Problem 83 - 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 changes with concentration; (d) False, can be single step if termolecular.

Step 1: Analyzing Statement (a)

The statement 'The rate-determining elementary step in a reaction is the slowest step in a mechanism.' is analyzed. In a reaction mechanism, the rate-determining step is indeed the slowest step because it acts as a bottleneck, controlling the overall rate of the reaction. Therefore, this statement is true.

Step 2: Analyzing Statement (b)

The statement 'It is possible to change the rate constant by changing the temperature.' is evaluated. The rate constant, typically denoted as \( k \), is dependent on temperature, as described by the Arrhenius equation \( k = Ae^{-Ea/RT} \). Changing the temperature alters the rate constant, making this statement true.

Step 3: Analyzing Statement (c)

The statement 'As a reaction proceeds at constant temperature, the rate remains constant.' requires examination. Reaction rates are dependent on the concentration of reactants. As the reaction proceeds, concentrations typically decrease, causing the rate to change unless it is a zero-order reaction. Thus, this statement is false. A corrected statement could be: 'As a reaction proceeds at constant temperature, the rate generally changes unless it is a zero-order reaction.'

Step 4: Analyzing Statement (d)

The statement 'A reaction that is third order overall must involve more than one step.' is assessed. A third order reaction can occur in a single step if it involves three molecules, which is termed a termolecular reaction, though such reactions are rare. Therefore, this statement is false. A corrected version could be: 'A reaction that is third order overall could involve a single step if it is termolecular, but this is uncommon.'

Key Concepts

Rate-Determining Step

In chemical kinetics, the rate-determining step is crucial because it is the slowest step in a reaction mechanism. This bottleneck effect determines the speed of the overall reaction. To visualize this, consider a scenario where cars are passing through various traffic lights. If one light is slower than the others, it delays all cars behind it, regardless of the quickness of other lights.

Similarly, in a chemical reaction sequence, if one step takes longer, it holds up the entire process. This slow step must be overcome first to raise the overall reaction rate. Understanding which step is rate-determining helps chemists develop effective catalysts and improve reaction efficiency.

• The slowest step in a series of reactions.
• Controls the overall reaction rate.
• Acts as a bottleneck in the mechanism.

Rate Constant

The rate constant, denoted by the symbol \( k \), is a crucial element in the rate equation of a reaction. It reflects the inherent speed of a reaction at a given temperature, independent of reactant concentrations.

The rate constant is directly influenced by temperature changes, meaning when the temperature increases or decreases, so does \( k \). This makes it an essential variable when studying reaction kinetics. The rate constant can tell us how fast a reaction will occur under specific conditions and help predict how changes in temperature impact reaction rates.

• Symbolized as \( k \).
• Impacted by temperature changes.
• Independent of reactant concentrations.

Reaction Order

The reaction order is a term used to describe the power to which the concentration of a reactant is raised in the rate equation. It tells us how the concentration of each reactant affects the overall rate of reaction. The sum of all the exponents in the rate equation gives the total reaction order.

For instance, a reaction with a rate equation \( Rate = k[A]^2[B] \) is second order in terms of \( A \), first order in terms of \( B \), and third order overall. Contrary to some assumptions, this can happen in a single step if three molecules collide and react simultaneously, but such occurrences are rare.

• Defines how reactant concentrations influence reaction rate.
• Sum of exponents provides overall reaction order.
• Third order does not necessitate multiple steps.

Arrhenius Equation

The Arrhenius equation is a vital formula in reaction kinetics that links the rate constant \( k \) to temperature and activation energy. It is expressed as \( k = Ae^{-Ea/RT} \), where \( A \) is the frequency factor, \( Ea \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

This equation helps explain why reaction rates increase with temperature. A higher temperature leads to more energetic collisions among reactants, overcoming the activation energy required to form products. By understanding the Arrhenius equation, scientists can predict how changes in temperature will affect the rate constant and, consequently, the rate of reaction.

• Relates rate constant to temperature and activation energy.
• Explains temperature's influence on reaction rates.
• Highlights the importance of activation energy.