Problem 89 - Chemistry and Chemical Reactivity

Question

Describe each of the following statements as true or false. If false, rewrite the sentence to make it correct. (a) The rate-determining elementary step in a reaction is the slowest step in a mechanism. (b) It is possible to change the rate constant by changing the temperature. (c) As a reaction proceeds at constant temperature, the rate remains constant. (d) A reaction that is third order overall must involve more than one step.

Step-by-Step Solution

Answer

(a) True. (b) True. (c) False; rate decreases as reactants decrease. (d) False; can be single-step but often multi-step.

Step 1: Analyze Statement (a)

The statement mentions the rate-determining step in a reaction mechanism. In chemical kinetics, the rate-determining step is indeed the slowest step in a mechanism. This is because the overall reaction rate is limited by the slowest step, which controls how fast the products can be formed. Therefore, this statement is true.

Step 2: Analyze Statement (b)

Statement (b) is about the dependency of the rate constant on temperature. According to the Arrhenius equation, the rate constant \( k \) is dependent on temperature, mathematically expressed as \ k = Ae^{-\frac{E_a}{RT}} \ where \ A \ is the pre-exponential factor, \ E_a \ is the activation energy, \ R \ is the gas constant, and \ T \ is the temperature. A change in temperature alters the value of \ k \, thus, the statement is true.

Step 3: Analyze Statement (c)

The statement claims that the reaction rate remains constant at a constant temperature as the reaction progresses. Typically, the rate of a reaction depends on concentration: as reactants are consumed, their concentrations decrease and therefore, the reaction rate usually decreases over time. Consequently, this statement is false. A correct version would be: 'As a reaction proceeds at constant temperature, the rate generally decreases as the concentration of reactants decreases.'

Step 4: Analyze Statement (d)

Statement (d) asserts that a third-order reaction must involve more than one step. Third-order reactions can theoretically occur in a single step involving three reactant molecules; however, this is rare due to the low probability of three species colliding simultaneously. Nonetheless, third-order mechanisms can be single-step, so the statement is false as it implies impossibility. A corrected version might be: 'A reaction that is third order overall can involve multiple steps, but being third order does not necessitate multiple steps.'

Key Concepts

Rate-determining step

In the realm of chemical kinetics, the concept of the rate-determining step is central to understanding reaction mechanisms. It refers to the slowest step within a sequence of events that make up a chemical reaction. Picture a series of dominoes falling: if one domino is heavier and falls slower, it will control how fast the entire sequence can proceed. Similarly, in a chemical reaction pathway, the rate-determining step is that slow 'domino' that dictates the speed at which the reaction progresses.

This step has the highest activation energy compared to the other steps, making it the bottleneck of the process. The overall reaction rate cannot exceed the rate of this slowest step, much like the speed of a convoy determined by the slowest vehicle. By focusing on the rate-determining step, chemists can identify how to optimize or simplify reactions.

Understanding this concept is particularly useful when dealing with complex mechanisms that involve multiple steps. By pinpointing the rate-determining step, one can influence the overall speed of the reaction by altering conditions or catalysts that specifically affect this slowest step.

Reaction rate dependency on temperature

Temperature plays a crucial role in chemical kinetics, and it has a significant effect on the rate of a reaction. The Arrhenius equation captures this relationship, illustrating how changes in temperature lead to variations in the rate constant, denoted as \( k \). This equation is expressed as:

\[ k = Ae^{-\frac{E_a}{RT}} \]

where \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Essentially, an increase in temperature generally results in an increase in the reaction rate. This occurs because higher temperatures provide more energy to reactant molecules, increasing the chances of successful collisions. It's akin to heating up water to turn it into steam faster; the energy supplied speeds up the process.

Conversely, lowering the temperature usually decreases the reaction rate since fewer molecules have the energy required to surpass the activation barrier. By controlling temperature, chemists can effectively control how quickly a reaction proceeds, which is especially valuable in industrial and laboratory settings.

Reaction order and mechanism

The reaction order is a key concept that describes how the rate of a reaction is affected by the concentration of its reactants. It provides insight into the reaction mechanism and can be determined experimentally. The overall reaction order is the sum of the exponents of the concentration terms in the rate law.

For example, in a reaction with a rate law \( ext{rate} = k[A]^x[B]^y \), the reaction is of order \( x + y \), where \( x \) and \( y \) are the orders with respect to reactants \( A \) and \( B \).

The reaction order has implications for the reaction mechanism, particularly for complex processes that may involve multiple steps. Not all reactions of a specific order require multiple steps; however, a third-order reaction, for instance, might involve one or more steps but does not necessarily have to be multi-step. This stems from the rarity of three molecules colliding at once, but it is possible in certain conditions.

Understanding reaction order helps in hypothesizing potential mechanisms and predicting how changes in concentration affect the reaction rate. It is an essential tool for chemists who aim to manipulate and control chemical reactions efficiently.