Question

If the rate constant for a first-order reaction is doubled by heating the reaction, what happens to the rate of the reaction if the concentration is kept the same?

Short answer

Doubling the rate constant for a first-order reaction, while keeping the concentration constant, will double the rate of the reaction.

Step-by-step solution

Understanding First-Order Reactions

First-order reactions are characterized by their rate being directly proportional to the concentration of one of the reactants. Mathematically, the rate of a first-order reaction can be described by the equation: \( rate = k[A] \), where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant.

Effect of Doubling the Rate Constant

For a first-order reaction, if the concentration \( [A] \) remains constant, but the rate constant \( k \) is doubled, the rate of the reaction would also double. This is because the rate is directly proportional to both the concentration and the rate constant. The new rate can be described by the equation: \( new\_rate = 2k[A] \), which is double the original rate.

Key concepts

Rate Constant

The rate constant is a crucial aspect in the study of chemical kinetics as it provides a quantitative measure of how quickly a reaction occurs. This constant, represented by the symbol 'k', is unique to each reaction at a given temperature. It is important to understand that the value of the rate constant is influenced by factors such as temperature, with higher temperatures typically increasing its value.

In the context of a first-order reaction, the rate constant directly affects the speed at which the reaction takes place. The equation that connects rate constant to reaction rate is commonly written as \( rate = k[A] \), where 'rate' is the speed of the reaction and \( [A] \) is the concentration of the reactant. When the rate constant 'k' is increased, such as by heating, the reaction accelerates correspondingly, even if the concentration remains unchanged. This linear relationship is a defining characteristic of first-order reactions.

Reaction Kinetics

Reaction kinetics, also known as chemical kinetics, is the branch of chemistry that studies the rates of chemical processes and the factors affecting them. It delves into how different conditions, like temperature, pressure, or the presence of a catalyst, can influence the speed of a reaction.

For instance, in a first-order reaction, such as the one described in the exercise, the kinetics are determined by observing how the rate changes in response to alterations in concentration and the rate constant. This particular type of reaction relies solely on the concentration of a single reactant, making the mathematics relatively straightforward. Reaction kinetics are not only useful in predicting how long a reaction will take, but also in understanding the reaction mechanism and finding the best conditions for a reaction to occur efficiently.

Chemical Kinetics

Chemical kinetics encompasses the broader principles highlighted in reaction kinetics but focuses on the sequence of steps that a chemical reaction undergoes and how each step contributes to the overall rate of the process. It seeks to answer the 'how' and 'why' a chemical reaction proceeds at a certain rate.

In a first-order reaction, the role of chemical kinetics might be to analyze how the exponential decay of reactants leads to the production of products over time. The relationships revealed through kinetics can be graphically represented, often showing a linear relationship between the natural logarithm of reactant concentration and time for a first-order reaction. Understanding chemical kinetics is critical in various industries, such as pharmaceuticals, where knowing the rate at which a drug will react in the body can determine its effectiveness and safety.