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Chemistry LibreTexts

4.S: Chemical Kinetics (Summary)

  • Page ID
    81888
  • These is a summary of key concepts of the chapter in the Textmap created for "Chemistry: The Central Science" by Brown et al. 

    14.1: Factors that Affect Reaction Rates

    chemical kinetics – area of chemistry dealing with speeds/rates of reactions

    • rates of reactions affected by four factors
      1. concentrations of reactants
      2. temperature at which reaction occurs
      3. presence of a catalyst
      4. surface area of solid or liquid reactants and/or catalysts

    14.2: Reaction Rates

    • reaction rate – speed of a chemical reaction

    \[\displaystyle \textit{average rate} = \frac{\textit{change #moles B}}{\textit{change in time}}= \frac{\Delta\textit{moles B}}{\Delta t}\textit{ if }A \to B\]

    \[\Delta\textit{moles B} = \textit{moles B at final time}- \textit{moles B at initial time}\]

    \[\displaystyle \textit{average rate} = -\frac{\Delta\textit{moles A}}{\Delta t}\textit{ if }A \to B\]

    14.2.1 Rates in Terms of Concentrations

    • rate calculated in units of M/s
    • brackets around a substance indicate the concentration
    • instantaneous rate – rate at a particular time
    • instantaneous rate obtained from the straight line tangent that touches the curve at a specific point
    • slopes give instantaneous rates
    • instantaneous rate also referred to as the rate

    14.2.2 Reaction Rates and Stoichiometry

    • for the irreversible reaction \(aA+bB\to cC+dD\)

    \[\displaystyle\textit{rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t}  = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t} \]

    14.3: Concentration and Rate

    • equation used only if C and D only substances formed
    • Rate = k[A][B]
    • Rate law – expression that shows that rate depends on concentrations of reactants
    • k = rate constant

    14.3.1 Reaction Order

    • Rate = k[reactant 1]m[reactant 2]n
    • m, n are called reaction orders
    • m+n, overall reaction order
    • reaction orders do not have to correspond with coefficients in balanced equation
    • values of reaction order determined experimentally
    • reaction order can be fractional or negative

    14.3.2 Units of Rates Constants

    • units of rate constant depend on overall reaction order of rate law
    • for reaction of second order overall
    • units of rate = (units of rate constant)(units of concentration)2
    • units of rate constant = M-1s-1

    14.3.3 Using Initial Rates to Determine Rate Laws

    • zero order – no change in rate when concentration changed
    • first order – change in concentration gives proportional changes in rate
    • second order – change in concentration changes rate by the square of the concentration change, such as 22 or 32, etc…
    • rate constant does not depend on concentration

    14.4: The Change of Concentration with Time

    • rate laws can be converted into equations that give concentrations of reactants or products

    14.4.1 First-Order Reactions

    \[\textit{rate} = -\frac{\Delta [A]}{\Delta t} = k[A]\]

    and in integral form:

    \[\ln[A]_t - \ln[A]_0 =-kt\]

    or

    \[\ln\frac{[A]_t}{[A]_0} = -kt\]

    \[\ln[A]_t =   - kt + \ln[A]_0\]

    • corresponds to a straight line with \(y = mx + b\)
    • equations used to determine:
      1. concentration of reactant remaining at any time
      2. time required for given fraction of sample to react
      3. time required for reactant concentration to reach a certain level

    14.3.2 Half-Life

    • half-life of first order reaction

    \[\displaystyle t_{\frac{1}{2}} = -\frac{\ln\frac{1}{2}}{k} = \frac{0.693}{k}\]

    • half-life – time required for concentration of reactant to drop to one-half of initial value
    • \(t_{1/2}\) of first order independent of initial concentrations
    • half-life same at any given time of reaction
    • in first order reaction – concentrations of reactant decreases by ½ in each series of regularly spaced time intervals

    14.3.3 Second-Order Reactions

    • rate depends on reactant concentration raised to second power or concentrations of two different reactants each raised to first power

    \[\text{Rate} = k[A]^2\]

    \[\displaystyle\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}\]

    \[\displaystyle\textit{half life} = t_{\frac{1}{2}} = \frac{1}{k[A]_0} \]

    • half life dependent on initial concentration of reactant

    14.5: Temperature and Rate

    • rate constant must increase with increasing temperature, thus increasing the rate of reaction

    14.5.1 The Collision Model

    • collision model – molecules must collide to react
    • greater frequency of collisions the greater the reaction rate
    • for most reactions only a small fraction of collisions leads to a reaction

    14.5.2 Activation Energy

    • Svante August Arrhenius
    • Molecules must have a minimum amount of energy to react
    • Energy comes from kinetic energy of collisions
    • Kinetic energy used to break bonds
    • Activation energy, Ea – minimum energy required to initiate a chemical reaction
    • Activated complex or transition state – atoms at the top of the energy barrier
    • Rate depends on temperature and Ea
    • Lower Ea means faster reaction
    • Reactions occur when collisions between molecules occur with enough energy and proper orientation

    14.5.3 The Arrhenius Equation

    • reaction rate data: 
    • theArrhenius Equation:

    \[\displaystyle k = A e^{\frac{-E_a}{RT}}\]

    • \(k\) = rate constant, \(E_a\) = activation energy, \(R\) = gas constant (8.314 J/(mol K)), \(T\) = absolute temperature, \(A\) = frequency factor
    • \(A\) relates to frequency of collisions, favorable orientations

    \[\displaystyle \ln k = -\frac{E_a}{RT} + \ln A\]

    • the \(\ln k\) vs. \(1/t\) graph (also known as an Arrhenius plot) has a slope \(–E_a/R\) and the y-intercept \(\ln A\)
    • for two temperatures:

    \[\displaystyle \ln \frac{k_1}{k_2} = \frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)\]

    • used to calculate rate constant, \(k_1\) and \(T_1\)

    14.6: Reaction Mechanisms

    • reaction mechanism – process by which a reaction occurs

    14.6.1 Elementary Steps

    • elementary steps – each step in a reaction
    • molecularity – if only one molecule involved in step
    • unimolecular – if only one molecule involved in step
    • bimolecular – elementary step involving collision of two reactant molecules
    • termolecular – elementary step involving simultaneous collision of three molecules
    • elementary steps in multi-step mechanism must always add to give chemical equation of overall process
    • intermediate – product formed in one step and consumed in a later step

    14.6.2 Rate Laws of Elementary Steps

    • if reaction is known to be an elementary step then the rate law is known
    • rate of unimolecular step is first order (Rate = k[A])
    • rate of bimolecular steps is second order (Rate = k[A][B])
    • first order in [A] and [B]
    • if double [A] than number of collisions of A and B will double

    14.6.3 Rate Laws of Multi-step Mechanisms

    • rate-determining step – slowest elementary step
    • determines rate law of overall reaction

    14.6.4 Mechanisms with an Initial First Step

    • intermediates usually unstable, low and unknown concentrations
    • whenever a fast step precedes a slow one, solve for concentration of intermediate by assuming that equilibrium is established in fast step

    14.7: Catalysis

    • catalyst – substance that changes speed of chemical reaction without undergoing a permanent chemical change

    14.7.1 Homogeneous Catalysis

    • homogeneous catalyst – catalyst that is present in same phase as reacting molecule
    • catalysts alter Ea or A
    • generally catalysts lowers overall Ea for chemical reaction
    • catalysts provides a different mechanism for reaction

    14.7.2 Heterogeneous Catalysis

    • exists in different phase from reactants
    • initial step in heterogeneous catalyst is adsorption
    • adsorption – binding of molecules to surface
    • adsorption occurs because ions/atoms at surface of solid extremely reactive

    14.7.3 Enzymes

    • biological catalysts
    • large protein molecules with molecular weights 10,000 – 1 million amu
    • catalase – enzyme in blood and liver that decomposes hydrogen peroxide into water and oxygen
    • substrates – substances that undergo reaction at the active site
    • lock-and-key model – substrate molecules bind specifically to the active site
    • enzyme-substrate complex – combination of enzyme and substrate
    • binding between enzyme and substrate involves intermolecular forces (dipole-dipole, hydrogen bonding, and London dispersion forces)
    • product from reaction leaves enzyme allowing for another substrate to enter enzyme
    • enzyme inhibitors – molecules that bind strongly to enzymes
    • turnover number – number of catalyzed reactions occurring at a particular active site
    • large turnover numbers = low activation energies