Problem 93 - Chemistry The Molecular Science

Question

Indicate whether each of these statements is true or false. Change the wording of each false statement to make it true. (a) It is possible to change the rate constant for a reaction by changing the temperature. (b) The reaction rate remains constant as a first-order reaction proceeds at a constant temperature. (c) The rate constant for a reaction is independent of reactant concentrations. (d) As a second-order reaction proceeds at a constant temperature, the rate constant changes.

Step-by-Step Solution

Answer

(a) True, (b) False: rate decreases as reaction proceeds, (c) True, (d) False: rate constant is constant at a given temperature.

Step 1: Analyze statement (a)

The statement claims that it is possible to change the rate constant of a reaction by varying the temperature. According to the Arrhenius equation, the rate constant \( k \) varies with temperature \( T \) because \( k = Ae^{-Ea/(RT)} \), where \( A \) is the frequency factor, \( Ea \) is the activation energy, and \( R \) is the gas constant. Therefore, this statement is true.

Step 2: Analyze statement (b)

The statement suggests that in a first-order reaction, the reaction rate remains constant at a constant temperature. First-order reaction rates depend linearly on the concentration of one reactant. As the concentration of the reactant decreases over time, the reaction rate also decreases. Hence, this statement is false. A correct statement would be: "The reaction rate decreases as a first-order reaction proceeds at a constant temperature."

Step 3: Analyze statement (c)

This statement asserts that the rate constant is independent of the concentrations of reactants. The rate constant \( k \) indeed does not change with the concentration of reactants, as it is a constant at a given temperature for a specific reaction. Thus, this statement is true.

Step 4: Analyze statement (d)

The statement claims that the rate constant changes for a second-order reaction at a constant temperature. The rate constant for any reaction remains constant at a given temperature, regardless of the order of the reaction. Therefore, this statement is false. A correct statement would be: "As a second-order reaction proceeds at a constant temperature, the rate constant remains unchanged."

Key Concepts

Rate Constant

The rate constant, often denoted by the symbol \( k \), is a crucial factor in chemical kinetics. It gives us a sense of how fast or slow a reaction occurs under a set of conditions. The rate constant is specific to a particular reaction at a given temperature. It doesn't change with the concentration of reactants or products.
To understand it better, imagine you have a recipe for baking a cake. The rate constant is like the baking time needed for the cake to cook perfectly. Changing the ingredients will not change the baking time, but changing the oven temperature might! Similarly, in chemical reactions, while concentrations can vary, the rate constant remains unaffected unless temperature changes are introduced.

• The rate constant tells the intrinsic speed of a chemical reaction.
• It is unique for each reaction at a given temperature.
• It's independent of reactant or product concentrations.

Arrhenius Equation

The Arrhenius equation provides a clear understanding of how temperature affects the rate constant of a reaction. The formula is \( k = Ae^{-Ea/(RT)} \), where \( A \) is the frequency factor, \( Ea \) is the activation energy, , \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
Simply put, the Arrhenius equation shows that as the temperature increases, the rate constant \( k \) typically increases too, meaning the reaction will likely happen faster. This is because higher temperatures provide reactant molecules with more energy to overcome the activation energy barrier.

• \( A \) represents the number of times reactants approach the activation barrier per unit time.
• \( Ea \) is the energy required to start the reaction.
• Higher temperatures increase molecular energy, often increasing reaction rates.

Reaction Order

The reaction order is a key concept that helps us understand how the concentration of reactants affects the rate of a chemical reaction. It can be zero, first, second, or even higher, determining the mathematical relationship between concentration and the rate.
For instance, in a first-order reaction, the rate is directly proportional to the concentration of one reactant. This means if you double the concentration, the rate also doubles. Conversely, in a second-order reaction, the rate might be proportional to the square of the concentration of a single reactant, or to the product of the concentrations of two different reactants.

• Zero-Order: Rate is independent of concentration.
• First-Order: Rate changes linearly with concentration.
• Second-Order: Rate changes with the square of a concentration or product of two concentrations.

Temperature Dependence

Temperature is a critical factor in determining how swiftly a reaction occurs. Most chemical reactions speed up as the temperature increases. This is well-explained by the Arrhenius equation, showing that a higher temperature decreases the impact of the activation energy barrier, allowing molecules to react more quickly.
In practical terms, think about how ice melts faster on a hot day or how cooking on high heat quickens the process compared to low heat. Similarly, in chemistry, raising the temperature provides reactant molecules with more energy, leading to more collisions, and more successful reactions.

• Increased temperature generally speeds up reaction rates.
• More molecular energy at higher temperatures helps molecules overcome activation energy more easily.
• Understanding temperature dependence is key for controlling reaction rates in lab and industrial processes.