Chemical Kinetics
Kinetics
the speed at which a chemical reaction occurs (Reaction rate)
also sheds light on reaction mechanism (exactly how the reaction occurs)
Factors that Affect Reaction Rates
1. Physical state of the reactants
in order to react, molecules must come in contact with each other
the more homogenous (same structure) the mixture of reactants, the faster the molecules can react
the heterogenous reactions with solids proceed more rapidly if the surface area is increased
powder medicine—>stomach, enters blood quickly
tablet medicine—>slower
2. Concentration of reactants
as the concentration of reactants increases, so does the likelihood that reactant molecules will collide
3. Temperature
at higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy
ex: bacterial reaction (spoil milk) proceed rapidly at room temperature than at lower temperature (in the refrigerator)
4. Presence of a catalyst
catalysts speed up reactions by changing the mechanism of the reaction (they affect the collisions)
catalysts are not consumed during the course of the reaction
Reaction Rates
rates of reactions can be determined by monitoring the change in concentration of either reactants or products as function of time (unit for reaction rate: M/s)
ex: hypothetical reaction A—>B
Average rate of appearance B= change in concentration of B/change in time = delta [B]/delta t
Average rate of disappearance of A = - change in concentration of A/change in time = - delta [A]/delta t
Sample exercise 14.1
Change of Rate with Time
rates decrease as reaction proceeds because the concentration of the reactants decrease.
as the reaction goes forward, there are fewer collisions between reactant molecules
Instantaneous Rate
the plot of [C4H9Cl] versus time for this reaction yields a curve like this
it shows how the concentration of the reactant changes with time which allows us to get the instantaneous rate of a reaction
the rate at particular instant during the reaction
the slope of a line tangent to the curve at any point is the instantaneous rate at that time
instantaneous rate = - 0.017M -0.042M / 800s - 400s = 6.3×10^-5 M/s
use the concentrations of the highest point of concentration subtracted from the lowest point of concentration
all reactions slow down over time
therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning of the reaction (initial rate)
instantaneous rate at t=0 is called the initial rate
Sample exercise 14.2
Reaction Rates and Stoichiometry
in this reaction, the ratio of C4H9Cl to C4H9OH is 1:1
thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH
-delta[C4H9Cl]/delta t = [C4H9OH]/delta t
if the ratio is NOT 1:1…
ex: 2HI —> H2 + I2
rate = -1/2 (delta [HI] / delta t) = (delta [H2] / delta t) = (delta [I2] / delta t)
sample exercise 14.3
Concentration and Rate Laws
one can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration
the equation is called rate law, and k is the rate constant
a A + b B —> c C + d D
[A]^a [B]^b —> [C]^c + [D]^d
the exponents tell the order of the reaction with respect to each reactant
since the rate law of the reaction…
rate = k[NH4+] [NO2^-]
the reaction is first order in [NH4+] and first order in [NO2^-]
Rate Constants
rate = k[NH4+][NO2^-]
k = rate/[NH4+][NO2]
larger value of k means fast reaction
Integrated Rate Laws
Rate = k[A] = d[A]/dt
rate laws can be converted into equations that show the relationship between concentration of the reactants and or products and time
calculus is used to integrate the rate law applied to: Overall order: 0, 1, and 2
for first order process…
ln[A]t - ln[A]0 = -kt or ln [A]t/[A]0 = -kt —> y = mx + b
[A]0 = initial concentration of A and [A]t is the concentration of A at some time, t, during the course of the reaction
Therefore, if a reaction is first-order, a plot of ln[A] vs. t will yield a straight line, and the slop of the line will be -k.
Second Order Reactions
Rate = k[A]²
1/[A]t = it + 1/[A]0
also in the form of y = mx + b
So if a process is second order in A, a plot of t vs 1/[A] yields a straight line, and the slope of the line is k.
Zero Order Reactions
Rate of disappearance of reactant is independent of reaction concentration
Half Life
defined as time required for one-half of a reactant to react
Because [A] at t1/2 is one half of original [A], [A]t = 0.5 [A]0
For first order process, the half life does not depend on [A]0
Second order process half life depends on initial concentration
Temperature and Rate
as temperature increases, so does the reaction rate
k is temperature-dependent
Collision Model
in chemical reaction, bonds are broken and new bonds are formed
molecules can only react if they collide with eachother
Orientation Factor
In order for a reaction to occur, molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation
Activation Energy
reactants need minimum amount of energy required for the product formation: Activation Energy (Ea)
just as a ball cannot get over a hill if it does not roll up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation energy barrier
Energy Profile Diagrams
it is helpful to visualize energy changes throughout a process on a energy profile [or] reaction coordinate diagram
the diagram shows the energy of the reactants and products (and therefore, delta E)
the high point on the diagram is the transition state
the species present at the transition state is called the activated complex
the energy gap between the reactants and the activated complex is the activation energy. Lower the Ea, faster the reaction
Effect Temperature
the fraction of molecules can be found through the expression f=e^-Ea/RT
the larger the fraction of molecules, reacts at a higher temperature
where R is the gas constant and T is the Kelvin temperature
Arrhenius Equation
a developed mathematical relationship between k and Ea
k = Ae^-Ea/RT
A=frequency factor, represents frequency of collision and probability of collisions with the proper orientation for reaction
Determination of Ea
taking the natural log Arrhenius equation
lnk = -Ea/RT + lnA
y = mx +b
therefore, if k is determined experimentally at several temperatures Ea can be calculated from the slope of a plot of ln k vs. 1/T
to find slope, m
m = delta y/delta x = (ln k2 - ln k1)/(1/T2 - 1/T1) or ln(k2/k1)/(1/T2 - 1/T1)
Ea is given by the plot of lnk against 1/T means that, higher the Ea, the stronger the temperature dependence of the rate constant (steeper the slope)
A high Ea signifies that the rate constant depends strongly on the temperature
If reaction has zero activation energy, its rate is independent of temperature
Reaction Mechanisms
sequence of events that describes the actual process by which reactants become products is called the reaction mechanism
reactions may occur all at once or through several discrete steps
each of these processes is known as an elementary reaction or elementary process
Molecularity
tells how many molecules are involved in the process
unimolecular; A—>products; Rate = k[A]
bimolecular; A+A—>products; Rate = [A]²
bimolecular; A+B—>products; Rate = [A][B]
termolecular; A+A+A—>products; Rate = [A]³
termolecular; A+A+B—>products; Rate = [A]²[B]
termolecular; A+B+C—>products; Rate = [A][B][C]
Multistep Mechanisms
consists of sequence of elementary reactions
ex: No2+CO—>NO+CO2
Experimentally, Rate = k[NO2]²
a proposed mechanism for this reaction is
step 1: NO2+NO2—>NO3+NO
step 2: NO3+CO—>NO2+CO2
The NO3 intermediate is consumed in the second step (product from step 1 used in step 2 = cancel out)
Rate-Determining Step
in a multistep process, one of the steps will be slower than all the others
the overall reaction cannot occur faster than this slowest, rate-determining step
NO2+CO—>NO+CO2
Experimentally, rate = k[NO2}²
a proposed mechanism for this reaction is
step 1: NO2+NO2—>NO3+NO (slow)
step 2: NO3+CO—>NO2+CO2 (fast)
rate constant for step 2 (k2) is much greater than step 1 rate constant k1. This observation supports the proposed mechanism
Fast initial step
2NO+Br2—>2NOBr
the rate law for this reaction is found to be Rate = [NO]²[Br2]
because termolecular processes are rare, this rate law suggests a two-step mechanism
step 1: NO+Br2—>←-NOBr2 (fast)
step 2: NOBr2+NO—>2 NOBr (slow)
step 1 includes the forward and reverse reactions
the rate law for that step would be rate = k2[NOBr2][NO]
NOBr can react two ways::
With NO to form NOBr
by decomposition to reform NO and Br2
the reactants and products of the first step are in equilibrium with each other
therefore, Rate f = Rate r
k1[NO][Br2] = k-1[NOBr2]
solving for [NOBr2], gives us k1/k-1 [NO][Br2] = [NOBr2]
Rate = k2k1/k-1 [NO][Br2][NO] = k[NO]²[Br2] (overall rate)
Catalyst
increase the rate of reaction by decreasing the activation energy of the reaction
catalysts change the mechanism by which the process occurs
Homogenous Catalysis
Heterogenous Catalysis
one way a catalyst can speed up a reaction is by holding reactants together and helping bonds to break
Enzymes
are catalysts in biological systems
the substrate fits into the active site of the enzyme much like a key fits into a lock