13.7
Temperature Dependence on Reaction Rate
The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds…
Chemical reaction rates are sensitive to changes in temperature. A rise in 10 °C can accelerate the reaction rate by 3 to 4 times, but why?
A reaction’s rate law defines the relationship between a reactant concentration and the reaction rate. Since the concentration is temperature independent, only the rate constant remains to influence the reaction rate depending on the temperature. Thus, in 1889 the Swedish chemist Svante Arrhenius concluded that a reaction rate’s temperature dependence is encompassed in the rate constant.
The rate constant describes the relationship between temperature and kinetic parameters relating to the collision, orientation, and activation energy of reacting molecules via the Arrhenius equation. A is a constant called the Arrhenius factor or frequency factor, e is an exponential factor integrating activation energy measured in joules-per-mole, the gas constant, and the temperature in kelvin.
The parameters’ temperature dependence can be explained with the collision model, which states that reacting molecules should collide with sufficient energy in the correct orientation to initiate a chemical reaction.
The frequency factor constitutes two components—the collision frequency and the orientation factor. The collision frequency is the number of molecular collisions per unit time, whereas the orientation factor describes the probability of collisions with a favorable orientation.
Still, only a small fraction of collisions leads to a reaction. This is because the reacting molecules have to overcome an energy barrier, called the activation energy, to transform into products.
Only those molecules colliding with sufficient kinetic energy will have enough potential energy to bend, stretch, or break bonds, to transform into a high-energy intermediate called the transition state, or the activated complex. The short-lived, unstable activated complex loses energy to form stable products, whose total energy is lower than that of the reactants.
The exponential factor in the Arrhenius equation represents the fraction of successful collisions resulting in products. An increase in temperature influences both the frequency factor and the exponential factor.
At elevated temperatures, molecules move faster, more forcefully, and with higher thermal energies, leading to more favorable collisions.
Thus, a temperature increase results in higher frequency and exponential factors leading to a rise in the rate constant, consequently translating to an accelerated reaction rate.
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Q1: Why does a 10-degree temperature increase speed up chemical reactions so dramatically?
A 10°C temperature rise accelerates reaction rates by 3 to 4 times because higher temperatures increase molecular kinetic energy. Molecules move faster and collide more frequently with greater force. Since only the rate constant in the rate law varies with temperature, elevated thermal energy directly increases both collision frequency and the fraction of collisions with sufficient energy to overcome the activation energy barrier, dramatically accelerating the reaction.
Q2: What role does the Arrhenius equation play in understanding temperature effects on reactions?
The Arrhenius equation, k = Ae−Ea/RT, quantifies how temperature influences the rate constant through two components: the frequency factor A and the exponential term representing activation energy. This equation encapsulates collision theory by showing that temperature affects both collision frequency and the fraction of molecules with sufficient energy to react. It demonstrates why even small temperature increases produce large rate increases, especially for reactions with high activation energies.
Q3: How do molecular collisions determine whether a reaction occurs?
According to collision theory, reacting molecules must collide with correct orientation and sufficient kinetic energy to form products. The collision frequency represents the number of molecular collisions per unit time, while the orientation factor describes the probability of favorable collision geometry. Only collisions exceeding the activation energy barrier allow molecules to form a transition state, an unstable high-energy intermediate that decays into stable products with lower total energy.
Q4: What is activation energy and why does it control reaction rates?
Activation energy is the minimum energy required for reactant molecules to form an activated complex during collision. If activation energy is much larger than average molecular kinetic energy, few molecules possess sufficient energy and reactions proceed slowly. Conversely, if activation energy is much smaller than average kinetic energy, a large fraction of molecules can react, and the reaction proceeds rapidly. Temperature directly affects how many molecules exceed this energy threshold.
Q5: What happens to molecules when they collide with sufficient energy?
When molecules collide with adequate energy and correct orientation, they form a short-lived, unstable species called the transition state or activated complex. This high-energy intermediate is formed as bonds bend, stretch, or break during the collision. The activated complex then rapidly decays, releasing energy to form stable products whose total energy is lower than the reactants. This process represents the conversion of reactants to products through a temporary high-energy state.
Q6: How do the frequency factor and exponential factor in the Arrhenius equation respond to temperature changes?
Both components increase with temperature. The frequency factor reflects collision frequency and orientation probability; higher temperatures increase molecular motion, raising collision rates. The exponential factor, e−Ea/RT, represents the fraction of successful collisions; elevated temperatures increase the proportion of molecules with kinetic energy exceeding the activation energy. Together, these temperature-dependent terms explain why reaction rates increase exponentially rather than linearly with temperature.
Q7: How does a reaction diagram illustrate the relationship between activation energy and reaction rate?
Reaction diagrams show energy changes as reactants convert to products, displaying the activation energy as the energy difference between reactants and the transition state. A lower activation energy means a larger fraction of molecules possess sufficient energy to react at any given temperature, resulting in faster reaction rates. The diagram also shows enthalpy change; exothermic reactions release energy, while the activation energy barrier determines how quickly this process occurs regardless of whether the reaction is favorable.