KINETICS
A. Reaction Rate -- the speed with which its reactants disappear and its products form
1. Mechanism of the reaction -- series of individual steps that add up to the overall observed reaction
2. Kinetics --study of reaction rates
II. Factors That Affect Reaction Rates
A. Chemical nature of the Reactants
1. What are the inherent tendencies of their atoms, molecules, or ions to undergo changes in chemical bonds
B. Ability of the Reactants to Meet
1. Homogeneous reaction -- all in the same phase, happen most easily in gaseous and aqueous systems (molecules are able to move and collide)
2. Heterogeneous reaction -- two different phases, reaction is determined by the area of contact between the phases
a. Powdered solids increase surface area, therefore increase reaction
C. concentrations of the Reactants
1. Increase concentration, increase reaction rate
D. Temperature of the system
1. Generally, increase temperature, increase reaction rate
E. Presence of Catalysts
1. Catalyst speed up reaction but do not change themselves
III. Measuring a Rate of Reaction
A. Rates of Chemical Reactions
1. Rate is always with respect a certain species
2. Units = mol/L/s
3. Usually given as a positive value whether it increases or decreases
B. Rates and Coefficients
1. The magnitudes of the rates relative to each other are in the same relationship as the coefficients in the balanced equation
C. Change of Reaction Rate with Time
1. A reaction rate is not constant throughout the reaction, but changes as the reactants are used up
a. Rate usually depends on the concentration of the reactants
b. When concentration is graphed versus time, the steeper the slope the higher the rate
IV. Concentration and Rate
A. Rate Laws -- equation to determine the rate of reaction between reactants
1. Rate of a homogeneous reaction at any instant is proportional to the product of the concentrations of the reactants raised to some exponent that has to be found experimentally
2. Rate constant (k) -- proportionality constant for the reaction
3. Rate = k[A]m[B]n
a. A & B = reactant concentrations, m & n = exponents
B. Exponents in the Rate Law
1. Order of Reaction -- the exponent in the rate law (first order, second order, etc.)
a. never assume the exponents and the coefficients are the same
2. Overall order of a reaction -- the sum of the orders with respect to each reactant in the rate law
3. Negative exponent -> concetration term belongs in denominator
a. Concentration increases, rate decreases
4. Zero exponent -> reaction rate is independent of the concentrations
C. Determining the Exponents in Rate Laws
1. experimentation is the only way for us to know for sure what the exponents are
2. If concentration doubles and rate doubles, exponent is 1 (2^1), first order rate
3. If concentration doubles and rate increases by a factor of 4 (2^2), exponent is 2, second order
4. If concentration doubles and rate increases by a factor of 9 (3^2), exponent is 3, third order
V. Concentration and Time
A. Concentration versus Time for First-Order Reactions
1. Involves a differential equation (calculus)
2. ln([A]o/[A]t) = kt
a. [A]o = initial concentration, [A]t = concentration at some time
3. Rearrange equation to represent a straight line equation (y = mx +b)
a. ln[A]t = -kt + ln[A]o
b. A plot of ln[A]t versus t should give a straight line with slope = -k
B. Concentration versus Time for Second-Order Reactions
1. (1/[B]t) - (1/[B]o) = kt
2. Rearrange equation to represent a straight line equation
a. (1/[B]t) = kt + (1/[B]o)
b. A plot of 1/[B]t versus t should give a straight line with slope = k
C. Half-Life for First- and Second-Order Reactions
1. Half-Life t(1/2) -- the amount of time required for half of the reactants to disappear
2. Half-Life of First-Order Reactions
a. After some substituting and algebra...
b. t(1/2) = (ln 2)/k
c. t(1/2) is a constant since k is a constant for first order reactions at any temperature
d. t(1/2) is not afected by the initial concentration of the reactants
3. Half-life of Second-Order Reactions
a. Does depend on the inital concentration
b. t(1/2) = (1/k[B]o)
VI. Theories about Reaction Rates
A. Collision Theory
1. the rate of reaction is proportional to the number of effective (actually produces products) collisions per second among reactant molecules
a. Not all collisions actually result in chemical change
b. Most reactions occur at very small fractions of all the collisions possible (would be explosive if all do occur)
2. Concentration -- increase concentration, increase collisions, increase rate
3. Molecular Orientation
a. Correct parts of each molecule need to be facing each other during the collision
4. Molecular Kinetic Energy
a. Activation Energy (Ea) -- minimum amount of energy needed to cause a reaction at collision
b. fast molecules with large kinetic energy can overcom repulsive forces and collide in such a way to break bonds
5. How Temperature Greatly Affects Rates
a. Higher temperatures, a greater fraction of the collisions occuring each second results in a chemical change
B. Transition State Theory
1. used to explain in detail what happens when reactant molecules come together in a collision
a. As molecules collide, they slow down, so KE is changed into PE
b. Plot PE versus reaction coordinate -- (extent to which reactants have changed into products)
1. If combined KE is greater than Ea, then reaction does occur
2. If combined KE is less than Ea, then reaction does not occur
2. Heats of Reaction, Energies of Activation, and Potential-Energy Diagrams
a. Exothermic reation -> products have lower potential energy than reactants
b. Endothermic reaction -> products have higher potential energy than reactants
c. Heat of Reaction (DeltaH) is the difference between PE(reactant) and PE(products)
d. if DeltaH = positive and high, Ea must also be high, reaction is very slow
e. If Delta H = negative, we can not determine th magnitude of Ea
f. Transition State -- brief moment during a successful collision when all bonds (ones broken and ones made) are present equally
1. Activated complex -- unstable chemical species that momentarily exists at this instant
2. Happens at the highest peak on the graph
VII. Measuring the Activation Energy
A. Arrhenius equation -- k = Ae^(-Ea/RT)
1. A = proportionality constant called frequency factor, R = 8.31 J/mol/K
2. small increase in T, great increase in rate
B. Determining the Activation Energy Graphically
1. rewrite above equation in linear form...
2. ln k = ln A + (-Ea/R) x (1/T)
a. A plot of ln k versus 1/T should give a straight line with slope = -Ea/R
C. Calculating the Activation Energy
1. ln(k2/k1) = (-Ea/R)(1/T2 - 1/T1)
VIII. Collision Theory and Reaction Mechanisms
A. elementary Process -- a reaction whose rate law can be written from its own chemical equation
1. Mechanism -- entire series of elementary processes
2. the overall rate law derived from the mechanism must agree with the observed rate law for the overall reaction
B. Predicting the Rate Law for an Elementary Process
1. Rate is proportional to the number of effective collisions per second between reactants
2. the exponents in the rate law of an elementary process are equal to the coefficients of the reactants in the chemical equation for that elementary process
C. Predicting Reaction Mechanisms
1. A test: Being able to add the elementary processes and thus to obtain the overall reaction
2. Rate-determining step (rate-limiting step) -- the slowest step in the mechanism
a. Rate law for the rate-determining step is directly related to the rate for the overall reaction
b. Chemist try to use only bimolecular collisions in elementary processes
3. Usually one step is view as being in dynamic equilibrium
a. Rate forward = Rate reverse
b. Use this to derive rate law for overall mechanism (substitution)
IX. Catalysts -- a substance that changes the rate of a chemical reaction without itself being used up
A. Positive versus Negative Catalyst
1. Positive -- speeds up reaction, Negative slows down reaction
B. Homogeneous Catalysts
1. same phase, lowers activation energy
C. Heterogeneous Catalysts
1. Commonly a solid, promotes a reaction on its surface
Outline based upon:
Brady, J. E., Holum, J. R., Russell, J. W. (2000). Chemistry: The Study of Matter and Its Changes. (3rd ed.). New York: John Wiley & Sons, Inc. pp. 573-614.
