Rate Of Chemical Reaction and Factors Affecting It

Rate Of A Chemical Reaction

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Chemical Kinetics: Chemical kinetics is the study of the rates of chemical reactions and the factors that affect these rates.

Rate of Reaction: The rate of a chemical reaction is defined as the change in the concentration of reactants or products per unit time. It essentially tells us how fast a reaction is proceeding.

Expression for Rate: For a general reaction:

$$aA + bB \rightarrow cC + dD$$

The rate of reaction can be expressed as:

$$\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$$

Where:

• $[A], [B], [C], [D]$ represent the molar concentrations of reactants and products.
• $t$ represents time.
• $\frac{d[A]}{dt}$ represents the rate of decrease in the concentration of reactant A. The negative sign indicates that the concentration of reactants decreases over time.
• $\frac{d[C]}{dt}$ represents the rate of increase in the concentration of product C. The positive sign indicates that the concentration of products increases over time.
• $a, b, c, d$ are the stoichiometric coefficients of the reactants and products in the balanced chemical equation. We divide by these coefficients to express the rate of reaction in a consistent way, independent of which reactant or product is monitored.

Units of Rate of Reaction: The units of rate of reaction are typically expressed as concentration per unit time, such as moles per liter per second (mol L$^{-1}$ s$^{-1}$) or molarity per minute (M min$^{-1}$).

Average Rate vs. Instantaneous Rate:

• Average Rate: The change in concentration over a finite interval of time ($\Delta t$).
$$\text{Average Rate} = -\frac{\Delta[A]}{\Delta t} = +\frac{\Delta[C]}{\Delta t}$$
• Instantaneous Rate: The rate of reaction at a particular instant in time. It is the slope of the tangent to the concentration-time graph at that point. Mathematically, it is the derivative of concentration with respect to time.

Example: For the reaction $2NO_2(g) \rightarrow 2NO(g) + O_2(g)$, if the concentration of $NO_2$ decreases from 0.50 M to 0.40 M in 10 seconds, calculate the average rate of reaction in terms of $NO_2$ disappearance and the average rate of formation of $O_2$.

Answer:

Factors Influencing Rate Of A Reaction

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The rate of a chemical reaction can be influenced by several factors, which are crucial for controlling and understanding chemical processes.

Dependence Of Rate On Concentration

General Trend: For most reactions, the rate of reaction increases as the concentration of the reactants increases. This is because a higher concentration means there are more reactant particles in a given volume, leading to more frequent collisions between reactant molecules.

Collision Theory: This theory states that for a reaction to occur, reactant molecules must collide with each other. Not all collisions lead to a reaction; only effective collisions result in product formation. Effective collisions have two requirements:

1. Sufficient Energy: The colliding molecules must possess a minimum amount of kinetic energy, known as the activation energy ($E_a$), to overcome the energy barrier for bond breaking and formation.
2. Proper Orientation: The colliding molecules must have the correct spatial orientation for the reactive parts of the molecules to interact.

Concentration and Collision Frequency: Increasing the concentration of reactants increases the number of reactant particles per unit volume. This, in turn, increases the frequency of collisions between reactant molecules. A higher collision frequency, assuming other factors remain constant, leads to a higher rate of effective collisions and thus a faster reaction rate.

Rate Expression And Rate Constant

Rate Law (Rate Expression): The rate law is an experimentally determined mathematical expression that relates the rate of a reaction to the concentration of reactants. For a general reaction:

$$aA + bB \rightarrow \text{Products}$$

The rate law is typically written as:

$$\text{Rate} = k[A]^x[B]^y$$

Where:

• $k$ is the rate constant (also called the velocity constant). It is a proportionality constant that is specific to a particular reaction at a given temperature.
• $[A]$ and $[B]$ are the molar concentrations of reactants A and B, respectively.
• $x$ and $y$ are the order of reaction with respect to reactants A and B, respectively. These exponents are not necessarily equal to the stoichiometric coefficients ($a$ and $b$) and must be determined experimentally.

Rate Constant (k):

• The rate constant ($k$) is a temperature-dependent constant. It reflects the intrinsic rate of the reaction at a given temperature. A larger value of $k$ indicates a faster reaction.
• The units of $k$ depend on the overall order of the reaction.
• The rate law shows that even when reactant concentrations are zero, the rate constant ($k$) still exists, representing the potential for reaction under those conditions (though practically, the rate would be zero if all reactants are zero).

Order Of A Reaction

Definition: The order of a reaction is the sum of the exponents of the concentration terms in the rate law.

For the rate law: $\text{Rate} = k[A]^x[B]^y$

• The order with respect to reactant A is $x$.
• The order with respect to reactant B is $y$.
• The overall order of the reaction is $x + y$.

Characteristics of Reaction Orders:

• Experimental Determination: The order of a reaction cannot be predicted from the stoichiometry of the balanced chemical equation; it must be determined experimentally.
• Possible Values: Orders can be zero, positive integers, or even fractions.
• Zero Order: If $x=0$, the rate is independent of the concentration of A: $\text{Rate} = k[B]^y$.
• First Order: If $x=1$, the rate is directly proportional to the concentration of A: $\text{Rate} = k[A]$.
• Second Order: If $x=2$, the rate is proportional to the square of the concentration of A: $\text{Rate} = k[A]^2$.

Integrated Rate Laws: These laws relate concentration to time for reactions of specific orders.

• Zero-Order Reaction: $[A]_t = [A]_0 - kt$. (Plot of $[A]_t$ vs $t$ is linear with slope $-k$).
• First-Order Reaction: $\ln[A]_t = \ln[A]_0 - kt$ or $[A]_t = [A]_0 e^{-kt}$. (Plot of $\ln[A]_t$ vs $t$ is linear with slope $-k$).
• Second-Order Reaction: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$. (Plot of $\frac{1}{[A]_t}$ vs $t$ is linear with slope $k$).

Half-Life ($t_{1/2}$): The time required for the concentration of a reactant to decrease to half its initial value.

• For zero-order: $t_{1/2} = \frac{[A]_0}{2k}$ (Half-life depends on initial concentration)
• For first-order: $t_{1/2} = \frac{\ln 2}{k} \approx \frac{0.693}{k}$ (Half-life is independent of initial concentration)
• For second-order: $t_{1/2} = \frac{1}{k[A]_0}$ (Half-life depends on initial concentration)

Molecularity Of A Reaction

Definition: Molecularity is the number of reactant molecules (or atoms or ions) that must collide simultaneously in order for a chemical reaction to occur. It is determined from the rate-determining step (slowest step) of a reaction mechanism.

Types of Molecularity:

• Unimolecular: Involves a single molecule undergoing a chemical change (e.g., isomerisation, decomposition). Example: $N_2O_4 \rightarrow 2NO_2$.
• Bimolecular: Involves the collision of two molecules. Example: $NO + O_3 \rightarrow NO_2 + O_2$.
• Termolecular: Involves the simultaneous collision of three molecules. These are very rare because the probability of three molecules colliding with the correct orientation and sufficient energy at the same time is very low. Example: $2CO + O_2 \rightarrow 2CO_2$ (catalyzed reaction).

Key Differences Between Order and Molecularity:

Here's a comparison:

Feature	Order of Reaction	Molecularity
Definition	Sum of exponents of concentration terms in the rate law.	Number of molecules colliding simultaneously in the rate-determining step.
Determination	Experimentally determined.	Determined from the reaction mechanism (specifically, the slowest step).
Values	Can be zero, positive integers, or fractions.	Must be a positive integer (1, 2, or 3). Termolecular is very rare.
Relation to Stoichiometry	Not necessarily related to stoichiometric coefficients.	Relates to the number of reacting species in an elementary step.
Applicability	Applies to elementary and complex reactions.	Applies only to elementary reactions (or the slowest step of a complex reaction).

Complex Reactions: For complex reactions (reactions that proceed through multiple steps), the molecularity is often referred to in terms of the elementary steps. The overall order of the reaction is determined by the rate-determining step, while the molecularity of the overall reaction is not defined in the same way as for elementary reactions.