# Chemical Kinetics: Rate of Reaction, Formulas and Equations

The study of chemical reaction rates and the variables that affect these rates is the main goal of the field of physical chemistry known as chemical kinetics. Understanding the processes by which reactant molecules rearrange and change into product molecules is one of its goals.

Contrary to thermodynamics, which deals with the overall energy changes and stability of a system, chemical kinetics focuses on the time-dependent aspects of reactions. While thermodynamics provides information about the feasibility and equilibrium state of a reaction, kinetics provides insights into the actual rate at which reactants are converted into products.

Chemical kinetics involves experimental measurements and theoretical modeling to determine the rate of a reaction. Experimental techniques such as monitoring changes in concentration, pressure, or spectroscopic properties over time are used to obtain data on reaction rates. These data are then analyzed to derive rate laws, reaction orders, and rate constants.

#### Chemical Reactions in Chemical Kinetics

In chemical kinetics, a chemical reaction involves the rearrangement of atoms in reactant molecules to form new products. This rearrangement occurs through the breaking and formation of chemical bonds.
Chemical reactions can be represented using chemical equations, which provide a concise way to describe the reactants and products involved. Reactants are written on the left side of the equation, while products are written on the right side. For example, the chemical equation for the reaction between hydrogen gas (H2) and oxygen gas (O2) to form water (H2O) is:
2H2 + O2 → 2H2O

Chemical reactions can be classified into different types based on the nature of the reactants and products. Some common types of reactions include:

Combination reactions: Two or more substances combine to form a single product. For example: A + B → AB

Decomposition reactions: A single compound breaks down into two or more simpler substances. For example: AB → A + B

Displacement reactions: An element displaces another element in a compound, resulting in the formation of a new compound. For example: A + BC → AC + B

Redox reactions: These involve the transfer of electrons between reactants. Oxidation-reduction (redox) reactions are important in many biological and industrial processes.

Examples of Chemical Reactions:

• Burning wood
• Souring milk
• Mixing acid and base
• Digesting food
• Cooking an egg
• Heating sugar to form caramel
• Baking a cake
• Rusting of iron

#### Rate of Chemical Reaction

The rate of a Chemical Reaction can be expressed as follows:

• The rate at which the reactant’s concentration is dropping.
• The speed at which product is rising.

The Molar unit, also expressed as mol/L to indicate the number of moles in 1 liter of the chemical, is used in the SI to measure a chemical’s concentration.

If R → P is a chemical reaction where R= Reactant and P= Product

Let’s assume [R]1 and [R]2 are concentrations of reactants (R) at time T1 and T2 respectively. [P]1 and [P]2 are concentrations of product (P) at time T1 and T2 respectively.

• Rate of disappearance of reactant [R] =(-1) X [R]2 – [R]1 / T2 – T1 . Since it is calculating the disappearance of reactant it is multiplied with (-1).
• Rate of appearance of product [P] = [P]2 – [P]1 / T2 – T1

Depending on the input variables, the aforementioned formulas can also be used to compute the average and instantaneous rates of reaction. A differential equation is the rate reaction equation.

• When calculating average rate, the difference between reactants, products, and time is taken into account from the start of the reaction until its conclusion. Chemical concentration is where the reaction’s beginning and ending times are known.
• In the case of an instantaneous rate, the chemical concentration difference only exists for a brief period of time during the reaction. where the chemical concentrations are measured twice during the reaction. In this scenario, the time difference is hardly noticeable.

#### Factors Influencing the Rate of Reaction in Chemical Kinetics

The rate of reaction depends upon experimental conditions as follows:

#### Concentration of Chemicals

Chemical concentration on the reactant and product sides of the reaction is very important. The term “rate equation” or “rate law” refers to the depiction of response rate in terms of concentration. As Rate [A] x [B] y, where x and y are the stoichiometric coefficients of Reactant A and Reactant B, respectively, the rate of expression can also be expressed.

To balance an equation on both ends, the stoichiometric coefficient—a number that is placed in front of the ions and molecules of a chemical—must be present.

#### Order of Reaction

The sum of powers of the reactants in rate expression is termed as order of reaction. If Rate = K [A] x [B] y  then order of reaction = x+y

#### Molecularity of Reaction

The term “of reaction” refers to the total number of atoms, ions, and molecules that contribute to the successful completion of an elementary reaction by concurrently hitting against one another. This must always be a full number and cannot be less than one or greater than three.

A single-step chemical reaction is referred to as an elementary reaction.

#### Rate of Constant

When the concentrations of the two reactants are the same, the computed rate of reaction is known as the rate constant, which is typically represented by the letter “K” and is occasionally referred to as the proportionality constant in rate expression. Additional notation for the rate of expression is Rate = K [A] x [B] y.

#### Effect of Temperature

The majority of chemical processes are shown to speed up with an increase in temperature. Additionally, it has been noted that a 10° increase in temperature causes the rate constant (k) for that reaction to double.

Arrhenius equation: k = A e -Ea /RT shows the relation between temperature and rate constant.

Here k = rate constant

A= Frequency factor

Ea = Activation Energy

R= Gas constant

T= Temperature

Comparing rate constant of a reaction at 2 different temperatures

Log k 2 / k 1 = Ea / 2.303R [ T 2 – T 1 / T 12

#### Effect of Catalyst

Catalysts are substances that speed up chemical reactions without permanently changing their own chemical composition.

#### Zero Order Reactions

The rate of chemical reaction is proportional to the zero power to that of the reactant’s concentration.

Rate ∝ [A] 0

Rate = K[A] 0 which gives Rate = K

Further the zero order reactionequation can be written as K = [R] 0 – [R] / t

R 0 = Initial concentration of Reactant R

T = time

K= Reaction Constant

R = Concentration of Reactant.

Deriving Zero Order Reaction

Equation for the R-P reaction

Rate is equal to -d[R]/dt = k[R]=0.

Rate = – d[R] / dt = k x 1, where k is the power of 0 and 1 is the result.

k x dt = d[R]

R = -kt + I, where I is the integration constant and both sides are integrated.

At time t=0, the reactant concentration is [R] 0, which represents the reactant’s initial concentration. The previous equation should have the same replacement.

[R] 0 = I

adding another substitution for I in the previous equation.

R = -kt + [R] 0

Thus, the zero order reaction equation is obtained:

K = [R] 0 – [R] / t

#### First Order Reaction

The first power of the reactant concentration [R] determines the rate of the chemical reaction.

After integrating the differential rate equation and inserting 1 to the power of the reactant, we obtain the equation for a first order chemical process.

Log [R] 1/[R] 2 = (T 2 – T 1) / 2.300

Where [R] 1 and [R] 2 represent the reactant concentrations at time T and time T2 respectively.

#### Pseudo First Order Reaction

Despite having two molecules on the reactant side, these reactions behave like first order reactions because one of the reactants is present in excess. Pseudo-first order reactions are what these reactions are known as.

#### Half-life of a Reaction

It is the amount of time required for a reactant’s concentration to drop to half that of its starting concentration.

A zero order reaction’s half life can be expressed as:

T 1/2 = R 0 / 2k

R 0 is the reactant concentration, T 1/2 is the reaction’s half-life period, and k is the reaction’s rate constant.

First order reaction half-life equation:

T 1/2 = 0.693 / k

#### Things to Keep in Mind

The rate of reaction is the rate of change of the response’s extent.
For a product, the rate of reaction is positive; for a reactant, it is negative.

Chemical kinetics, a phrase derived from a Greek word meaning “chemical movement,” is the area of chemistry that regulates the rate of reactions as well as their mechanics.

Due to a drop in reactant concentration, it keeps getting smaller while the reaction progresses.

Reactants and products are engaged in a chemical transformation. The concentration of the reactants lowers as the chemical reaction proceeds, resulting in the production of products.

#### Sample Questions

Answer: Chemical kinetics is the branch of chemistry that deals with the study of the rates at which chemical reactions occur and the factors that influence these rates.

Answer: The rate of a chemical reaction is the change in concentration of a reactant or product per unit time. It is usually expressed in terms of moles per liter per second (mol/L/s) or other appropriate units.

Answer: Several factors can influence the rate of a chemical reaction, including temperature, concentration of reactants, surface area, presence of a catalyst, and the nature of the reactants.

Answer: Increasing the temperature generally increases the rate of a chemical reaction. This is because higher temperatures provide more kinetic energy to the reactant molecules, leading to more frequent and energetic collisions, which in turn increases the reaction rate.

Answer: A catalyst is a substance that increases the rate of a chemical reaction by providing an alternative reaction pathway with lower activation energy. It does not get consumed in the reaction and can be used repeatedly.

Answer: The order of a chemical reaction refers to the relationship between the concentration of reactants and the rate of the reaction. It can be zero order, first order, second order, or even fractional order.

Answer: The rate law of a chemical reaction can be determined by conducting a series of experiments in which the initial concentrations of reactants are varied. By measuring the reaction rates under different conditions, the order of the reaction with respect to each reactant can be determined.

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