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.