Question

The ratio of the velocity constant for a reaction at two temperatures differing by \(10^{\circ} \mathrm{C}\) is called its (a) rate constant (b) temperature coefficient (c) activation energy (d) specific reaction rate

Short answer

The correct answer is (b) temperature coefficient. This term refers to the ratio of the velocity constant for a reaction at two temperatures differing by \(10^{\circ} \mathrm{C}\).

Step-by-step solution

Understand the Terminologies

List down and understand the terminologies given in the question: rate constant, temperature coefficient, activation energy and specific rate reaction.

Link the Terminologies to the Definition

The next step is determining which term fits the description of the ratio of the velocity constant for a reaction at two temperatures differing by \(10^{\circ} \mathrm{C}\).

Choose the Correct Answer

The correct term that describes the proportionality between the rate constant for a reaction at two different temperatures with a difference of \(10^{\circ} \mathrm{C}\) is the temperature coefficient.

Key concepts

Rate Constant

Understanding the rate constant is essential for comprehending the kinetics of a chemical reaction. The rate constant is a proportionality factor in the chemical kinetics equation that relates the reaction rate to the concentrations of reactants. It is denoted by the symbol 'k' and can vary with temperature, as described by the Arrhenius equation:

\[ k = A \times e^{-\frac{E_a}{RT}} \]
Here, 'A' represents the frequency factor, which is a measure of how often particles collide with the correct orientation to react, while \(E_a\) is the activation energy of the reaction. 'R' stands for the universal gas constant, and 'T' is the absolute temperature in Kelvin.

As temperature increases, the rate constant typically increases, indicating that the reaction is proceeding at a quicker pace. This is due to more particles having enough energy to overcome the activation energy barrier to reaction. However, this relationship is not linear, and the specific manner in which the rate constant changes with temperature is encapsulated in the temperature coefficient.

Activation Energy

Activation energy (symbolized as \(E_a\)) is a fundamental concept in understanding why reactions occur at different rates. It is the minimum energy that must be overcome for reactants to be transformed into products. In a sense, it's like the energy 'hurdle' that molecules must jump over for a reaction to take place.

In the Arrhenius equation mentioned earlier, activation energy plays a critical role. It is present in the exponential factor, affecting the rate constant significantly. As the activation energy increases, the rate constant 'k' generally decreases for a given temperature, meaning fewer particles will have the energy needed to react because they cannot reach the threshold set by the activation energy. Thus, understanding this energy barrier is crucial when calculating reaction rates and modeling the behavior of reactions under various temperature conditions.

Specific Reaction Rate

The specific reaction rate, often referred to as the reaction rate, is the speed at which a chemical reaction proceeds. It is typically quantified in terms of the change in concentration of a reactant or product per unit time. The rate of a reaction can be influenced by several factors, including the nature of the reactants, their concentration, the presence of a catalyst, as well as temperature and pressure.

The specific reaction rate is different from the rate constant. While the rate constant is a measure that only changes with temperature or the presence of a catalyst, the specific reaction rate is the actual observable rate at which reactants turn into products. Changes in reactant concentrations over time affect the specific reaction rate and are described by the rate equation:

\[ \text{rate} = k \times [\text{Reactant}]^n \]
Where 'k' is the rate constant, '[Reactant]' represents the concentration of the reactant, and 'n' is the reaction order. This highlights how the concentration of reactants at any given moment directly impacts the velocity of the reaction.