Question

The specific rate constant of a first order reaction depends on the a. temperature b. time c. concentration of the reactant d. concentration of the product

Short answer

The specific rate constant of a first order reaction depends on temperature.

Step-by-step solution

Understanding First Order Reaction

In a first order reaction, the reaction rate is directly proportional to the concentration of one reactant. The rate law for a first order reaction is typically given by: \( r = k[A] \), where \( r \) is the rate, \( k \) is the rate constant, and \( [A] \) is the concentration of the reactant.

Identifying the Influence of Temperature

The specific rate constant \( k \) for any reaction, including first order reactions, is influenced by temperature. This is described by the Arrhenius equation: \( k = Ae^{-Ea/(RT)} \), where \( Ea \) is the activation energy, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( A \) is the pre-exponential factor. As temperature increases, the rate constant usually increases.

Analyzing Other Factors

The specific rate constant \( k \) is not affected by time, concentration of reactant, or concentration of product in a first order reaction. The rate of reaction depends on the concentration of the reactant, but \( k \) itself is a constant that is independent of concentration and time, under constant temperature.

Conclusion

Based on the analysis, the specific rate constant \( k \) in a first order reaction is primarily influenced by temperature. Other factors like time, reactant concentration, and product concentration do not affect \( k \).

Key concepts

Rate Law

In chemical kinetics, a rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. Specifically, for a first order reaction, this relationship is straightforward. The rate of reaction is directly proportional to the concentration of a single reactant. This relationship can be expressed by the formula:
\[ r = k[A] \]
Here:

• \( r \) is the reaction rate.
• \( k \) is the specific rate constant.
• \( [A] \) is the concentration of the reactant.

The beauty of the rate law for a first order reaction is its simplicity. Because only one reactant influences the rate, it allows scientists and students to focus on how changes in concentration directly affect the rate. This simplicity provides a foundational understanding of how reactions progress over time, especially as reactants are consumed.
It is vital to remember that while concentration affects the rate, it does not alter the specific rate constant \( k \), which remains constant at a given temperature.

Arrhenius Equation

The Arrhenius Equation is a foundational concept in understanding how temperature affects the rate constants of chemical reactions. This relationship is crucial, especially in understanding how reactions behave under different conditions.
The Arrhenius Equation is expressed as:
\[ k = Ae^{-Ea/(RT)} \]
Within this equation:

• \( k \) is the rate constant.
• \( A \) is the pre-exponential factor or frequency factor, representing the number of collisions that result in a reaction.
• \( Ea \) is the activation energy, the minimum energy required for a reaction to occur.
• \( R \) is the gas constant \((8.314 J/mol·K)\).
• \( T \) represents the temperature in Kelvin.

What this equation tells us is that as the temperature \( T \) increases, the exponential term becomes less negative, which in turn increases the value of \( k \). This explains why reactions tend to speed up as temperature rises. The Arrhenius Equation elegantly shows this temperature dependence, aligning well with our observations in many natural and experimental settings.

Activation Energy

Activation energy is a fundamental concept describing the energy barrier that must be overcome for a reaction to occur. It is the minimum energy that colliding molecules need to have to result in a chemical reaction. This concept is crucial for understanding the dynamics of chemical processes.
In an energy profile diagram, the activation energy is represented as the peak of the energy barrier that reactants must surpass to transition into products.
Here's why activation energy is important:

• A higher activation energy means the reaction is slower, as fewer molecules can reach the necessary energy threshold.
• A lower activation energy implies a faster reaction, as more reactant molecules have the required energy to react.

Incorporated into the Arrhenius Equation, activation energy allows us to quantitatively understand and predict how changes in temperature affect reaction rates. Understanding this concept helps in manipulating conditions to control reaction speeds, whether you're speeding things up in industrial chemistry or slowing them down in preservation processes.