Reaction Orders: Videos & Practice Problems

In the study of chemical kinetics, understanding reaction orders is crucial for analyzing how the rate of a reaction depends on the concentrations of reactants. The rate law expresses this relationship mathematically, stating that the reaction velocity \( v \) is equal to the rate constant \( k \) multiplied by the concentrations of the reactants raised to their respective reaction orders. This can be represented as:

\[ v = k [A]^{m} [B]^{n} \]

Here, \( [A] \) and \( [B] \) are the concentrations of reactants, while \( m \) and \( n \) are the reaction orders for each reactant. It's important to note that the reaction orders are not always equal to the coefficients of the reactants in the balanced equation; they must be determined experimentally.

For elementary reactions, which have a single transition state, the coefficients do correspond to the reaction orders. For example, in the reaction of ozone gas with oxygen gas to produce oxygen dioxide, both reactants have a coefficient of 1, indicating a first-order reaction for each. Thus, the overall reaction order is the sum of the individual orders, resulting in a second-order reaction:

\[ \text{Overall Reaction Order} = 1 + 1 = 2 \]

Conversely, non-elementary reactions involve multiple transition states and do not follow the same rules. For instance, in the reaction between nitrogen dioxide and carbon monoxide, the reaction order for nitrogen dioxide may be 2, while for carbon monoxide it could be 0, despite their coefficients being different. This leads to an overall reaction order of:

\[ \text{Overall Reaction Order} = 2 + 0 = 2 \]

This illustrates that the overall reaction order does not provide specific information about the individual reaction orders, which must be determined through experimental data. As we progress, we will explore the three common overall reaction orders: zero-order, first-order, and second-order reactions, each with distinct characteristics and implications for reaction kinetics.

In the study of chemical kinetics, understanding zero-order reactions is crucial. A zero-order reaction is characterized by a reaction rate that remains constant regardless of changes in substrate concentration. This means that even if the concentration of the reactant is altered, the rate of the reaction does not change. This phenomenon typically occurs in enzyme-catalyzed reactions when the enzyme is fully saturated with substrate.

The rate constant for zero-order reactions has specific units of molarity per second (M/s), although the focus on these units will be addressed in more detail later in the course. For a zero-order reaction involving a reactant A converting to product B, the rate law can be expressed as:

$$ \text{Rate} = k \cdot [A]^0 $$

Since any number raised to the power of zero equals one, this simplifies to:

$$ \text{Rate} = k $$

This indicates that the reaction rate is equal to the rate constant, k. Graphically, when plotting the reaction rate against substrate concentration, a zero-order reaction will display a horizontal line, indicating that the reaction rate remains constant despite variations in substrate concentration. This plateau occurs when the enzyme is saturated, meaning it has reached its maximum capacity to process the substrate.

In summary, zero-order kinetics highlight the relationship between enzyme saturation and reaction rate, emphasizing that under certain conditions, the reaction rate is independent of substrate concentration. This concept is essential for understanding enzyme behavior and reaction dynamics in biochemical processes.

In the context of enzyme kinetics, zero-order reactions are characterized by a reaction rate that remains constant regardless of substrate concentration. This means that the reaction velocity is independent of the amount of substrate present. To illustrate this concept, consider an analogy where cars represent substrate molecules lined up to cross a one-lane bridge, which symbolizes the enzyme. When the bridge is fully occupied, it becomes saturated with cars, indicating that the enzyme is operating at its maximum capacity.

In this scenario, even if more cars (substrate) are added, the rate at which they can cross the bridge (the reaction rate) does not increase. This is because the single lane (enzyme) cannot accommodate additional cars beyond its saturation point. Therefore, the answer to whether increasing substrate concentration enhances the reaction rate is no; the reaction remains at a constant rate due to saturation.

To increase the reaction rate in a zero-order reaction, one must introduce more enzymes (additional lanes on the bridge). By doing so, the overall capacity for substrate conversion increases, allowing more cars to cross in a given time frame. This highlights the importance of enzyme availability in influencing reaction rates, particularly when dealing with saturated conditions.

First order reactions are characterized by a reaction rate that is directly proportional to the concentration of a single substrate. This type of reaction typically involves unimolecular processes, meaning it involves only one molecule, such as the conversion of substrate A into product B. In these reactions, the rate law can be expressed as:

$$ \text{Rate} = k [A] $$

where k is the first order rate constant, and [A] represents the concentration of the substrate. The units of the first order rate constant are inverse seconds (s^-1), although a detailed understanding of these units will be covered later in the course.

Graphically, first order reactions are represented by a diagonal line on a plot of reaction rate versus substrate concentration, indicating that as the concentration of the substrate increases, the reaction rate also increases proportionally. This contrasts with zero order reactions, which display a horizontal line, indicating that the reaction rate remains constant regardless of substrate concentration.

In enzyme-catalyzed reactions, the behavior can shift depending on substrate concentration. At low concentrations, the reaction follows first order kinetics, where the rate is dependent on substrate concentration. However, as the substrate concentration increases and approaches saturation, the reaction may transition to zero order kinetics, where the rate becomes independent of substrate concentration.

Understanding these concepts is crucial as they form the foundation for analyzing reaction kinetics and enzyme behavior in biochemical processes.

Second order reactions are characterized by their rates being directly proportional to the concentrations of two substrates or to the square of a single substrate concentration. This distinction is crucial as it allows for two common expressions of the rate law for second order reactions. In the first case, the rate law can be expressed as:

\[ v = k [A][B] \]

where \( v \) is the reaction velocity, \( k \) is the rate constant, and \([A]\) and \([B]\) are the concentrations of the substrates. This indicates that the reaction involves two substrates, A and B, each contributing to the rate of the reaction.

Alternatively, the rate law can also be expressed as:

\[ v = k [A]^2 \]

In this scenario, the reaction rate is dependent solely on the square of the concentration of substrate A, while substrate B has no effect on the reaction rate, indicating it is zero order with respect to B.

Second order reactions often involve bimolecular interactions, where two molecules collide to form products. The units of the second order rate constant \( k \) are expressed as inverse molarity and inverse seconds, specifically \(\text{M}^{-1}\text{s}^{-1}\).

Graphically, the relationship between the reaction rate and substrate concentration for second order reactions is represented by an exponential curve, contrasting with the horizontal line seen in zero order reactions and the straight line of first order reactions. This behavior reflects the complexity of the reaction dynamics as substrate concentrations change.

An example of a second order reaction in biological systems is the breakdown of glycogen, a polysaccharide composed of glucose units. In this reaction, glycogen interacts with inorganic phosphate to produce glucose-1-phosphate and a modified glycogen molecule. The rate law for this reaction can be expressed as:

\[ v = k [\text{Glycogen}][\text{Inorganic Phosphate}] \]

Assuming both substrates have a coefficient of 1, the overall reaction order sums to 2, confirming it as a second order reaction. Understanding these principles is essential for analyzing reaction kinetics and predicting how changes in substrate concentrations will affect reaction rates.

Pseudo first order reactions are intriguing because they mimic first order kinetics while actually being second order reactions. The term "pseudo" indicates that these reactions are not genuinely first order; instead, they occur under specific conditions where one reactant's concentration is significantly higher than the other's. For example, if the concentration of substrate B is much greater than that of substrate A, the reaction can be classified as pseudo first order.

In such scenarios, the high concentration of B leads to saturation, resulting in zero order kinetics concerning B. This means that changes in the concentration of B do not influence the reaction rate, even though it is a second order reaction overall. The limiting reagent in this case is substrate A, which dictates the reaction rate, giving the appearance that only A's concentration affects the kinetics.

When graphing pseudo first order reactions, the data resembles that of first order reactions due to the overwhelming presence of one substrate. This can create challenges for biochemists, as the apparent simplicity of first order kinetics can obscure the underlying second order nature of the reaction. Understanding this distinction is crucial for accurately interpreting reaction mechanisms and kinetics.