13.2 Collision theory

Collision theory explains how chemical reactions occur at the molecular level. It states that molecules must collide with enough energy and proper orientation to react. This theory helps us understand why reaction rates depend on concentration, temperature, and catalysts.

The theory connects to the broader topic of activation energy and temperature dependence. It explains why higher temperatures increase reaction rates and how catalysts work by lowering the activation energy barrier, making successful collisions more likely.

Collision theory fundamentals

Basic principles

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• Collision theory states that for a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation
• The rate of a reaction depends on the frequency of successful collisions between reactant molecules
• Successful collisions require that reactant molecules possess a minimum amount of energy, known as the activation energy, to overcome the energy barrier and initiate the reaction
• The collision frequency and the fraction of collisions with sufficient energy determine the overall reaction rate

Explaining observed reaction rate dependence

• Collision theory explains the observed dependence of reaction rates on concentration, temperature, and the presence of catalysts
• Higher concentrations lead to more collisions per unit time, increasing the reaction rate
• Higher temperatures result in faster-moving molecules, increasing the collision frequency and the likelihood of collisions with sufficient energy to overcome the activation energy barrier
• The presence of a catalyst lowers the activation energy barrier, increasing the fraction of collisions with sufficient energy to result in a successful reaction, thus enhancing the reaction rate

Factors influencing collisions

Concentration and collision frequency

• The concentration of reactants directly affects the collision frequency
• Higher concentrations lead to more collisions per unit time, increasing the reaction rate
• Doubling the concentration of a reactant will double the collision frequency, leading to a proportional increase in the reaction rate, assuming the reaction is elementary and follows the rate law

Temperature and kinetic energy

• Temperature influences the average kinetic energy of molecules
• Higher temperatures result in faster-moving molecules, increasing the collision frequency and the likelihood of collisions with sufficient energy to overcome the activation energy barrier
• Increasing the temperature of a reaction system will increase the average kinetic energy of molecules, leading to a higher collision frequency and a greater fraction of collisions with sufficient energy to overcome the activation energy barrier, resulting in a faster reaction rate

Catalysts and activation energy

• The presence of a catalyst lowers the activation energy barrier, increasing the fraction of collisions with sufficient energy to result in a successful reaction, thus enhancing the reaction rate
• Catalysts increase the reaction rate without being consumed in the reaction
• Examples of catalysts include enzymes in biological systems and transition metals in industrial processes (platinum in catalytic converters)

Molecular orientation and geometry

• The orientation of molecules during a collision is crucial for a successful reaction
• Molecules must collide with the correct geometry to allow for the formation of new bonds or the breaking of existing bonds
• The size and shape of reactant molecules can affect the collision frequency and the probability of successful collisions
• Example: In the reaction between hydrogen and iodine ($H_2 + I_2 \rightarrow 2HI$), the H-H and I-I bonds must be aligned correctly for the reaction to occur

Kinetic energy vs activation energy

Maxwell-Boltzmann distribution

• The kinetic energy of molecules in a system follows a Maxwell-Boltzmann distribution, which describes the fraction of molecules with a given energy at a specific temperature
• As temperature increases, the Maxwell-Boltzmann distribution shifts towards higher energies, increasing the fraction of molecules with sufficient energy to overcome the activation energy barrier
• The area under the Maxwell-Boltzmann distribution curve to the right of the activation energy represents the fraction of molecules with sufficient energy for a successful collision

Activation energy and successful collisions

• The activation energy is the minimum energy required for a collision to result in a successful reaction
• Only collisions with energy equal to or greater than the activation energy can lead to a reaction
• The relationship between the activation energy and the Maxwell-Boltzmann distribution determines the temperature dependence of reaction rates, as described by the Arrhenius equation
• Example: In the decomposition of nitrogen pentoxide ($2N_2O_5 \rightarrow 4NO_2 + O_2$), the activation energy is approximately 100 kJ/mol

Predicting reaction rate changes

Effect of temperature

• Increasing the temperature of a reaction system will increase the average kinetic energy of molecules, leading to a higher collision frequency and a greater fraction of collisions with sufficient energy to overcome the activation energy barrier, resulting in a faster reaction rate
• The Arrhenius equation, $k = Ae^{-E_a/RT}$, relates the rate constant ($k$) to temperature ($T$), activation energy ($E_a$), and the pre-exponential factor ($A$)
• A general rule of thumb is that for every 10°C increase in temperature, the reaction rate doubles

Effect of concentration

• Doubling the concentration of a reactant will double the collision frequency, leading to a proportional increase in the reaction rate, assuming the reaction is elementary and follows the rate law
• For a reaction $aA + bB \rightarrow products$, the rate law is given by $rate = k[A]^m[B]^n$, where $m$ and $n$ are the orders of the reaction with respect to reactants $A$ and $B$, respectively
• Example: In the reaction $2NO + O_2 \rightarrow 2NO_2$, doubling the concentration of NO will quadruple the reaction rate (second-order with respect to NO)

Effect of surface area

• The effect of surface area on reaction rates can be explained by collision theory, as increasing the surface area of solid reactants exposes more molecules to potential collisions, thereby increasing the reaction rate
• Example: In the reaction between hydrochloric acid and calcium carbonate ($2HCl + CaCO_3 \rightarrow CaCl_2 + H_2O + CO_2$), using powdered calcium carbonate will result in a faster reaction rate compared to using larger chunks of the solid

Effect of pressure

• Increasing the pressure of a gaseous reaction system will increase the concentration of reactants, leading to a higher collision frequency and a faster reaction rate
• Pressure changes do not affect the reaction rates of solids or liquids, as their concentrations are not significantly altered by pressure
• Example: In the Haber-Bosch process for ammonia synthesis ($N_2 + 3H_2 \rightleftharpoons 2NH_3$), increasing the pressure shifts the equilibrium towards the production of ammonia and increases the reaction rate