January 27, 2012
CH-112
Chapter 14
Chemical Kinetics
Reaction rate: the speed at which a reaction occurs.
Reaction mechanism: a step-by-step, molecular-level view of the pathway from reactants to products.
Chemical kinetics: the area of chemistry concerned with the speeds, or rates, of reactions.
Four factors allow us to change the rate at which any particular reaction occurs:
1. Physical state of the reactants. Reactants must come together to react. The more readily reactant molecules collide with one another, the more rapidly they react. Most of the reactions we consider are homogeneous, involving either all gases or all liquids. When reactants are in different phases, however, we have heterogeneous conditions, and the reaction is limited by the area of contact of the reactants. Thus, heterogeneous reactions that involve solids tend to proceed faster if the surface area of the solid is increased.
2. Reactant concentrations. Most chemical reactions proceed faster if the concentration of one or more reactants is increased. As reactant concentration increases, the frequency with which the reactant molecules collide increases, leading to increased rates.
3. Reaction temperature. Reaction rates generally increase as temperature is increased. Increasing temperature increases the kinetic energies of molecules. As molecules move more rapidly, they collide more frequently and with higher energy, leading to increased reaction rates.
4. The presence of a catalyst. Catalysts are agents that increase reaction rates without themselves being used up. They affect the kinds of collisions (and therefore alter the mechanism) that lead to reaction.
*The speed of an event is defined as the change that occurs in a given time interval, which means that whenever we talk about speed, we necessarily bring in the notion of time.
*The units for reaction rate are usually molarity per second M/s, the change in concentration measured in molarity divided by a time interval measured in seconds.
*The rate of reaction can be expressed either as the rate of disappearance of reactant A or as the rate of appearance of product B. The formula for the average is as such:
Average rate of appearance of B = (change in concentration of B) / (change in time)
Or! Average rate of appearance of B = [B] at t2 - [B] at t1 / t2-t1
OR! Average rate of appearance of B = Δ[B] / Δt
The brackets around the chemical formula, in this case [B], are used to indicate molarity.
The same formula can be used to find the average for the disappearance of A, although it is written as:
Average rate of disappearance of A = -Δ[A] / Δt
Note the negative sign, used for a very specific purpose. Rates are always expressed in positive numbers, you can't have a negative time, that doesn't make sense, so because [A] decreases, it is a negative number. The minus sign in the equation converts [A] to a positive rate of disappearance, which is necessary if we prefer to abide by the laws of nature. Rates are not negative. No, no, no.
*It is typical for rates to decrease as a reaction proceeds because the concentration of reactants decreases.
Instantaneous rate: the rate at a particular instant during the reaction. Determined from the slope of the curve at a particular point in time.
Instantaneous rate = Δ[concentration, M, of A or B] / Δt
Initial rate: instantaneous rate at t = 0
Reaction Rates & Stoichiometry:
Stoichiometry requires the rate of disappearance of A to equal the rate of appearance of B. Once again, we are abiding by the laws of nature. Law of conservation of mass and all that.
Consider the reaction C4H9Cl(aq) + H2O ------> C4H9OH(aq) + HCl(aq)
By looking at the stoichiometry of of the reaction we see that 1 mol of C4H9OH is produced for each mole of C4H9Cl consumed, making the rate of appearance of C4H9OH equal the rate of disappearance of C4H9Cl, as described in the formula:
Rate = - Δ[C4H9Cl] / Δt = Δ[C4H9OH] / Δt
When stoichiometric relationships are not one-to-one, we need to take into account the reaction stoichiometry. To arrive at a number for the reaction rate that does not depend on which component we measured, we must divide the rate of disappearance of the component by its coefficient in the balance chemical equation.
Concept is better understood upon it's application to something:
EXERCISE: RELATING RATES AT WHICH PRODUCTS APPEAR AND REACTANTS DISAPPEAR
1. How is the rate at which ozone disappears related to the rate at which oxygen appears in the reaction 2O3(g) -----> 3O2(g)
SOOOO... here we are going to use the coefficients of each part of the chemical equation in the rate formula, -2(ΔO3 / Δt) and 3(ΔO2 / Δt), but since we're dealing in fractions, as is change in concentration of O3 divided by change in time, we have to MULTIPLY by the reciprocal, as is our rule in multiplying fractions. The reciprocal of 2 is 1/2 SOOOOOOOOOOOOO..........
Rate = -(1/2)(Δ[O3]/Δt) = (1/3)(Δ[O2]/Δt)
God that looks just awful. BECAUSE IT IS. No, really it's not that bad though. You're just multiplying by the reciprocal of the coefficient of each component because in dividing fractions that's the mathematical rule.
2. If the rate at which O2 appears, Δ[O2] / Δt, is 6.0 x 10^-5 M/s at a particular instant, at what rate is O3 disappearing at this same time, -Δ[O3] / Δt ?
So for this we are given the rate at which O2 appears, and asked for the rate in which O3 with disappear. To solve this, we simply take the mole ration of O2 to O3, which is 2:3, and set it up as a stoichiometry problem:
-Δ[O3] / Δt = (6.0 x 10^-5 mol O2/L/s) (2 mol O3 / 3 mol O2 ) = 4.0 x 10^-5 mol O3/L/s
It's incredibly hard to get the idea of stoich problems in this format, as there is a great deal of division involved in them and it's hard to visualize in typed text.
Rate law: an equation that shows how the rate depends on reactant concentrations.
Rate law generally has the form: Rate = k[A]^m[B]^n, where aA + bB ------> cC + dD
k is the rate constant
[A] is the reactant 1
[B] is the reactant 2
m and n are exponents typically representing small whole numbers.
Reaction orders: the exponents m and n are reaction orders.
Consider the following: NH4+(aq) + NO2-(aq) ----------> N2(g) + 2H2O(l)
Given our rules, as they are stated above, we can fill the rate law formula as:
k[NH4+][NO2-]
When exponents are not shown, they are assumed to be the value 1, so m = 1 and n = 1.
Overall reaction order: the sum of the orders with respect to each reactant represented in the rate law.
For the above reaction, the rate law has an overall reaction number of 2 (m + n or 1+1).
Doubling or tripling components likewise doubles and triples rates.
**Although rate laws are sometimes the same as coefficients in a balanced equation, this is not necessarily a rule. Rate law must be determined experimentally!! Although it is rare, rate orders are sometimes fractional or negative.
The rate constant is the value used to evaluate whether a reaction is fast or slow. The larger the value of k, the faster the reaction with the general rule being:
k ~ 10^9 or higher = fast reaction
k ~ 10 or lower = slow reaction
I'm stopping here and spending the remainder of my day watching chemistry (nurd rage) and Ron Paul videos on YouTube. Chuck em' up.
The units of rate constant depend on the overall reaction order of the rate law.
Units of rate = (units of rate constant)(units of concentraton)^2
Hence, in the usual units of molarity for concentration and seconds for time,
Units of rate constant = (units of rate) / (units of concentration)^2 = M/s / M^2 = M^-1s^-1
First-order reaction: on whose rate depends on the concentration of a single reactant raised to the first power.
For the reaction of the type A ---> products, the rate law may be first order:
Rate = -Δ[A] / Δt = k[A]
Differential rate law: an expression of how rate depnds on concentration.
This type of expression can be transformed into an equation that related the initial concentration of A, Azero, to its concentration at any other time t, [A]time (integrated rate law):
ln[A]time - ln[A]zero = -kt
OR ln [A]time / [A]zero = -kt
OR!! ln[A]time = -kt + ln[A]zero
*** the function "ln" is the natural logarithm.
These equations can be used to:
1. determine the concentration of a reactant remaining at any time after the reation has started
2. determine the time interval required for a given fraction of a sample to react
3. determine the time interval required for a reactant concentration to fall to a certain level
The equation ln[A]time = -kt + ln[A]zero has the form of the general equation for a straight line: y = mx + b.
Second order reaction: one whose rate depends either on a reactant concentration raised to the second power or on the concentrations of two reactants each raised to the first power.
Rate = -Δ[A] / Δt = k[A]^2
This differential rate law can be used to derive the integrated rate law:
1 / [A]time = kt + 1 / [A]zero
The above equation also has a y = mx + b format
One way to distinguish between first and second order rate laws is to graph both ln[A]time and 1/[A]time against t. If the ln[A]time plot is linear, the reaction is first order; if the 1/[A]time plot is linear, the reaction is second order.
Zero-order reaction: one in which the rate of disappearance of A is independent of [A] :
Rate = -Δ[A] / Δt = k
The integrated rate law for a zero-order reaction is [A]time = -kt + [A]zero
Half-life: the time required for the concentration of a reactant to reach half its initial value, [A]time1/2 = 1/2[A]zero.
*Half-life for second order and other reactions depends on reactant concentrations and therefore changes as the reaction progresses.
The rates of most chemical reactions increase as the temperature rises. The faster rate at higher temperature is due to an increase in the rate constant with increasing temperature.
Reaction rates are affected both by reactant concentrations and by temperature.
Collision model: based on kinetic-molecular theory, accounts for both concentration and temperature a the molecular level.
The central idea of the collision model is that molecules must collide to react.
Reactant concentration increases - number of molecules available for collsion increases.
Temperature increases - speed of molecules increases, thus increasing probability of collision.
Result? Increasing reaction rates.
Orientation factor: Not every collision results in a reaction, molecules must be oriented in a certain position to bond and allow the reaction to occur.
Activation energy: the minimum energy required to initiate a chemical reaction. Another important factor in determining whether a particular collision results in a reaction.
Activation energy is written as Ea.
Energy barrier: the minimum energy molecules require to break existing bonds during a chemical reaction.
Activated complex: the molecule having the arrangement of atoms at the top of the barrier, also called transition state. That is, in a chemical reaction we can imagine a molecule breaking apart with an intermediary stage in which one portion of the molecule is sideways. The sideways molecule represents the barrier to formation of x molecule and the energy required to force the molecule through this relatively unstable sideways stage is called the activation energy, or Ea.
*Reverse reactions are endothermic. Activation energy for the reverse reaction is equal to the energy that must be overcome if approaching the barrier from the right: ΔE + Ea.
The rate depends on the magnitude of Ea; generally the lower the value of Ea, the fast the reaction.
The fraction of molecules with an energy greater than or equal to Ea is given by the expression:
f = e^-Ea/RT
R is the gas constant 8.314 J/mol-K
T is the absolute temperature
Arrhenius Equation: k = Ae^-Ea/RT
The equation is based on the fraction of molecules possessing energy Ea or greater, the number of collisions per second, and the fraction of collsions that have the appropriate orientation. Most reaction-rate data obeys the equation.
k = rate constant
Ea = activation energy
R = gas constant 8.314 J/mol-K
T = absolute temperature
A = frequency factor...
Frequency factor: constant, or nearly constant, as temperature is varied. Related to requency of collisions and the probability that the collisions are favorably oriented for reaction.
*As the magnitude of Ea increases, k decreases because the fraction of molecules that possess the required energy is small. Thus, reaction rates decrease as Ea increases.
Determination of activation energy is calculated by taking the natural log of both sides of the Arrhenius equation: ln k = -Ea/RT + ln A
Which is in line form y = mx + b
We can use that same equation (obviously with a little manipulation) to evaluate Ea in a nongraphical way if we know the rate constant at two or more temperatures:
ln k1 = -Ea / RT1 + ln A and ln k2 = - Ea / RT2 + ln A
Therefore subtracting k2 from k1 is equivalent to:
k1 - k2 = ( - Ea / RT1 + ln A ) - ( - Ea / RT2 + ln A )
Simplified and rearranged we are left with the equation:
ln k1 / k2 = Ea / R (1 / T2 - 1 / T1)
It looks god awful, doesn't it? That's because it IS god awful. I hates me some math.
But anyway, that equation is useful in determining the rate constant at one temperature by knowing the activation energy and rate constant of another temperature. So it's all just plug and play, but god awful looking plug and play at that. I like calling fomulas "plug and play". I think because you just plug numbers in and then you can play with it... I don't know, I'm strange.
Reaction mechanism: the steps by which a reaction occurs.
Elementary reactions: occurring in a single event or step.
Molecularity: the number of molecules that participate as reactants in an elementary reaction.
Unimelecular: molecularity is one, only a single molecule involved.
Biomolecular: Involving the collision of two molecules.
Termolecular: elementary reaction involving the simultaneous collision of three molecules.
Anything more than 3 simultaneous molecule collisions is considered extremely rare and therefore are not considered part of the reaction mechanism.
Multistep mechanism: consisting of a sequence of elementary reacitons.
Consider:
NO2(g) + CO(g) ------> NO(g) + CO2(g)
Proceeds in two biomolecular steps, in the first of which two NO2 molecules collide and an O atom is transferred from one to the other:
NO2(g) + NO2(g) --------> NO3(g) + NO(g)
The resulting NO3 molecule then collides with CO, transferring the O atom to it:
NO3(g) + CO(g) --------> NO2(g) + CO2(g)
The chemical equations for the elementary reactions in a multistep mechanism must always add to give the chemical equation of the overall process:
2NO2(g) + NO3(g) + CO(g) -----> NO2(g) + NO3(g) + NO(g) + CO2(g)
*Notice that there are the same amount of each type of atom in each side of the reaction.
*Notice NO3 is neither reactant nor product, it is considered an "intermediate" because it is formed in one elementary reaction and consumed in the next.
*Intermediates can be stable and sometimes identified and even isolated. Transition states, on the other hand, are always inherently unstable and can never be isolated.
Elementary Reactions and Their Rate Laws:
Unimolecular | A -----> products | Rate = k[A]
Biomolecular | A + A ----> products | Rate = k[A]^2
Biomolecular | A + B ----> products | Rate = k[A] [B]
Termolecular | A + A + A -------> products | Rate = k[A]^3
Termolecular | A + A + B -------> products | Rate = k[A]^2[B]
Termolecular | A + B + C ------> products | Rate = k[A][B][C]
*The slowest step in a multistep reaction limites the overall rate
*The rate determining step governs the rate law for the overall reaction
Catalyst: a substance that changes the speed of a chemical reaction without undergoing a permament chemical change itself. Most natural reactions occur with the help of some sort of catalyst.
Homogenous catalyst: a catalyst that is present in the same phase as the reactants in a reaction mixture is called a homogeneous catalyst.
*As a general rule, a catalyst lowers the overall activation energy for a chemical reaction.
Heterogeneous catalyst: one that exists in a phase different from the phase of the reactant molecules, usually as a solid in contact with either gaseous reactants or with reactants in a liquid solution.
Initial step is adsorption (not to be confused with ABsorption).
Adsorption: refers to the binding of molecules to a surface. Occurs because the atoms or ions at the surface of a solid are extremely reactive.
Enzymes: biological catalysts.
*Most enzymes are large protein molecules.
Catalase: enzyme that decomposes hydrogen peroxide into H2O:
2H2O2 ------> 2H2O + O2
The reaction that any given enzyme catalyzes takes place at a specific location in the enzyme, which is called the "active site".
The substances reacting at these sites are called "substrates".
Enzyme-substrate complex: the combination of enzyme and substrate.
Enzyme inhibitors: a molecule other than the substrate specific to a given enzyme that binds to the active site and blocks entry of the substrate.
*Nerve poisons and some toxic metal ions (lead, mercury) are believed to act in this way.
Turnover number: the number of individual catalyzed reaction events occurring at a particular active site. Large turnover numbers correspond to very low activation energies.
That's it!! In particular, I found the last portion the most interesting, which makes me think majoring in biochem is quite the fit for me. Cheers!