A Model for Reaction Rates and Collision Theory

Chemical Reaction Rates

• Definition: The change in concentration of a reactant or product per unit of time, generally expressed in units of $mol\,L^{-1}\,s^{-1}$ or $M\,s^{-1}$.

• Experimental Determination: Reaction rates are determined experimentally and cannot be calculated solely from a balanced chemical equation.

• Average Reaction Rate Equation:

$\text{Average Rate} = -\frac{\Delta \text{quantity}}{\Delta t} = -\frac{[R]_2 - [R]_1}{t_2 - t_1}$

• Sign Convention: The negative sign ensures that the rate of reactant consumption is expressed as a positive value.

Collision Theory

• Core Principle: Reacting substances (atoms, ions, or molecules) must collide with one another to react.

• Three Criteria for a Successful Reaction:

  • Reacting substances must collide.

  • Reacting substances must collide in the correct molecular orientation.

  • Reacting substances must collide with sufficient energy to form an activated complex.

• Activated Complex (Transition State): A temporary, unstable arrangement of atoms in which old bonds break and new bonds form.

Activation Energy

• Definition: The minimum amount of energy that reacting particles must possess to form the activated complex and initiate a reaction.

• Effect on Rate: A high activation energy means fewer collisions possess sufficient energy, resulting in a slow reaction rate.

Energy Diagrams: Exothermic vs. Endothermic

• Exothermic Reaction:

  • Reactants start at a higher energy level than products.

  • Energy is released to the surroundings ($\Delta H < 0$ ).

• Endothermic Reaction:

  • Reactants start at a lower energy level than products.

  • Energy is absorbed from the surroundings ($\Delta H > 0$).

Reaction Spontaneity

• Gibbs Free Energy Change ($\Delta G$): Determines whether a reaction occurs naturally without continuous external energy input.

  • $\Delta G < 0$: Reaction is spontaneous.

  • $\Delta G > 0$: Reaction is non-spontaneous.

• Independence: Reaction spontaneity ($\Delta G$) is completely unrelated to the rate of a chemical reaction.

Calculations & Worked Examples

• Example 1: Concentration Change Over Time

  • Reactant concentration changes from $0.03\,M$ to $0.02\,M$ over $t = 25\,min$:

  • Rate in $M\,min^{-1}$:

$\text{Average Rate} = -\frac{0.02\,M - 0.03\,M}{25\,min} = 4 \times 10^{-4}\,M\,min^{-1}$

• Rate in $M\,s^{-1}$:

$\text{Average Rate} = -\frac{0.02\,M - 0.03\,M}{25 \times 60\,s} = 6.66 \times 10^{-6}\,M\,s^{-1}$

• Example 2: Reaction of Butyl Chloride ($C_4H_9Cl$) with Water

  • Initial concentration $[C_4H_9Cl]_1 = 0.220\,M$ at $t_1 = 0.00\,s$; final concentration $[C_4H_9Cl]_2 = 0.100\,M$ at $t_2 = 4.00\,s$:

$\text{Average Rate} = -\frac{0.100\,M - 0.220\,M}{4.00\,s - 0.00\,s} = 0.0300\,mol\,L^{-1}\,s^{-1}$

• Example 3: Combustion of Hydrogen Gas

  • Reaction: $2H_2 + O_2 \rightarrow 2H_2O$

  • Given $[H_2]$ changes from $1\,mol\,L^{-1}$ to $0.5\,mol\,L^{-1}$ in $2\,s$, with $\Delta G = -458\,kJ$ and $\Delta H = -484\,kJ$:

$\text{Average Rate} = -\frac{0.5\,mol\,L^{-1} - 1\,mol\,L^{-1}}{2\,s} = 0.25\,mol\,L^{-1}\,s^{-1}$

• Characterization: Exothermic ($\Delta H < 0$) and spontaneous ($\Delta G < 0$).

Concept Checks & Discussion

• Question: What happens to the rate of salt removal if seawater is heated during desalination at plants such as Jebel Ali Desalination Plant?

  • Response: Heating seawater increases the rate of salt removal because higher temperatures increase reaction and separation rates.

• Question: Which statement is NOT true of the reaction rate of a chemical reaction?

  • Response: It can be calculated purely from a balanced equation (false; it must be determined experimentally).

• Question: Which condition is NOT required by collision theory?

  • Response: Reacting substances colliding at a high rate (the core requirements are physical collision, correct orientation, and sufficient energy).