant or a product.
Reaction intermediates are often difficult to detect.
Rate-Determining Step
The slowest step in a proposed mechanism. The overall reaction cannot proceed faster than this step.
Rate
Consider a reaction 2A + B –> C, where one mole of C is produced from every two moles of A and one mole of B. The rate of this reaction may be described in terms of either the disappearance of reactants over time or the appearance of products over time.
Rate = decrease in concentration of reactants/time = increase in concentration of products/time
aA + bB –> cC + dD
Rate = (-1/a)(deltaA/deltat) = (-1/b)(deltaB/deltat) = (1/c)(deltaC/deltat) = (1/d)(deltaD/deltat)
Rate is expressed in units of moles per liter per second (mol/L x S) or molarity per second (molarity/s),
Rate Law
For nearly all forward, irreversible reactions, the rate is proportional to the product of the concentrations of the reactants, each raised to some power. For the general reaction
aA + bB –> cC + dD
the rate is proportional to [A]^x x [B]^y, that is:
rate = k x [A]^x x [B]^y
This is the rate law expression where k is the rate constant. The exponents x and y are called the orders of reaction.
Rate Constant
k in the rate law expression. It is defined as a constant of proportionality between the chemical reaction rate and the concentration of the reactants. Multiplying the units of k by the concentration factors raised to the appropriate powers gives the rate in units of concentration/time.
Orders of Reaction
The exponents x and y in the rate law expression. X is the order with respect to A, and y is the order with respect to B. These exponents may be integers, fractions, or zero and must be determined experimentally.
Important to note that the exponents or the rate law are not necessarily equal to the stochiometric coefficients in the overall reaction equation. The exponents are equal to the stochiometric coefficients of the rate-determining step. If one of the reactants or products in this step is an intermediate not included in the overall reaction, then calculating the rate law in terms of the original reactants is more complex.
Reaction Order
Or overall order of reaction. It’s the sum of the exponents.
Zero-Order Reactions
Has a constant rate, which is independent of the reactant’s concentrations.
rate = k
WRT the administration of medication, a zero order reaction is one in which the amount of drug administered/eliminated per unit time remains constant. The concentration of Drug A can be calculated by
A = A0 - (k0)(t)
A0 = initial concentration of drug A in the body. k0 = zero order rate constant t = time
The zero order half life changes with time and is proportional to the initial drug concentration. It is inversely proportional to the zero order rate constant and can be represented with the following equation.
Half-Life = (1/2)(A0/k0)
First-Order Reactions
Order=1. It has a rate proportional to the concentration of one reactant.
rate = k[A]
Have units of s^-1.
The classic example of first-order reaction is the process of radioactive decay. The concentration of radioactive substance A at any time t can be expressed by
[At] = [A0]e^-kt
[A0] = initial concentration of A [At] = concentration of A at time t k = rate constant t = elapsed time
The half-life (t1/2) of a reaction is time needed for the concentration of the radioactive substance to decrease to half of its original value.
t1/2 = ln2/k = 0.693/k
Where k is the first order rate constant.
Second-Order Reactions
Order=2. Has a rate proportional to the product of the concentration of two reactants or to the square of the concentration of a single reactant.
For example, rate = k[A]^2, rate = k[B]^2, or rate = k[A][B].
Units are (M^-1)/(s^-1)
Higher-Order Reactions
Has an order greater than 2.
Mixed-Order Reactions
Has a fractional order.
Collision Theory of Chemical Kinetics
For a reaction to occur, molecules must collide with each other. The collision theory of chemical kinetics states that the rate of a reaction to the number of collisions per second between the reacting molecules. It is important to note that reaction rates almost always increase with increasing temperatures. On the other hand, reaction rates decrease with decreasing temperatures.
Not all collisions result in a chemical reaction. A effective collision occurs only if the molecules collide with correct orientation and sufficient force to break the existing bonds and form new ones. The minimum energy of collision necessary for a reaction to occur is called the activation energy, Ea, or the energy barrier. Only a fraction of colliding particles have enough kinetic energy to exceed the activation energy. This means that only a fraction of all collisions are effective.
rate = fZ
where Z is total number of collisions occurring per second and f is the fraction of collisions that are effective.
Transition State Theory
WHen molecules collide with sufficient energy, they form a transition state, in which the old bonds are weakened and the new bonds are beginning to form. The transition state then dissociates into products, and the new bonds are fully formed.
Also called the activated complex, the transition state has greater energy than either the reactants or the products. The activation energy is required to bring the reactants to this particular energy level. Once an activated complex is formed, it can either dissociate into products or revert to reactants without any additional energy input. Transition states are distinguished from intermediates in that, existing as they do at energy maxima, transition states do not have a finite lifetime.
Potential Energy Diagram
Illustrates the relationship between the activation energy, the heats of reaction, and the potential energy of the system. The most important factors in such diagrams are the relative energies of the products and reactants.
The activated complex exists at top of the energy barrier. The difference in potential energies between the activated complex and the reactants is the activation energy of the forward reaction; the difference in potential energies between the activated complex and the products is the activation energy of the reverse reaction.
Enthalpy
Difference between the potential energy of the products and reactants.
A negative enthalpy change indicates an exothermic reaction (where heat is given off).
A positive enthalpy change indicates an endothermic reaction (where heat is absorbed).
How Reactant Concentrations Effect Reaction Rate
Greater the concentrations of reactants, the greater will be the number of effective collisions per unit time, and therefore the reaction rate will increase for all but zero-order reactions. For reactions occurring in the gaseous state, the partial pressures of the reactants can serve as a measure of concentration.
How Temperature Affects Reaction Rate
For nearly all reactions, reaction rate will increase as the temperature increases. Since the temperature of a substance is a measure of the particle’s kinetic energy, increasing temperature increases kinetic energy. Consequently, the proportion of molecules having energies greater than Ea increases with higher temperature.
How Medium Affects Reaction Rate
The rate of a reaction may also be affected by the medium in which it takes place. Certain reactions proceed more rapidly in aqueous solution, whereas other reactions may proceed more rapidly in benzene. The state of the medium can also have an effect.
Catalysts
Substances that increase reaction rate without themselves being consumed; they do this by lowering activation energy. Enzymes are biological catalysts.
Catalysts may increase frequency of collision between the reactants, change the relative orientation of the reactants to make a higher percentage of collisions effective, donate electron density to the reactants, or reduce intramolecular bonding with reactant molecules.
Equilibrium Constant (Kc)
2A B+C
Since the reaction occurs in one step, the rates of the forward and reverse reaction are given by
ratef = kf[A]^2 and rater = kr[B][C]
When ratef = rater, equilibrium is achieved.
kf[A]^2 = kr[B][C] = kf/kr = [B][C]/[A]^2
Since both ks are constant,
Kc = [B][C]/[A]^2
Kc is the equilibrium constant. And the subscript c indicates it is in terms of concentration. For dilute solutions, Kc and Keq are used interchangeably.
While the forward and reverse reactions are equal at equilibrium, the molar concentrations of the reactants and products are usually not equal. This means that the forward and reverse rate constants are also usually unequal.
kf[A]^2 = kr[B][C]
kf = kr{[B][C]/[A]^2}
In a reaction with more than one step, the equilibrium constant for the overall reaction is found by multiplying together the equilibrium constants for each step of the reaction. When this is done, the equilibrium constant for the overall reaction is equal to the concentrations of products divided by reactants in the overall reaction, each raised to its stochiometric coefficient. The forward and reverse rate constants for any step n are designated kn and k-n respectively. If
aA + bB cC + dD
occurs in 3 steps, then
Kc = k1k2k3/k-1k-2k-3 = {([C]^c}{([D]^d)}/{([A]^a)([B]^b)}
This expression is known as the law of mass action.
