Which Of The Following Is Not A Speed Law

The concept of speed laws, especially in the context of chemical reactions, dictates how reaction rates change with varying concentrations of reactants. Understanding these laws is crucial for controlling and optimizing chemical processes. However, not everything related to reaction rates can be considered a speed law. Let's delve into the specifics to clarify which factors influence reaction rates and which do not fall under the definition of a speed law.

Fundamentals of Speed Laws

A speed law, also known as a rate law, is an equation that links the rate of a chemical reaction to the concentrations of the reactants involved. This law is determined experimentally and provides valuable insight into the reaction mechanism.

The general form of a rate law is:

rate = k[A]^m[B]^n

Where:

• rate is the speed at which the reaction proceeds.
• k is the rate constant, a value that depends on temperature and other factors but is independent of concentration.
• [A] and [B] are the concentrations of reactants A and B, respectively.
• m and n are the reaction orders with respect to reactants A and B. These exponents are determined experimentally and indicate how the concentration of each reactant affects the rate of the reaction.

Factors That Influence Reaction Rates

Several factors influence how quickly a chemical reaction occurs. It's important to distinguish between these general influencing factors and the specific parameters included in the speed law.

1. Concentration of Reactants: As dictated by the rate law, increasing the concentration of reactants generally increases the reaction rate because there are more reactant molecules available to collide and react.

2. Temperature: Higher temperatures usually increase the reaction rate. This is because higher temperatures provide more energy to the molecules, increasing the likelihood of successful collisions (collisions with enough energy to break bonds and form new ones).

3. Catalysts: Catalysts are substances that speed up a reaction without being consumed in the process. They work by providing an alternative reaction pathway with a lower activation energy.

4. Surface Area of Solid Reactants: For reactions involving solid reactants, increasing the surface area (e.g., by grinding a solid into a powder) increases the reaction rate because more reactant surface is exposed to the other reactants.

5. Pressure: For reactions involving gases, increasing the pressure can increase the reaction rate by increasing the concentration of the gaseous reactants.

What Is NOT a Speed Law?

While the factors listed above influence reaction rates, not all of them are directly incorporated into the rate law equation itself. Here are some key distinctions:

1. Temperature: Temperature affects the rate constant (k) in the rate law, but it is not a variable directly included in the concentration terms. The relationship between temperature and the rate constant is described by the Arrhenius equation:

   k = A * e^(-Ea/RT)

   Where:

   • A is the pre-exponential factor.
   • Ea is the activation energy.
   • R is the gas constant.
   • T is the absolute temperature.

   While temperature profoundly impacts reaction rates, it does so through its effect on k, not as a direct concentration term within the rate law. Therefore, temperature is not a speed law in itself.

2. Catalysts: Catalysts influence reaction rates by altering the reaction mechanism and lowering the activation energy. They do not appear directly in the rate law unless the catalyst is also a reactant. The effect of a catalyst is reflected in the changed rate constant (k), which encapsulates the catalytic effect. Thus, the presence of a catalyst is not a speed law. The altered reaction rate due to the catalyst is accommodated by the adjusted value of k.

3. Surface Area: The surface area of a solid reactant affects the reaction rate but is generally not included as a variable in the rate law. The rate law focuses on the concentrations of reactants in the solution or gas phase. The effect of surface area is more about the frequency of contact between reactants. Therefore, surface area is not a speed law.

4. Pressure (in general): While pressure can affect the concentration of gaseous reactants, and thus influence the reaction rate, pressure itself is not a direct component of the rate law. The rate law uses concentration terms to reflect the amount of reactants available. Therefore, pressure alone is not a speed law unless it directly translates into a concentration term in the rate law.

5. Stoichiometry: The stoichiometric coefficients from the balanced chemical equation are not necessarily the same as the reaction orders (m and n) in the rate law. The reaction orders are determined experimentally and reflect the actual mechanism of the reaction, which may involve multiple steps. Stoichiometry simply describes the overall ratio of reactants and products. Therefore, stoichiometry is not a speed law.

Examples to Illustrate

Let's consider a few examples to clarify what constitutes a speed law and what does not.

Example 1: Reaction between Hydrogen and Iodine

The gas-phase reaction between hydrogen (H2) and iodine (I2) to form hydrogen iodide (HI) is:

H2(g) + I2(g) → 2HI(g)

The experimentally determined rate law is:

rate = k[H2][I2]

In this case, the rate law directly relates the reaction rate to the concentrations of H2 and I2, each raised to the power of 1. This is a clear example of a speed law.

Example 2: Decomposition of Nitrogen Dioxide

The decomposition of nitrogen dioxide (NO2) into nitrogen monoxide (NO) and oxygen (O2) is:

2NO2(g) → 2NO(g) + O2(g)

The experimentally determined rate law is:

rate = k[NO2]^2

Here, the rate law shows that the reaction rate is proportional to the square of the concentration of NO2. This is another example of a valid speed law.

Example 3: Reaction with a Catalyst

Consider a reaction that is significantly sped up by a catalyst. While the rate increases dramatically with the addition of the catalyst, the catalyst itself might not appear in the rate law if it doesn't directly participate in the rate-determining step. The effect of the catalyst is reflected in the value of k, which would be much larger with the catalyst than without it. However, the presence of the catalyst itself is not the speed law; it merely modifies the existing one.

Common Misconceptions

1. Stoichiometric Coefficients as Reaction Orders: A common mistake is assuming that the stoichiometric coefficients in a balanced chemical equation directly translate to the reaction orders in the rate law. This is only true for elementary reactions (reactions that occur in a single step). Most reactions involve multiple steps, and the rate law is determined by the slowest step (the rate-determining step).

2. Temperature as Part of the Rate Law: While temperature greatly affects the reaction rate, it does so by influencing the rate constant (k), not by being directly included as a concentration term in the rate law.

3. Confusing Rate and Rate Constant: The rate is the speed of the reaction, while the rate constant is a proportionality constant that relates the rate to the concentrations of the reactants. They are distinct concepts, and only concentrations of reactants are part of the speed law.

Determining the Correct Speed Law

To determine the correct speed law for a reaction, one must rely on experimental data. Several methods are commonly used:

1. Method of Initial Rates: This involves measuring the initial rate of a reaction for different initial concentrations of reactants. By comparing how the initial rate changes with changes in concentration, one can determine the reaction orders.

2. Integrated Rate Laws: These are equations that relate the concentration of a reactant to time. By comparing experimental data to the integrated rate laws for different reaction orders, one can determine the correct rate law.

3. Isolation Method: In this method, the concentration of one reactant is varied while the concentrations of all other reactants are kept constant. This allows one to determine the reaction order with respect to the reactant that is being varied.

The Significance of Understanding Speed Laws

Understanding speed laws is essential for several reasons:

1. Predicting Reaction Rates: Knowing the rate law allows one to predict how the reaction rate will change under different conditions (e.g., different concentrations of reactants).

2. Optimizing Reaction Conditions: By understanding how different factors affect the reaction rate, one can optimize reaction conditions to maximize the yield of desired products.

3. Understanding Reaction Mechanisms: The rate law provides valuable insight into the reaction mechanism. It can help determine which steps are involved in the reaction and which step is the rate-determining step.

4. Industrial Applications: In the chemical industry, understanding and controlling reaction rates is crucial for designing and operating chemical reactors.

Advanced Concepts

1. Complex Reactions: Many reactions involve multiple steps and intermediates. The rate law for a complex reaction is determined by the slowest step (the rate-determining step).

2. Reversible Reactions: In reversible reactions, the products can react to reform the reactants. The rate law for a reversible reaction includes terms for both the forward and reverse reactions.

3. Chain Reactions: These involve a series of elementary steps, with reactive intermediates (e.g., free radicals) being produced and consumed. The rate law for a chain reaction can be complex.

4. Enzyme Kinetics: Enzyme-catalyzed reactions follow a specific type of kinetics known as Michaelis-Menten kinetics. This involves the formation of an enzyme-substrate complex.

Conclusion

In summary, a speed law (or rate law) is an equation that relates the rate of a chemical reaction to the concentrations of the reactants. Factors like temperature, catalysts, surface area, and pressure can influence reaction rates but are not speed laws themselves. Temperature affects the rate constant, catalysts provide alternative reaction pathways, surface area influences contact frequency, and pressure impacts the concentration of gaseous reactants. The reaction orders in the rate law are determined experimentally and are not necessarily the same as the stoichiometric coefficients in the balanced chemical equation. Understanding speed laws is crucial for predicting reaction rates, optimizing reaction conditions, and gaining insight into reaction mechanisms, making it a fundamental concept in chemistry and chemical engineering. Therefore, while temperature, catalysts, surface area, and pressure influence the speed of a reaction, it is the rate law that defines how concentration impacts reaction speed, making the rate law the true "speed law" in chemical kinetics.