16Chemical kinetics

📚
RATE OF REACTION
▢ Definition: Speed with which reactants are converted into products.
▢ Scope:
  • •
    Study of rate of reaction
  • •
    Study of mechanism of reaction
▢ Expression:
  • •
    \(\text{Rate of reaction}=\dfrac{\text{Change in concentration of reactant or product}}{\text{Time taken}}\)
  • •
    For gases: \(\text{Rate}=\dfrac{\text{Change in pressure of reactant or product}}{\text{Time taken}}\)
  • •
    Rate of formation of product
  • •
    Rate of disappearance of reactant
▢ Average Rate:
  • •
    Rate measured over long time interval.
  • •
    \(\text{Average rate}= -\dfrac{\text{decrease in concentration of reactant}}{\text{time taken}}\)
  • •
    \(\text{Average rate}= +\dfrac{\text{increase in concentration of product}}{\text{time taken}}\)
Sign convention
  • •
    \(-ve\) sign → decrease in concentration of reactant
  • •
    \(+ve\) sign → increase in concentration of product
  • •
    Rate of reaction is always positive
▢ General Reaction:
❖ Reaction: \(n_1A+n_2B+n_3C+\cdots \rightarrow m_1X+m_2Y+m_3Z+\cdots\)
❖ Rate:
  • •
    \(\text{Rate}= -\dfrac{1}{n_1}\dfrac{\Delta[A]}{\Delta t}= -\dfrac{1}{n_2}\dfrac{\Delta[B]}{\Delta t}= -\dfrac{1}{n_3}\dfrac{\Delta[C]}{\Delta t}=\cdots\)
  • •
    \(=\dfrac{1}{m_1}\dfrac{\Delta[X]}{\Delta t}=\dfrac{1}{m_2}\dfrac{\Delta[Y]}{\Delta t}=\dfrac{1}{m_3}\dfrac{\Delta[Z]}{\Delta t}=\cdots\)
  • •
    \(\text{Rate}=K[A]^x[B]^y[C]^z\)
  • •
    \(x,y,z=\) orders with respect to individual reactants
  • •
    Overall order \(=x+y+z\)
▢ Instantaneous Rate:
❖ Definition: Rate of change of concentration of any reactant/product over very small interval of time.
❖ Formulae:
    ◈ _*type: bullet
  1. \(\text{Rate}= -\dfrac{dx}{dt}\) for reactant
  2. \(\text{Rate}= +\dfrac{dx}{dt}\) for product
  3. For \(A\rightarrow B\): \(\text{Rate}= -\dfrac{\Delta[A]}{\Delta t}=\dfrac{\Delta[B]}{\Delta t}\)
  4. \(\text{Instantaneous rate}=\lim*{\Delta t\to0}\left(-\dfrac{\Delta[A]}{\Delta t}\right)= -\dfrac{d[A]}{dt}\)
▢ Unit of Rate: \(\text{concentration}\times\text{time}^{-1}\), e.g. \(mol\,L^{-1}s^{-1}\).
📚
RATE OF DISAPPEARANCE AND FORMATION
▢ For \(nA\rightarrow mB\):
  • •
    \(\text{Rate}= -\dfrac{1}{n}\dfrac{d[A]}{dt}\)
  • •
    \(\text{Rate of disappearance of A}= -\dfrac{d[A]}{dt}\)
  • •
    \(\text{Rate of formation of B}= +\dfrac{d[B]}{dt}\)
Important
While calculating rate of formation or rate of disappearance, do not divide by stoichiometric coefficients.
📚
ELEMENTARY AND COMPLEX REACTIONS

Table 1: Elementary vs complex reaction

Type
Meaning
Example
Elementary reaction
Reaction occurring in single step / one step
\(H_2+I_2\rightarrow2HI\)
Complex reaction
Reaction occurring in multiple steps / more than one step
\(R_3C-Cl+NaOH(aq)\rightarrow R_3COH+NaCl\)
▢ Complex Reaction Note: Consists of several elementary reactions; gives mechanism of reaction.
📚
RATE CONSTANT
▢ Definition: Rate of reaction when concentration of each reactant is unity.
▢ Other Names:
  • •
    Specific rate constant
  • •
    Specific reaction rate
  • •
    Velocity constant
▢ General Reaction: \(aA+bB+\cdots\rightarrow products\)
▢ Rate Law: \(\dfrac{dx}{dt}=K[A]^a[B]^b\cdots\)
▢ If Concentrations Are Unity:
  • •
    If \(C_A=C_B=1\) or \([A]=[B]=1\)
  • •
    \(\dfrac{dx}{dt}=K\)
Properties
  • •
    Constant for particular reaction at given temperature
  • •
    Depends only on temperature
  • •
    Does not depend on concentration
  • •
    For gaseous reaction, concentration may be expressed as pressure in atm
  • •
    Rate at which substance reacts depends on active mass [MOE 2063]
▢ Unit of Rate Constant:
  • •
    \(K=(mol\,L^{-1})^{1-n}time^{-1}\)
  • •
    \(n=\) order of reaction

Table 1: Units of rate constant

Order
\(n\)
Unit of \(K\)
Zero order
0
\(mol\,L^{-1}s^{-1}\)
First order
1
\(s^{-1}\) [IOM]
Second order
2
\(L\,mol^{-1}s^{-1}\)
📚
COLLISION THEORY OF REACTION RATE
▢ Concept: Effective collisions bringing chemical change are few despite large number of actual collisions.
▢ Conditions for Effective Collision:
  • •
    Reacting species must possess adequate energy to overcome energy barrier.
  • •
    Reacting molecules must be properly oriented at collision.
▢ Threshold Energy: Minimum energy colliding particles must possess to make chemical reaction occur.
▢ Activation Energy: Excess energy over average energy of reacting species required to undergo chemical reaction.
▢ Formulae:
    ◉ **type: bullet
  1. \(\text{Activation energy}=\text{Threshold energy}-\text{Average kinetic energy}\)
  2. \(E_a=E*{th}-E*{KE}\)
▢ Important Points:
  • •
    Lower \(E_a\) → more effective collisions → faster reaction.
  • •
    Every chemical reaction has energy barrier.
  • •
    Temperature rise → effective collisions increase → rate increases.
  • •
    Activation energy can never be negative, zero or infinite.
  • •
    Collision theory satisfactorily explains bimolecular reactions.
📚
FACTORS INFLUENCING REACTION RATE

Table 1: Factors affecting reaction rate

Factor
Effect
Nature of reactants
Molecular reactions generally slow; ionic reactions fast
Physical state
Solid < liquid < gas in rate tendency
Surface area
Greater surface area → faster reaction
Bond strength
Weaker bond in reactant molecule → faster reaction
Orientation
Proper orientation of reactant molecules required for fast reaction
Concentration
Concentration increased → collisions increased → rate increased
Catalyst
Positive catalyst increases rate by alternative path with lower activation energy [MOE Model 2008]
Temperature
Temperature increased → effective collisions increased → rate increased
▢ Nature of Reactants Examples:
    ◉ _*type: bullet
  1. Amorphous solid reacts faster than crystalline solid.
  2. \(2NO+O_2\rightarrow2NO_2\) is faster than \(CH_4+O_2\rightarrow CO_2+H_2O\).
▢ Temperature Coefficient:
❖ Definition: Ratio of specific reaction rates of a reaction at two temperatures differing by \(10^\circ C\).
❖ Formulae:
    ◈ **type: bullet
  1. \(\text{Temperature coefficient}=\dfrac{K*{35^\circ C}}{K*{25^\circ C}}\)
  2. \(\text{Temperature coefficient}=\dfrac{K*{t+10}}{K_t}\)
❖ Value: Generally 2–3 [BPKIHS]
❖ Important:
  • •
    Rate of many reactions approximately doubles or triples for every \(10^\circ C\) rise.
  • •
    \(NO+\dfrac{1}{2}O_2\rightarrow NO_2\) exhibits negative temperature coefficient; rate decreases with rise in temperature.
📚
ARRHENIUS EQUATION
▢ Equation: \(K=Ae^{-E_a/RT}\)
▢ Terms:
  • •
    \(K=\) rate constant
  • •
    \(A=\) pre-exponential factor / frequency factor
  • •
    \(E_a=\) activation energy
  • •
    \(R=\) gas constant
  • •
    \(T=\) absolute temperature
  • •
    \(e^{-E_a/RT}=\) Boltzmann factor
▢ Log Form: \(\log K=\log A-\dfrac{E_a}{2.303RT}\)
▢ Graph:
    ◉ _*type: bullet
  1. Plot of \(\log K\) vs \(\dfrac{1}{T}\) gives straight line.
  2. \(\text{slope}= -\dfrac{E_a}{2.303R}\)
  3. Intercept on Y-axis = \(\log A\)
  4. \(E_a= -\text{slope}\times2.303R\)
▢ Two Temperature Form: \(\log*{10}\left(\dfrac{K_2}{K_1}\right)=\dfrac{E_a}{2.303R}\left(\dfrac{1}{T_1}-\dfrac{1}{T_2}\right)\)
▢ Special Case:
  • •
    If \(E_a=0\), rate of reaction is independent of temperature.
  • •
    Rate of reaction generally increases with rise in temperature.
📚
MOLECULARITY
▢ Definition: Minimum number of reacting particles, molecules, atoms or ions colliding in rate-determining step to form product/products.
▢ Characters:
  • •
    Always whole number
  • •
    Never zero
  • •
    Unimolecular, bimolecular, trimolecular etc.
  • •
    Simultaneous collisions involving more than three molecules are very rare
  • •
    Reactions with molecularity more than three are rare

Table 1: Examples of molecularity

Reaction
Molecularity
\(NH_4NO_2\rightarrow N_2+2H_2O\)
Unimolecular
\(NO+O_3\rightarrow NO_2+O_2\)
Bimolecular
\(2FeCl_3+SnCl_2\rightarrow2FeCl_2+SnCl_4\)
Trimolecular
▢ Simple Reaction: For simple one-step reactions, molecularity equals sum of molecules in balanced equation.
▢ Complex Reaction: For complex reactions, molecularity is determined by slowest step.
📚
ORDER OF REACTION
▢ Definition: Experimentally determined sum of powers of concentration terms in the rate law.
▢ General Reaction: \(n_1A+n_2B+n_3C+\cdots\rightarrow products\)
▢ Rate Law: \(\text{Rate}=\dfrac{dx}{dt}=K[A]^x[B]^y[C]^z\cdots\)
▢ Overall Order: \(x+y+z+\cdots\)
▢ Characters:
  • •
    Experimentally determined quantity
  • •
    Usually ranges between 0 and 2; may be 3
  • •
    Cannot be determined from balanced stoichiometric equation
  • •
    May be positive, negative, zero or fractional
  • •
    Classified as zero, first, second or third order when total order is 0, 1, 2 or 3
  • •
    Can be expressed with respect to a specific reactant or overall reaction

Table 1: Order examples

Reaction
Rate law
Order
\(CH_3CHO\rightarrow CH_4+CO\)
\(r=K[CH_3CHO]^{3/2}\)
1.5 with respect to \(CH_3CHO\); molecularity = 1
\(2O_3\rightarrow3O_2\)
\(r=K[O_3]^2[O_2]^{-1}\)
Order wrt \(O_3=2\); wrt \(O_2=-1\); overall = 1
📚
PSEUDO UNIMOLECULAR REACTION
▢ Definition: Reaction obeying first-order rate equation although not unimolecular.
▢ Condition: One active reactant is present in large excess, so change in its concentration is negligible.

Table 1: Examples

Reaction type
Molecularity
Order
Inversion of sucrose
2
1
Hydrolysis of organic chlorides
2
1
Acidified hydrolysis of ester
2
1
Alkaline hydrolysis of ester / saponification
2
2
📚
ZERO ORDER REACTION
▢ Definition: Reaction in which rate is independent of concentration of reactant.
▢ Rate Law:
  • •
    \(-\dfrac{dx}{dt}=K[A]^0=K\)
  • •
    Reaction velocity remains constant throughout progress [IOM 1998]
▢ Integrated Form:
  • •
    \([A]_t=[A]*0-Kt\)
  • •
    \(P_0-P_t=Kt\)
  • •
    \(t*{completion}=\dfrac{[A]_0}{K}=\dfrac{P_0}{K}\)
▢ Unit of \(K\): \(mol\,L^{-1}time^{-1}\) [MOE]
▢ Half Life:
    ◉ **type: bullet
  1. Half life directly proportional to initial concentration.
  2. \(t*{1/2}=\dfrac{a}{2K}\)
  3. \(t*{1/2}=\dfrac{P_0}{2K}\)
▢ Graph: Plot of \([A]_t\) vs \(t\) gives straight line with negative slope and intercept on Y-axis.
▢ Examples:
  • •
    Photochemical reaction: \(H_2(g)+Cl_2(g)\xrightarrow{h\nu}2HCl(g)\)
  • •
    Photochemical reaction: \(CH_4+Cl_2\xrightarrow{h\nu}CH_3Cl+HCl\)
  • •
    Dissociation on metal surface: \(2NH_3\rightarrow N_2+3H_2\)
  • •
    Decomposition of HI on gold surface
  • •
    Iodination of acetone in presence of \(H^+\) ions
📚
FIRST ORDER REACTION
▢ Definition: Rate depends on concentration of one reactant only.
▢ Rate Law: \(-\dfrac{dx}{dt}=K[A]\)
▢ Integrated Equation:
    ◉ _*type: bullet
  1. \(K=\dfrac{2.303}{t}\log\dfrac{a}{a-x}\)
  2. \(K=\dfrac{2.303}{t}\log*{10}\dfrac{[A]_0}{[A]_t}\)
▢ Terms:
  • •
    \(t=\) time
  • •
    \(a=\) initial concentration
  • •
    \(a-x=\) concentration at time \(t\)
▢ Graph: Plot of \(\log\dfrac{a}{a-x}\) vs time is linear through origin.
▢ Half Life:
    ◉ **type: bullet
  1. \(t*{1/2}=\dfrac{0.693}{K}\)
  2. \(t*{1/2}\) independent of initial concentration [IOM 2008]
▢ Important Points:
  • •
    Change in concentration unit does not affect numerical value of \(K\).
  • •
    Any concentration unit proportional to concentration can be used in integrated equation.
  • •
    Time of completion for radioactive decay is infinite.
  • •
    Radioactive decay follows first-order kinetics.
  • •
    Reactant remaining after \(n\) half lives: \(a_n=\left(\dfrac{1}{2}\right)^n a\)
▢ Examples:
  • •
    Decomposition of \(H_2O_2\) in aqueous solution: \(H_2O_2\rightarrow H_2O+\dfrac{1}{2}O_2\)
  • •
    Decomposition of ammonium nitrite in aqueous solution: \(NH_4NO_2\rightarrow N_2+2H_2O\)
  • •
    \(2N_2O_5\rightarrow4NO_2+O_2\)
  • •
    \(SO_2Cl_2\rightarrow SO_2+Cl_2\)
📚
SECOND ORDER REACTION
▢ Rate Law: \(r=K[A]^2\)
▢ Integrated Equation:
    ◉ _*type: bullet
  1. \(K=\dfrac{1}{t}\left[\dfrac{1}{a-x}-\dfrac{1}{a}\right]\)
  2. \(Kt=\dfrac{1}{a-x}-\dfrac{1}{a}\)
  3. \(\dfrac{1}{a-x}=Kt+\dfrac{1}{a}\)
▢ Graph Form: \(y=mx+c\)
▢ Half Life: \(t*{1/2}=\dfrac{1}{aK}\)
▢ Examples:
  • •
    Hydrolysis of ester by alkali / saponification
  • •
    Decomposition of \(NO_2\): \(2NO_2\rightarrow2NO+O_2\)
  • •
    Conversion of ozone into oxygen at \(100^\circ C\): \(2O_3\rightarrow3O_2\)
  • •
    \(H_2+I_2\rightarrow2HI\)
  • •
    \(2HI\rightarrow H_2+I_2\)
  • •
    \(2NO\rightarrow N_2+O_2\)
  • •
    \(2N_2O\rightarrow2N_2+O_2\)
📚
THIRD, FOURTH, FRACTIONAL AND NEGATIVE ORDER
📖
_*c
📝
Third Order Reaction
📄
Integrated Equation
\(K=\dfrac{1}{2t}\left[\dfrac{1}{(a-x)^2}-\dfrac{1}{a^2}\right]\)
📄
Half Life
\(t*{1/2}=\dfrac{3}{2Ka^2}\)
📄
Examples
  • •
    Reaction between nitric oxide and oxygen: \(2NO+O_2\rightarrow2NO_2\)
  • •
    Reduction of \(FeCl_3\) by \(SnCl_2\): \(2FeCl_3+SnCl_2\rightarrow SnCl_4+2FeCl_2\)
📝
Fourth Order Reaction
📄
Example
\(4KClO_3\rightarrow3KClO_4+KCl\)
📝
Fractional Order
📄
Example
  • •
    \(CH_3CHO\rightarrow CH_4+CO\)
  • •
    \(r=K[CH_3CHO]^{3/2}\)
  • •
    Order = 1.5
📝
Negative Order
📄
Example
  • •
    \(2O_3\rightarrow3O_2\)
  • •
    \(r=K[O_3]^2[O_2]^{-1}\)
  • •
    Order with respect to oxygen = \(-1\)
📚
METHODS FOR DETERMINATION OF ORDER
▢ Methods:
  1. Integration method
  2. Graphical method
  3. Half-life method
  4. Van't Hoff differential method
  5. Isolation method
📚
PHOTOCHEMICAL REACTIONS
▢ Definition: Chemical reaction occurring only in presence of light.
▢ Properties:
  • •
    Less affected by temperature
  • •
    Highly affected by intensity of light
  • •
    Reactions initiated by red light can be initiated by all other visible light
  • •
    Follows free radical mechanism
▢ Free Radical Mechanism for \(H_2+Cl_2\):
❖ Chain Initiation:
  • •
    \(Cl_2\xrightarrow{h\nu}2Cl\cdot\)
❖ Chain Propagation:
  • •
    \(Cl\cdot+H_2\rightarrow HCl+H\cdot\)
  • •
    \(H\cdot+Cl_2\rightarrow HCl+Cl\cdot\)
❖ Chain Termination:
  • •
    \(H\cdot+H\cdot\rightarrow H_2\)
  • •
    \(Cl\cdot+Cl\cdot\rightarrow Cl_2\)
  • •
    \(H\cdot+Cl\cdot\rightarrow HCl\)
▢ Photosensitization:
  • •
    Photosensitizer initiates photochemical reaction without itself being utilized.
  • •
    Example: chlorophyll
  • •
    \(H_2\) dissociates in presence of light only when Hg vapours are present.
  • •
    Hg is photosensitizer.
  • •
    \(Hg\xrightarrow{h\nu}\) no dissociation
  • •
    \(H_2+Hg\xrightarrow{h\nu}\) dissociation
📚
REACTION AND TEMPERATURE GRAPHS
▢ Types:
  • •
    Normal reaction: rate increases regularly with temperature
  • •
    Explosive reaction: sudden rapid rise in rate at certain temperature
  • •
    Biological reaction: optimum temperature around \(45^\circ C\)
  • •
    Complex/S-shaped variation with temperature
  • •
    Negative temperature coefficient reaction: rate decreases with rise in temperature
▢ Special Example: \(2NO+O_2\rightarrow2NO_2\): only reaction mentioned with negative temperature coefficient.
▢ Typical Linear Plots:
    ◉ _*type: bullet
  1. Rate vs concentration: zero order → rate independent of concentration
  2. Rate vs concentration: first order → rate proportional to concentration
  3. Integrated zero order: \([A]\) vs \(t\) straight line
  4. Integrated first order: \(\log[A]\) vs \(t\) straight line
📚
REACTION QUOTIENT
📖
**c
📝
Definition
Designed like equilibrium constant \(K_c\), but concentrations in \(Q_c\) are not necessarily equilibrium values.
📝
Formula
\(Q_c=\dfrac{[Product]}{[Reactant]}\)
📝
**table
    📚
    USEFUL FIRST-ORDER TIME RELATIONS
    📖
    **c
    📝
    Percent Completion
      ■ **type: bullet
    1. \(t*{50\%}=1t*{1/2}\)
    2. \(t*{75\%}=2t*{1/2}\)
    3. \(t*{90\%}=3.3t*{1/2}\)
    4. \(t*{99.9\%}=10t*{1/2}\)
    5. \(t*{x\%}=\) time for \(x\%\) decomposition
    📝
    Examples
    • •
      If 99% of reaction is completed in 32 min, 99.9% will be completed in 48 min [BPKIHS].
    • •
      In 10 half-lives, atoms left = 0.1% of initial; 99.9% decays.
    • •
      If 50% radioactive substance decomposes in 10 years, time for 99.9% decomposition = 100 years.
    📝
    Time to Reduce to \(n^{th}\) Fraction
    \(t=\dfrac{2.303}{K}\log n\)
    📝
    Amount Left After \(n\) Half-lives
    \(\dfrac{A_0}{2^n}\)
    📚
    CATALYST AND ACTIVATION ENERGY
    📖
    **c
    📝
    Catalyst
      ■ **type: bullet
    1. Used to increase or decrease reaction rate.
    2. Positive catalyst decreases \(E_a\).
    3. Catalyst alters mechanism of reaction.
    4. Greater rate constant → smaller activation energy.
    📝
    Activation Energy Points
      ■ **type: bullet
    1. Minimum additional energy required for reacting molecules to undergo reaction = activation energy.
    2. Threshold energy is minimum energy required during collision to produce effective collision, not activation energy [MOE 2010].
    3. Activation energy for reverse reaction may be less than or more than forward activation energy.
    4. Minimum activation energy of exothermic reaction is zero.
    5. For endothermic reaction, minimum value of activation energy equals \(\Delta H\).
    📝
    Acid-Base Catalysis
    In acid-base catalysis, real catalyst is \(H^+\).
    📚
    IMPORTANT TABLE
    📖
    **c
    📝
    **table
      📝
      Terms
      • •
        \(a=\) initial concentration
      • •
        \(n=\) order of reaction
      • •
        \((a-x)=\) concentration at time \(t\)
      📚
      READ & DIGEST
      ▢ Important Points:
      • •
        Rate of reaction depends on initial concentration of reactants, but rate constant is independent of initial concentration.
      • •
        Rate constant has constant value at fixed temperature.
      • •
        Rate of reaction is never negative.
      • •
        Minus sign in rate law indicates decreasing concentration of reactant.
      • •
        Generally rate increases with temperature.
      • •
        \(2NO+O_2\rightarrow2NO_2\): rate decreases slightly with rise in temperature.
      • •
        If \(E_a=0\), reaction rate becomes independent of temperature.
      • •
        If reaction rate becomes twice when concentration of reactants is increased 4 times, order = \(\dfrac{1}{2}\).
      • •
        In \(2A+B\rightarrow A_2B\), if concentration of A is doubled and B is halved, rate increases by 2 times.
      • •
        Rate doubles for every \(10^\circ C\) rise because number of activated molecules increases.
      • •
        If temperature coefficient = 2 and temperature rises from \(30^\circ C\) to \(100^\circ C\), rate increases \(128\) times.
      • •
        For \(2A+B\rightarrow A_2B\), reactant A disappears at twice the rate at which B decreases.
      • •
        If 50% reaction completes in 16 minutes, 75% completes in 32 minutes [BPKIHS 2010, MOE 2053].
      • •
        At given temperature, if activation energies of two reactions are same, specific rate constants are same.
      Q1.
      The rate of reaction doesn't depend on
      📅MOE 2008
      Q2.
      The rate of reaction depends upon
      📅MOE 2064
      Q3.
      The factor which does not influence the rate of reaction is
      📅MOE 2062
      Q4.
      75% of a first order reaction was completed in 32 minutes, when was 50% of the reaction completed?
      📅MOE 2058•BPKIHS 2010
      Q5.
      Suppose that the rate law for the reaction A → B is of the form Rate = K[A]n. What is the overall order based on the given data?
      📅MOE 2000
      Q6.
      A radioactive substance remains 1/8 of its original mass after 96 days. What is its half-life?
      📅MOE 2056
      Q7.
      The rate constant of a zero-order reaction is 'K' and initial concentration is 'a'. The half-life will be
      📅IOM 2004
      Q8.
      The order of a reaction is
      📅B.E. 2009
      Q9.
      The half-life of a reaction is 20 min. The reaction will be completed after
      📅MOE 2065
      Q10.
      When concentrations of both reactants A and B are doubled, the rate becomes 8 times. When only B is doubled, the rate becomes 2 times. The overall order is
      📅IOM 09
      Q11.
      The average minimum energy required for reactant molecules to form products is called
      📅MOE 09
      Q12.
      A lump of coal burns slowly while coal dust burns explosively. This is because of
      📅BPKIHS 2005