Chapter 6: Reaction Kinetics

Rate of Reaction

Definition:

• The rate of a reaction is defined as the change in concentration of a reactant or a product per unit time

Units of Rate:

• mol dm⁻³s⁻¹

• mol dm⁻³min⁻¹ (other units of time)

Example: H₂ + I₂ → 2HI

• Change in concentrations of H₂ and I₂ are the same

• Change in concentration of HI 2x faster

• Rate of [H₂] = ½ rate of [HI]

Concentration-Time Graph

Rate of Reaction = Gradient of the tangent of a concentration-time graph

• y₁-y₂ / x₁-x₂

• Draw a tangent at t = x to find the gradient

Initial Rate of Reaction:

• When t = 0

Instantaneous Rate of Reaction:

• Specified time t

Average Rate of Reaction:

• The change in concentration of a reactant or a product over a specified time interval

Negative Gradient:

• It indicates a decrease in concentration

• Usually for reactants

Positive Gradient:

• It indicates an increase in concentration

• Usually for products

Gradients:

• Steeper the gradient = Faster the rate of reaction

• When gradient =0 , there is no change in concentration

  • This means rate of reaction is zero

  • The reaction has stopped

Rate Equation

Definition:

• The rate equation is an experimentally determined equation that relates the rate of reaction to the concentrations of the reactants raised to appropriate powers

Rate Equation:

rate (mol dm^-3s^-1) = k [A]^m [B]ⁿ (mol dm^-3)

• m and n are the orders of reaction with respect to [A] and [B] respectively

• k is the rate constant

Order of Reaction

Definition:

• The order of reaction with respect to a reactant is the power on its concentration term in the rate equation. The order of reaction must be determined experimentally.

Overall / Total Order of Reaction:

• It is the sum of the individual orders

Order of Reaction & Reaction Rate:

• The order of reaction with respect to a reactant, A, tells us how the concentration of that reactant affects the reaction rate

• The order of reaction are usually positive integers

  • Although they can also be fractional or even negative

• Conditions:

  • If rate of reaction is independent of the concentration of A (changes in [A] do not change the rate of reaction):

    • Rate ∝ [A]⁰

    • Order of reaction is 0 order with respect to [A]

    • Usually can just remove [A]⁰ from the rate equation

  • If rate of reaction directly proportional to [A] (when [A] doubles, rate doubles)

    • Rate ∝ [A]¹

    • Order of reaction is first order with respect to [A]

    • Usually can just be written without the 1

  • If rate of reaction directly proportional to [A]² (when [A] doubles, rate quadruples [increases 4 times])

    • Rate ∝ [A]²

    • Order of reaction is second order with respect to [A]

Examples:

• 2NO(g) + 2H₂(g) → N₂(g) + 2H₂O(g)

  • Given: rate = k[NO]²[H2]

  • The reaction is second order with respect to [NO]

  • The reaction is first order with respect to [H₂].

  • Overall order: Third order (2 + 1 = 3)

Rate Constant (k)

Definition:

• The rate constant, k, is the proportionality constant in the experimentally-determined rate equation.

• It is a constant at a given temperature.

k:

• Temperature and presence of catalysts are included in the rate constant, k.

  • As these factors also affect the rate of a reaction

Arrhenius Equation: k = A e^−Ea/RT

• A = Pre-exponential factor

• Ea = Activation energy of the reaction

• R = Molar gas constant

• T = Absolute temperature

From k = A e^−Ea/RT:

• k increases with increase in temperature

• k increases with decrease in activation energy (due to presence of catalyst)

• k is unaffected by changes in concentration (there is no concentration term)

k & Rate of Reaction:

• Larger k, the faster is the rate of reaction

Units for Rate Constant, k:

• Depend on the overall order of the reaction

• (see image)

Half-life

Definition:

• The half-life, t_1⁄2, of a reaction is the time taken for the concentration of a reactant to decrease to half its initial value.