Understanding Chemical Reaction Rates

Sep 24, 2024

Notes on Rate of Chemical Reactions

Definition of Reaction Rate

  • The rate of a chemical reaction is defined as the change in the concentration of a reactant or product over change in time.
  • Units: Concentration in moles per liter (molar) and time in seconds, leading to rate expressed in molar per second (mol/s).

Relationship to Physics

  • The concept of rate in chemistry is analogous to average velocity in physics.
  • Average velocity = Change in position (x) / Change in time.

Simple Reaction Example

Reaction Overview

  • Example: Reactant A turns into Product B.
  • Initial concentration of A at time = 0: 1 M (molar).
  • Initial concentration of B at time = 0: 0 M.

Time Interval

  • After 2 seconds:
    • Concentration of A: 0.98 M.
    • Concentration of B: 0.02 M (since 0.02 M of A has converted into B).

Calculation of Average Rate

  • For Product B:

    • Rate = (Final concentration of B - Initial concentration of B) / (Final time - Initial time)
    • Rate = (0.02 - 0) / (2 - 0) = 0.01 mol/s.
  • For Reactant A:

    • Rate = (Final concentration of A - Initial concentration of A) / (Final time - Initial time)
    • Rate = (0.98 - 1) / (2 - 0) = -0.02 / 2 = -0.01 mol/s.
    • In chemistry, rates are reported as positive, so:
    • Rate = -(-0.02) / 2 = 0.01 mol/s.

General Rate Expression

  • Rate can be expressed as:
    • Rate = - (Change in concentration of A / Change in time) = (Change in concentration of B / Change in time).

More Complex Reaction Example

Reaction Equation

  • Decomposition of dinitrogen pentoxide (N₂O₅) into nitrogen dioxide (NO₂) and oxygen (O₂).

Given Rate

  • Rate of formation of O₂ = 9 × 10⁻⁶ mol/s.

Calculating Rates for Other Products

  • For NO₂:

    • Mole Ratio: 4 moles NO₂ for every 1 mole O₂.
    • Rate of formation of NO₂ = 4 * (9 × 10⁻⁶) = 3.6 × 10⁻⁵ mol/s.
  • For N₂O₅:

    • Mole Ratio: 2 moles N₂O₅ lost for every 1 mole O₂ formed.
    • Rate of disappearance of N₂O₅ = -2 * (9 × 10⁻⁶) = -1.8 × 10⁻⁵ mol/s.

Expressing Overall Rate

  • The overall rate of reaction can be expressed in terms of:
    • Rate = Change in concentration of O₂ / Change in time = 9 × 10⁻⁶ mol/s.
    • Rate = Change in concentration of NO₂ / Change in time = 3.6 × 10⁻⁵ mol/s.
    • Rate = Change in concentration of N₂O₅ / Change in time = -1.8 × 10⁻⁵ mol/s.

Coefficient Patterns

  • Coefficients from the balanced equation dictate the relationship between the rates:
    • N₂O₅: Coefficient = 2 → Negative rate expression.
    • NO₂: Coefficient = 4 → Multiplier for rate expression.
    • O₂: Coefficient = 1 → Rate is directly expressed.