Question

On which of these quantities does the rate constant of a reaction depend: (a) concentrations of reactants, (b) nature of reactants, (c) temperature?

Short answer

The rate constant of a reaction depends on the nature of reactants (Factor B) and temperature (Factor C). It does not, however, depend on concentrations of reactants (Factor A).

Step-by-step solution

Analysis of Factor A: Concentrations of Reactants

The rate constant is independent of the concentration of the reactants. This is due to the definition of rate constant, k in the rate law equation \(rate = k[A]^[n]\), where [A] is the concentration of reactant and n is the order. The rate of reaction changes with changing concentration, but not the rate constant.

Analysis of Factor B: Nature of Reactants

The nature of reactants definitely affects the rate constant. Different reactions featuring different reactants will have different rate constants. This is because their physical and chemical properties, including the energy landscape of the reaction and structural properties, would vary, resulting in differences for the rate constants.

Analysis of Factor C: Temperature

The rate constant, k, is also dependent on temperature. According to the Arrhenius equation, \(k = A \exp(-Ea/RT)\), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Therefore, as temperature increases, the rate constant also increases, assuming all other factors are held constant.

Key concepts

Concentration of Reactants

The rate constant, often denoted as \(k\), plays a crucial role in determining how fast a chemical reaction proceeds. Interestingly, \(k\) remains constant irrespective of the concentration of the reactants. In the rate law equation, expressed as \( \text{rate} = k[A]^n \), \( [A] \) represents the concentration of the reactant, and \( n \) signifies the order of the reaction with respect to that reactant.
The concentration of the reactants affects the rate of reaction, but it does so by influencing the number of collisions between reactant molecules – not by altering \(k\). Therefore, while different concentrations expedite or slow down the reaction rate, they do not change the intrinsic rate constant.

• Concentration affects the rate of reaction, not the rate constant.
• Rate constant is a characteristic of a reaction at a given temperature.

Nature of Reactants

Not all reactants are created equal when it comes to how they influence the rate constant of a reaction. The physical and chemical nature of each reactant has a significant impact on \(k\). For example, if a reactant is more reactive due to its molecular structure or has a lower energy requirement to proceed with the reaction, it can have a higher rate constant.
Different bonds, electron configurations, and molecular shapes all contribute to these differences. The variations in the energy landscapes of reactants affect the rate at which a reaction can occur. For this reason, two different reactions featuring distinct reactants can exhibit quite different rate constants.

• The intrinsic properties of reactants affect their reactivity.
• The rate constant varies from one reactant to another based on their nature.

Temperature Effect on Reactions

Temperature exerts a powerful influence on the rate constant \(k\) of a reaction. According to the Arrhenius equation, \(k = A \exp(-E_a/RT)\), temperature directly increases \(k\). As temperature rises, the molecules possess more kinetic energy, leading to more frequent and energetic collisions.
The increased movement of molecules facilitates the overcoming of the activation energy barrier, \(E_a\), allowing reactions to occur more readily. As a result, the rate constant increases, speeding up the overall reaction rate, provided no other conditions are changed.

• Higher temperatures lead to an increase in the rate constant.
• The Arrhenius equation models this temperature dependence mathematically.