Question

The temperature coefficient of a reaction is : (a) The rate constant (b) The rate constant at a fixed temperature (c) The ratio of rate constant at two temperature (d) The ratio of rate constant differing by \(10^{\circ} \mathrm{C}\) preferably \(k_{308} / k_{298}\)

Short answer

The correct answer is (d) The ratio of rate constant differing by \(10^{\circ} \mathrm{C}\), preferably \(k_{308} / k_{298}\).

Step-by-step solution

Understanding the Temperature Coefficient

The temperature coefficient of a reaction is a measure that describes how much the rate of a reaction changes with a change in temperature. It is not actually the rate constant itself, but a ratio that reflects how much that constant changes when temperature is varied. The standard temperature coefficient compares the rate constants at two temperatures that are 10°C apart.

Identifying the Correct Option

The given options present different aspects of the temperature and rate constants. We need to identify which option correctly represents the temperature coefficient definition.

Choosing the Correct Option

Option (d) 'The ratio of rate constant differing by \(10^{\circ} \mathrm{C}\)' is the correct answer. This represents the standard way of expressing the temperature coefficient of a reaction, which is usually given by the ratio of the rate constants at temperatures that differ by 10°C (such as \(k_{308} / k_{298}\)).

Key concepts

Rate Constant

In chemical kinetics, the rate constant is a crucial parameter that quantifies the speed of a chemical reaction. It is denoted by the symbol \( k \) and is unique for every reaction at a given temperature. The value of the rate constant follows the Arrhenius equation:
\[ k = Ae^{-\frac{E_{a}}{RT}} \]
where \( A \) is the frequency factor representing the number of times reactants approach each other per unit time, \( E_{a} \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin. The rate constant is directly proportional to the reaction rate; as it increases, so does the speed at which the reaction proceeds. This value is integral in calculating the overall rate of reaction for chemical processes and is foundational for understanding reaction kinetics.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical processes and the factors that affect these rates. It involves understanding how different conditions such as concentration, pressure, temperature, and the presence of catalysts can influence the speed at which reactants are converted into products. One of the main objectives in this field is to determine the reaction rate, which is the speed at which a reaction proceeds toward equilibrium. The rate of a reaction is typically expressed as the change in concentration of a reactant or product per unit time.
Chemical kinetics also involves the study of reaction mechanisms, which detail the step-by-step sequence of elementary reactions leading to the overall chemical change. By analyzing these mechanisms, scientists can predict reaction behavior and design conditions for optimizing rates to improve industrial processes, synthesize new materials, and understand biological pathways.

Reaction Rate Temperature Dependence

The temperature dependence of reaction rates is a fundamental aspect of chemical kinetics. According to the Arrhenius equation, even a small increase in temperature can significantly increase the rate constant and therefore the speed of the reaction. This is because higher temperatures provide more energy to the reactant molecules, increasing the chances of collisions with enough energy to overcome the activation barrier—resulting in more effective collisions that can lead to product formation.
The temperature coefficient of a reaction, typically observed as the ratio of rate constants at temperatures differing by \(10^\circ\mathrm{C}\), offers a standardized way to express how a reaction rate changes with temperature. With this information, chemists and engineers can predict how a reaction will behave under different thermal conditions, which is critical for controlling industrial chemical reactions, preserving food, and conducting temperature-sensitive laboratory experiments.