Understanding Chemical Kinetics

Chemical Kinetics

• This field helps in understanding how chemical reactions take place.
• Chemistry is concerned with substances altering into other substances through chemical reactions.
• Chemists seek to determine:
  • The feasibility of reactions using thermodynamics (∆G < 0 at constant temperature and pressure).
  • The extent to which reactions proceed, determined by chemical equilibrium.
  • and the speed of reactions, which is the time it takes to reach equilibrium.
• Knowing the rate and controlling factors is important for complete understanding.
• Chemical kinetics studies reaction rates and mechanisms.
• Kinetics originates from the Greek word kinesis, meaning movement.
• Thermodynamics indicates reaction feasibility, while chemical kinetics shows the rate of a reaction.
• The speed of a reaction and conditions to alter rates involve concentration, temperature, pressure, and catalysts.
• Macroscopic level: amounts reacted or formed, and their consumption or formation rates
• Molecular level: reaction mechanisms detail molecule orientation, energy during collisions

Rate of a Chemical Reaction

• Focus is on average and instantaneous reaction rates, and factors affecting them
• Ionic reactions occur very fast
  • silver chloride precipitation
• Some reactions are very slow
  • rusting of iron
• Some reactions proceed at a moderate speed
  • inversion of cane sugar
  • hydrolysis of starch
• Reaction speed is the change in concentration of reactant or product per unit time, expressed as:
  • Rate of decrease in reactant concentration, or,
  • Rate of increase in product concentration.
• Hypothetical reaction: R → P, assuming constant volume.
• One mole of reactant R produces one mole product P
  • If [R]₁ and [P]₁ are the concentrations of R and P at time t₁ and [R]₂ and [P]₂ are at time t₂
  • Formulas
    • Δt = t₂ - t₁
    • Δ[R] = [R]₂ - [R]₁
    • Δ[P] = [P]₂ - [P]₁
• Square brackets denote molar concentration
• Rate of disappearance of R = -(Δ[R]/Δt) aka Decrease in concentration of R / Time taken
• Rate of appearance of P = +(Δ[P]/Δt) aka Increase in concentration of P / Time taken
• Δ[R] is negative, so a negative sign is added to the rate reaction to make it positive
• Average rate of a reaction depends on reactant/product concentration change and time taken.

Units and Example of Reaction Rates

• Units of rate are concentration/time shown by the formula concentration x time ⁻¹
• If concentration is in mol L⁻¹ and time in seconds, units are mol L⁻¹s⁻¹
• For gaseous reactions, using partial pressures, units are atm s⁻¹
• Average reaction calculated using concentrations of butyl chloride at different times
• Reaction formula is C₄H₉Cl + H₂O → C₄H₉OH + HCl
• Varying rates can be determined by concentration and the given time period

Instantaneous and Average Rates

• Average rate falls from 1.90 × 10⁻⁴ mol L⁻¹s⁻¹ to 0.4 × 10⁻⁴ mol L⁻¹s⁻¹
• Average rate cannot predict reaction rate at a specific time.
• Instantaneous rate is found when average rate is taken at the smallest time interval(dt)
• When Δt approaches zero, instantaneous rate: r(inst) = -d[R]/dt = d[P]/dt
• Can also be determined graphically by drawing a tangent at time t on either the curves for concentration of R and P vs time and calculating its slope *

Rate of Reactions and Stoichiometry

• For reactions with the same stoichiometric coefficients of reactants and products:
• Rate = -Δ[Hg]/Δt = -Δ[Cl₂]/Δt = Δ[HgCl₂]/Δt
• For reactions where the stoichiometric coefficients of reactants or products are not equal
  • Rate = -(1/2) Δ[HI]/Δt = Δ[H₂]/Δt = Δ[I₂]/Δt (2HI(g) → H2(g) + I2(g))
• For a reaction 5 Br⁻ (aq) + BrO₃⁻ (aq) + 6 H⁺ (aq) → 3 Br₂ (aq) + 3 H₂O (l)
  • Rate = -(1/5) Δ[Br⁻]/Δt = -Δ[BrO₃⁻]/Δt = -(1/6) Δ[H⁺]/Δt = (1/3) Δ[Br₂]/Δt = (1/3) Δ[H₂O]/Δt
• For reactions at a constant temperature
  • Rate is directly proportional to its partial preasure

Factors that Influence Reaction Speed

• Rate depends on reactants concentration/pressure (gases), temperature, and catalysts
• Rate may depend on reactants and products
• The representation of rate of reaction in terms of concentration of the reactants is known as rate law.
• Also called rate equation or rate expression
• A reaction rate decreases as the concentration of the reactants decrease

Rate Law

• aA + bB → cC + dD general reaction where a, b, c and d are represent stoichiometric coefficients
• The rate expression for this reaction is:
  • Rate α [A]ˣ[B]ʸ
  • Exponents x and y may or may not be equal to reactants stoichiometric coefficients
  • Rate = k[A]ˣ[B]ʸ where k is the rate constant(proportionality constant)
• Rate law is expression in which reaction rate is given in terms of molar concentration of reactants

Reaction Order

• x and y indicate how sensitive the rate is to the change in concentration
• Sum of exponents x + y in Rate = k [A]ˣ[B]ʸ indicates the overall order of reaction x and y indicates the order with respect to the reactants A and B
• Rate law expression is called the order of the chemical reaction

Order Types

• Order can be 0, 1, 2, 3, or a fraction
• Rate = k [A]ˣ [B]ʸ where k is the rate constant
• A zero order reaction rate does not depend on concentration of reactants
• Reactions are rarely completed in one step:
  • elementary reactions taking place in one step
  • complex reactions with sequences of elementary reactions in a mechanisms

Reaction Steps

• Consecutive reactions
  • oxidation of ethane to CO₂ and H₂O
• Reverse and side reactions
  • nitration of phenol yields o-nitrophenol and p-nitrophenol
• For a general reaction aA + bB → cC + dD: Rate = k [A]ˣ[B]ʸ where x + y = n (order of the reaction)
• Rate constant is the Rate/([A]ˣ[B]ʸ)
• Taking SI units of concentration, mol L⁻¹ and time, s, the units of k in different reaction orders:

Molecularity

• This helps in understanding its mechanism and it´s the number of reacting atoms, ions or molecules
• Molecularity is described an reaction in elementary step, colliding simultaneously

Molecularity Types

• The reaction can be unimolecular with only one reacting species, for example, decomposition of ammonium nitrite: NH₄NO₂ → N₂ + 2H₂O
• Bimolecular reactions involve simultaneous collision between two species, for example, dissociation of hydrogen iodide: 2HI → H₂ + I₂
• Trimolecular or termolecular reactions involve simultaneous collision between three reacting species, for example, 2NO + O₂ → 2NO₂
• Reactions with molecularity three are very rare and slow

Reactions Involving more than Three Molecules

• They must take place in more than one step such as in KClO₃ + 6FeSO₄ + 3H₂SO₄ → KCl + 3Fe₂(SO₄)₃ + 3H₂O
• This reaction appears to be of tenth order and is a second order reaction
• If we go through the mechanism of reaction for multiple steps we can find the rate determining step
• The oxidation of H₂O₂ is the rate determing step: 2H₂O₂ -(I⁻/(Alkaline medium))→ 2H₂O + O₂
• Rate = k[H₂O₂][I⁻] where Evidences suggest that this reaction takes place in two steps:
  • H₂O₂ + I⁻ → H₂O + IO⁻
  • H₂O₂ + IO⁻ → H₂O + I⁻ + O₂

Conclusions on Rate and Molecularity

• Order is determined experimentally; can be zero or a fraction
• Molecularity cannot be zero or non-integer
• Order is applicable to both elementary and complex reactions
• Molecularity applies only to elementary reactions
• Thus, molecularity has no meaning for complex reactions
• For complex reactions, order is given by the slowest step, and its molecularity is the order of the overall reaction

Integrated Rate Equations

• Differential rate equations relate concentration dependence and rate
• Determining instantaneous rate (slope of tangent at point 't' on concentration vs time plot) and so, order of the reaction is not a convenient way to study reaction kinetics
• Integrated rate equations relate experimental data i.e., concentrations at different times
• Different reaction orders have different integrated rate equations
• Integrated rate equations are determined only for zero and first order chemical reactions

Zero Order Reactions

• Rate is proportional to zero power of reactant concentration: R → P; Rate = -d[R]/dt = k[R]⁰
• Since any quantity raised to power zero is unity
  • Rate = -d[R]/dt = k × 1; d[R] = -k dt
• Integrating both sides results in [R] = −kt + I where, I is the constant of integration and t = 0 so [R] = [R]₀ therefore [R] = -kt + [R]₀
• [R] = −kt + I and k is gotten as K=([R]₀-[R])/t
• Zero order reactions are uncommon, occurs in reactions catalysed by enzymes and on metal surfaces
• Gaseous ammonia decomposition on hot platinum surface is an example:
  • 2NH₃(g) --(Pt catalyst/1130K)→ N₂(g) + 3H₂(g)
  • Rate = k [NH₃]⁰ = k

First Order Reactions

• In this class of reactions, Rate is proportional to reactant concentration.
• For this example: R → P
  • Rate=d[R]/dt = k[R]
• d[R]/[R]=-kdt
• After integration we can get:
  • In [R] = kt+I
• I here is the constant of integration. For t=0 R=[R]₀ is the initial concentration
• From those equations we can derive the following:
  • ln [R] = −kt + ln[R]₀
  • k=(In[R]₀/R])/t
  • In([R]/[R]₀)= −kt
  • [R] = [R]₀e^−kt
• The last equation can be used in a cartesian coordinate systems.
  • If there are to terms to know the value, the result would be.
    • kt ln [R]₁ / [R]₂

How this affect to Time

• Also If we need to know the value of first order equation then is also correct use the next formula:
  • *k = [2.030/t]log[R]₀/[R]

First order reaction examples

• If we need to plot the value log [R]₀/[R] we can see the slope if equal to (k/2.303) of value R
• Hydration of ethene: Rate [C₂H₄]
• All natural and artificial radioactive decay of unstable nuclei has a first order

Example 3.5

• N₂O equation with a pressure of 1.24 × 10⁻² mol L⁻¹ at 318 K but after 60 min 0.20 × 10⁻² mol L⁻¹
• The rate equation is: log [R]₁/[R]₂ = K(t2 - t1)/2.303

Zero order reaction

• (k=1/[t₂−t₁])In([R]₁)/([R]₂) Total pressure for a first order reaction will be PT=pA+pB+pC And the values of pt, pA and pB will be the partial pressure for A B and C Pt=0 P=pt-1 with this the general formulation will be, k= 2.303logp₀/2p₀-pt/t
• The following rate equation were obtained during the first Thermal of following example:

Table for example

• where k is the next formulation we got: k=2.303/t*log(P₀/P4 Decomposition 8 gives the most valuable expression for The half value of the rate concentration with the finality of knowing how many in time

Formula Half-Life

• Is defined in the equation from the expression of zero rate
• k= where [R]₀−[R] t
• And the k value has this expression 0.693 = kt1/2 Where 0.693 =t1/2 And in the half value of T and first rate equation, where we can see how this expression has
• And we have the value 0.0693/k

Pseudo First Order Reaction

• They are reactions that seem of 1st order but they are not
• C₁₂H₂₂O₁₁ + Water =rate [c₁₂h₂₂o₁₁]

Temperature dependence of the rate of a chemical reaction

• Can be accurately explained by Arrhenius equation
• The rate constant usually doubles
• With the Dutch chemist Jacobus Henricus van 't Hoff (1852 - 1911), The equation that the Arrhenius describes: k=Ae^Ea/RT where A is the Arrhenius factor