Chemical Kinetics

Kinetics

• Kinetics studies the time it takes for a chemical reaction to reach equilibrium.
• It is typically measured by the rate (amount/time) at which products appear.
• Kinetics provides insights into the reaction mechanism, detailing how the reaction occurs.

Factors Affecting Reaction Rates

• The collision model helps to understand these factors at an atomic level
• Molecules must collide with enough energy (activation energy) and proper orientation to react.

Concentration of Reactants

• Reaction rate depends on how often molecules collide (collision frequency).
• Since reactant molecules must first collide, more frequent collisions lead to faster reactions.
• Higher reactant concentration (Molarity) increases the likelihood of molecular collisions, thus increasing reaction rate.

Temperature

• At higher temperatures, reactant molecules have more kinetic energy and move faster, increasing collision frequency and speeding up reactions.
• Increased energy may overcome the minimum energy for the reaction to occur, also known as activation energy.

Reaction Rates

• Reaction rates are determined by monitoring concentration changes of reactants or products over time.

Average Reaction Rate

• Average rate is expressed as the change in concentration over a time interval.
• For a hypothetical reaction A + B → C, the average rate can be expressed in terms of the disappearance of reactants or the appearance of products.
• Avg. rate = -(change in amount of B) / (change in time) for disappearance of B
• Avg. rate = (change in concentration of C) / (change in time) for appearance of C
• It's also important then to note that (rate of appearance of C) = - (rate of disappearance of A)

Calculating Average Reaction Rate Using Experimental Data

• In the reaction C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq), the concentration of butyl chloride (C4H9Cl) was measured at various times.
• The average rate of the reaction over a time interval is the change in concentration (Δ[C4H9Cl]) divided by the change in time (Δt).
• The average rate decreases as the reaction proceeds, due to fewer collisions between reactant molecules.
• In this specific reaction, the ratio of C4H9Cl to C4H9OH is 1:1, so the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH.
• For example, the average rate from 100 to 200 seconds is calculated as -1.49 x 10^-4 M/s, where the negative sign indicates the reactant is disappearing.

Instantaneous Rate

• A plot of [C4H9Cl] versus time yields a curve, and the slope of a line tangent to the curve at any point represents the instantaneous rate at that instant.
• It is analogous to the derivative of the concentration function with respect to time.
• A plot of concentration versus time shows that reactions slow down over time.
• The best indicator of the reaction rate is the instantaneous rate near the beginning of the reaction.

Reaction Rates and Stoichiometry

• For a general reaction aA + bB → cC + dD, the rates are related by: -(1/a) (Δ[A]/Δt) = -(1/b) (Δ[B]/Δt) = (1/c) (Δ[C]/Δt) = (1/d) (Δ[D]/Δt).
• If the ratio is not 1:1, for the reaction 2 HI(g) → H2(g) + I2(g), then -(1/2) (Δ[HI]/Δt) = (Δ[I2]/Δt)

Determining the Rate Law

• The rate law expresses how the instantaneous reaction rate depends on reactant concentrations and can only be determined experimentally.
• The general form of the rate law is: Rate = k[A]^m [B]^n, where k is the rate constant, and m and n are reaction orders.

Method of Initial Rates

• By comparing experiments where initial concentrations of reactants are varied, the effect on the initial rate reveals the reaction order with respect to each reactant.
• For example, the reaction NH4+(aq) + NO2-(aq) → N2(g) + 2 H2O(l), if doubling [NH4+] doubles the rate, the reaction is first order in [NH4+].
• Similarly, if doubling [NO2-] doubles the rate, the reaction is first order in [NO2-].

Rate Constant

• A reaction where Rate ∝ [NH4+] [NO2-] can be expressed as Rate = k [NH4+] [NO2-].
• The above means Rate ∝ [NH4+] and Rate ∝ [NO2-].
• The rate constant (k) depends on temperature, but the overall reaction is second-order (sum of exponents in the rate law).

Rate Laws

• Shows the relationship between reaction rate and concentrations of reactants.
• Exponents indicate the order of the reaction with respect to each reactant.
• For the rate law Rate = k[NH4+] [NO2-], the reaction is first-order in [NH4+] and first-order in [NO2-].

Integrated Rate Laws

• Using calculus, the integrated rate law for a first-order process is ln([A]t/[A]0) = -kt.
• [A]0 is the initial concentration of A at t=0
• [A]t is the concentration of A at some time t during the reaction.
• Manipulating this equation results in ln [A]t = -kt + ln [A]0 with the form y = mx + b.
• If a reaction is first-order, a plot of ln[A] vs. t will yield a straight line, with a slope of -k. This method is a graphical way to determine the order of a reaction.
• For the conversion of methyl isonitrile (CH3NC) to acetonitrile (CH3CN), plotting ln P (pressure) as a function of time yields a straight line.
• This indicates the process is first-order with k as the negative of the slope: 5.1 × 10-5 s-1.

Second-Order Processes

• For a second-order process, integrating the rate law k[A]^2 with you get: 1/[A]t = kt + 1/[A]0.
• [A]0 is the initial concentration of A, and [A]t is the concentration of A at some time t.
• The equation, once simplified ends up also in the form y = mx + b
• If a process is second-order in A, a plot of 1/[A] vs. t gives a straight line, with the slope of that line being k. This is a useful graphical way to prove the order of reaction.
• For the decomposition of NO2 to NO + (1/2)O2 at 300 degrees C, plotting ln[NO2] vs time is not linear, so it's not first order in [A]
• However graphically plotting the inverse 1/[NO2] vs time is linear so its second order in A

Half-Life

• Half-life is the time required for a reactant's amount to reduce to one-half of its initial amount.
• [A] at t1/2 is equal to one-half of the original concentration such that [A]t is 0.5[A]0
• For a first-order process, the half-life equation becomes t1/2 = 0.693 / k, and is independent of the initial concentration, [A]0 .
• For a second-order process, the half-life equation becomes t1/2 = 1 / (k[A]0).

Temperature and Rate

• Generally, as temperature increases, so does the reaction rate.
• The rate constant k is temperature-dependent.

Collision Model

• In a chemical reaction, bonds are broken, and new bonds are formed.
• Molecules must collide with enough energy and the proper orientation to react.
• For example, Cl + ClNO needs enough energy and the correct orientation to form Cl2 + NO.

Activation Energy

• Activation energy is the minimum amount of energy required for a reaction.
• Reactions cannot occur unless molecules possess sufficient energy to overcome the activation-energy barrier.

Reaction Coordinate Diagrams

• Be familiar with reaction coordinate diagrams as they rearrange methyl isonitrile
• Also know the important points on it and related terms.
• Reaction Coordinate: A bond distance, usually the bond that is Being broken and the new bond being formed. (C-N, C-C)

Understanding Coordinate Diagrams

• The diagram shows the energy of the reactants and products.
• Also the difference, ∆E = activation energy
• The maximum on the diagram is the transition state.
• The geometry of the reactants and product at the transition state is called the activated complex.
• The energy gap between the reactants and the activated complex is the activation-energy barrier.

Maxwell-Boltzmann Distributions

• Temperature measures the average kinetic energy of molecules in a sample.
• There is a distribution of kinetic energies at any temperature.
• As the temperature increases, the curve flattens and broadens showing a larger population of molecules has higher energy.
• A way to calculate this is described by the Boltzmann distribution, where f=e^-(Ea/RT).

Arrhenius Equation

• A mathematical relationship between k and Ea, k in particular gives temperature dependence to the constant
• k = Ae^-Ea/RT, where 'A' is the frequency factor, and R = 8.314 J/mol. K
• Where A represents the probability of effective collision and to cause bond breakage or formation
• Taking the natural logarithm ln of both sides, simplifies the equation to - ln k = (Ea /R) * (1 / T) + ln A , which follows the function y = mx + b
• When given two temperatures it is possible to find two coordinates on a graph and calculate slope for accurate values

Reaction Mechanisms

• Reactions occur when atoms and molecules collide to break and make bonds, often involving multiple steps.
• The full process that occurs at an atomic level is known as the reaction mechanism.
• The chemical equations used are summaries of this complex process.
• Elementary steps include unimolecular, bimolecular, and termolecular

Multistep Mechanisms

• In a multistep process, the slowest step determines the overall reaction rate, and is called the rate-determining step..
• There are two major types of mechanisms: slow initial step and fast initial step, and in both of these the slow step of is what determines rate.

Slow Initial Step

• For a reaction like NO2(g) + CO(g) → NO(g) + CO2(g), if it's determined experimentally to be Rate = k[NO2]^2, then:
• CO is necessary but, the rate of reaction doesn't depend on concentration.
• This would then suggest that the reaction occurs in two steps:
• As an example, step 1: NO2 + NO2 gives NO3 + NO (slow), step 2 being NO3 + CO, gives NO2 + CO2
• Overall then, NO2(g) + CO(g) gives NO(g) + CO2(g).
• In doing all of these steps, NO3 then is an intermediate that us then consumed in the second step to cross it out.
• As CO is not involved with this rate determining step however, it makes it so it doesn't appear in that rate law.

Fast Initial Step

• For a reaction like: 2 NO(g) + Br2(g) → 2 NOBr(g), if the rate is found experimentally to be:
• Rate = k[NO]^2 [Br2], the rare finding of thermolecular rates suggests a two-step mechanisms:
• Where Step 1: NO + Br2 is reversible, and Step 2: NOBr2 + NO then goes forward with k1 for example gives 2 NOBr is much (slow)
• An intermediate in this would then be NOBr (intermediate)
• Since the slow set is rate-determining, we can say that Rate = k2[NOBr2] [NO], then we can conclude that because:
• The reactants and products the first were in an equilibrium, then Rate,1 = Rate,-1
• Leading tot he equation: k1[NO] [Br2] = k-1[NOBr2] by isolating the constants, and then leads to NOBr2 = NOBr2
• Then by substitution, we get: Rate Rate = (k2k1)/k1) * [NO] [Br2] [NO, which leads to R= k[NO]^2 * [Br2], checked by experiment!

Catalysts

• Catalysts increase the rate by decreasing their activation energy
• That said, they change the mechanisms in which the process occurs
• One way a catalyst will perform this action is by holding the reactants close so that reactions may be sped up. Especially with helping bonds to break

Enzymes

• Enzymes are a well known catalyst that work in biological systems
• Enzymes work like keys being inserted, in that the substrate the enzyme will bind to a select enzyme just as the key may open a lock.