Notes on Reaction Mechanism and Chemical Kinetics

CHAPTER FOURTEEN: Reaction Mechanism and Chemical Kinetics

A. Fundamental Concepts of Reaction Rates

• The rate of disappearance of HI is twice the rate of formation of I₂(g) and H₂(g).
  • Expressed mathematically:
    $ext{Rate} = -\frac{1}{2} \frac{d[HI]}{dt} = \frac{1}{2} \frac{d[H₂]}{dt}$
• By multiplying through by 2, we can express the rate of disappearance of HI:
  • $\frac{d[H₂]}{dt} = 2 imes 3.5 imes 10^{-5} = 7.0 imes 10^{-5} ext{ mol dm}^{-3} ext{s}^{-1}$.
  • This means the rate of disappearance of HI is:
  • $7.0 imes 10^{-5} ext{ mol dm}^{-3} ext{s}^{-1}$.

B. Reaction Rate and Rate Constant

• Experimental studies show that the rate of a reaction depends on the concentration of the reactants:
  • General reaction: A → P
  • Rate of reaction = -$\frac{d[A]}{dt} = k[A]^n$
    • Where n is the order of the reaction representing the degree to which the rate is affected by the concentration of A.
• The rate constant (k) is:
  • A proportionality constant that shows the relationship between the rate of a reaction and the concentrations of the reactants.
• Units of the rate constant vary with the order of the reaction.

Summary of Rate Expressions by Order:

1. For a reaction of the form:
   aA + bB → Products

• $ext{Rate} = k[A]^x[B]^y$
  • Where x is the order of reaction with respect to A, y is order of reaction with respect to B, and $x+y$ gives the overall order.

1. Examples of rate laws:
   • (i) $R = k[X]$ (First Order)
   • (ii) $R = k[X][Y]$ (Second Order)
   • (iii) $R = k[X]²$ (Second Order)
   • (iv) $R = k[X]²[Y]$ (Third Order)
   • (v) $R = k[X][Y]²$ (Third Order)

C. Order and Molecularity of Reactions

• Order of a reaction is defined as the sum of the exponents of the concentration terms of the reactants in the rate law.
• Molecularity is defined as the number of elementary entities (atoms, molecules, ions) participating in an elementary step of a reaction.
• The relationship between order and molecularity:
  • Order is not always equal to molecularity; for example,
  • $C<em>{12}H</em>{22}O<em>{11}(s) + H</em>{2}O (s) → C<em>{6}H</em>{12}O<em>{6} + C</em>{6}H<em>{12}O</em>{6}$
  • Rate $= k[C<em>{12}H</em>{22}O_{11}]$ reflects a first order reaction because water does not appear in the rate law.

D. Rate Limiting Steps and Pre-Equilibria

• Consider the reaction A → P; Mechanism can be depicted as:
  • K_1: A
    ightarrow X (Fast)
  • K_2: B + X
    ightarrow P (Slow)
  • X and Y are intermediate products.
• The overall rate of the reaction is the sum of the rates of individual steps and is determined by the slowest step (Rate Determining Step).
  • $R = R<em>1 + R</em>2 + R_3$;
• For multi-step reactions where the slowest step dictates the reaction rate:
  • Example:
  • A + B ightarrow P with a mechanism:
    • $R = R<em>2 = K</em>2[B][X]$;
  • Involves calculation of [X] from reactants A and B in terms of equilibrium relationships.

Example Observations

• Rate law of reaction involving 2NO₂ + F₂ → 2NO₂F:
  • Mechanism:
  • K_1: NO₂ + F₂
    ightarrow NO₂F + F (slow)
  • $R = R<em>1 = K</em>1[NO₂][F₂]$.

E. Factors Affecting Reaction Rate

1. Concentration: Increasing reactant concentration typically increases reaction rates.
2. Temperature: Generally, higher temperatures increase reaction rates due to higher kinetic energy.
3. Presence of Catalyst: Catalysts speed up reactions without being consumed.
4. Surface Area: Larger surface areas can increase the rate of reaction for solid reactants.
5. Pressure: Change in pressure can affect reactions involving gases.
6. Light: Can influence reactions involving free radicals.
7. Nature of Solvents: Alters reactant interaction and dynamics.
8. Nature of Reactants: Different reactants have different intrinsic reactivity.

F. Zero-Order Reactions

• A zero-order reaction indicates rate independence from reactant concentration:
  • $ext{Rate} = K$;
  • Characteristics include a linear plot of concentration vs. time.
  • Half-life of a zero-order reaction is directly proportional to initial concentration:
  • $t<em>{1/2} = \frac{[A]</em>0}{2K}$.
  • Unit of the zero-order rate constant: mol dm⁻³ s⁻¹

G. First-Order Reactions

• The rate for a first-order reaction depends linearly on the concentration of a reactant:
  • $ext{Rate} = k[A]$;
  • Example:
  • H2(g) + Br2(g)
    ightarrow 2HBr(g);
  • Reaction mechanisms and rate laws.
  • Half-life of first-order reactions are independent of initial concentration:
  • $t_{1/2} = \frac{0.693}{k}$.

Example of Kinetics

• Example calculation for a hydrolysis reaction:
  • Given K₁ and concentration at varying time intervals, calculate rate constants and show the behavior towards zero-order or first-order reaction characteristics.

Conclusion

• Rate of a reaction can be influenced by concentration, temperature, catalysts, surface area, and other factors. Identifying reaction orders and constants is essential in understanding kinetics and mechanisms.
• Experimental data must be used for accurate determination of rate laws.