Reaction Kinetics: Zero, Pseudo-zero, First & Second Order, Units of Basic Rate Constants, Determination of Reaction Order : Pharmaceutical Guidelines -->

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Reaction Kinetics: Zero, Pseudo-zero, First & Second Order, Units of Basic Rate Constants, Determination of Reaction Order

Reaction kinetics or Chemical kinetics is the study of the rate and mechanism of chemical changes that take place during the chemical reaction.
Reaction kinetics or Chemical kinetics is the study of the rate and mechanism of chemical changes that take place during the chemical reaction. In relation to the pharmaceutical formulation, it includes the study of physical and chemical changes in drugs as well as the dosage form. The pace of a chemical reaction, the stability test, and the half-life are all affected by a variety of circumstances.

The speed of a chemical reaction is defined by its velocity, while the order of the reaction is dictated by the concentration of molecules that influence its rate. The rate of response is usually represented as,

Rate of reaction= -dA/dt

When the rate of reaction is stated in, the concentration of A falls with time while the concentration of B grows as the reaction progresses.

Rate of reaction= -dB/dt

In an experiment with both A and B concentrations, it was revealed that the rate of response decreased with time in the drug A concentration.

Molecularity of Reaction is a concept used to describe how the concentration of a reactant or reactants affects the pace of a chemical reaction. The number of ions, atoms, or ions reacts in an elementary process to produce the reactants. Among them, the molecular that undergoes chemical changes and yields the product, the product is termed as unimolecular.

Drug Stability is the pharmaceutical dosage form that maintains the chemical and physical factors which influence the chemical degradation of the product. Temperature, solvent, ionic strength, dielectric constant, specific and general acid-base catalysis, and simple numerical issues are also determined by it. It also stabilizes the drugs against hydrolysis and oxidation. Expiration date of pharmaceutical dosage forms using accelerated stability testing, such as photolytic deterioration and its avoidance.

Zero Order Reaction

A constant rate process is used to describe a zero-order reaction. It is the reaction that is unaffected by the concentration parameters of the reactants. In this situation, increasing the rate of the reactants will not enhance the reaction rate. Other elements beyond concentration have a role in this response.

The rate of decomposition is expressed mathematically,

-dCx/dt = K ------- (1)

Whereas, K is the specific rate constant for a zero-order. Integrating the equation,

X= Kt + constant -------- (2)

A graph contains a plot of X. It results in a straight line equal to K. ‘K’ indicates the amount of drug degraded per unit time. It intersects the line at time zero, which is equal to constant, in the graph. Concentration/time is the unit of K.

Whereas, half-life = t ½ = Co/2k

Examples of zero-order kinetics are Vitamin A acetate to anhydrous Vitamin A and photolysis of cefotaxime

Pseudo-zero Order Reaction

It's the moment at which the chemical reaction starts. It cannot be physically observed. It is the phase that occurs very instant of a reaction. Practically, the phase ‘chemical reaction’ of reactants begins at a very certain time.

In a solid-state such as a tablet, the degradation of the drug is initiated by pseudo-zero order kinetics. It's the response between the medicine and the amount of moisture in the dose form. Due to the presence of excess solid drugs, it behaves like suspension. Mainly, the zero-order kinetic becomes the pseudo-order kinetics.

It intersects the line at time zero, which equals constant, in the graph. Concentration/time is the K unit. When decomposition occurs, more amount of drugs releases from the suspended particles. That’s why the concentration remains constant. Despite its deterioration over time, the most important point in suspension stays constant. The drug equilibrium solubility in a given solvent at a given time is the suspension concentration. The reservoir of the dispersed phase in suspension is responsible for the constant rate. The suspended drug reservoir ensures constant concentration which is why it follows a zero-order reaction. In the chemical reaction, the suspended particles convert to drug particles in solution. The order mostly shifts to a first-order response.

First Order Reaction

It's a reaction whose rate is determined by the concentration of one of the reactants. For example, absorption, distribution, elimination rates, and microbial death kinetics. As a result, the reaction rate is proportional to the concentration of the reacting chemicals.

It can be expressed as:

Rate of the concentration decreases, -dCx/dt= KCx ------------- (3)

Where,

X= ‘a’, when t=0

t=x, the amount X at time t is (a-x)

Therefore,

-dCx/dt = K (a-x)

dCx/ (a-x) = -Kdt ----------------(4)

Second-Order Reaction

It is the reaction in which the rate of reaction is dependent on the concentration of two reactants raised to the power one.

Therefore,

A + B Product

Therefore, the equation

-dA/dt = -dB/dt = k2[A]1 [B]1

Where,

[A] = The concentration of A

[B] = The concentration of B

k2 = rate constant

Units

Basic rate constants are measured in k. ‘k’ depending on the overall orders of the reactions.

In a zero-order reaction, the unit of k is M/s.

In a first-order reaction, the unit of k is 1/s.

In a second-order reaction, the unit of k is 1/(M-s).

Determination of Reaction Order

The order of the reaction defines the relationship of the rate and concentration of the chemical reaction. In the case of determining the order of the reaction, there are several methods to follow:

Substitution Method In a reaction of two molecules, the products show incompatible results in some cases. It will, however, be replaced with a different chemical molecule. It shows better results and effects in reaction results. In general, this strategy enhances the reaction's efficacy and outcomes.

Initial Rate Method

In the graph, the points are plotted against concentration. The gradient at time = 0 also defines the starting rate. In the graph, if the plot draws a straight line that signifies a first-order reaction. If the reaction is independent of the concentration, it is termed a zero-order reaction. If a curve appears in the graph at some point, it signals a second order reaction.

Data Plotting Method

If the plotting is linear such as concentration against time, it is a zero-order reaction.
If the plotting is linear such as c against time, it is a first-order reaction.
If the plotting is linear such as 1/c against time, it is a second-order reaction.

Half-Life Determination Method

It defines the relationship between the half-life of a reaction and the concentration of all reactant's id similar.

Whereas, n = order of the reaction.

t1/2 is directly proportional to 1/an-1

If the two reactions are occurring at different initial concentration, the half-lives of a1 and a2 is,

n = log (t1/2(1))/(t1/2(2))/ log (a2/a1) + 1

The process of chemical kinetics in relation to pharmaceutical ingredients determines the degradation of the drug according to the concentration against time. The degradation starts after exposing the drug to air and absorbing moisture. Chemical kinetics, on the other hand, explains the chemical changes that occur in a medicine based on the reaction order.
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Ankur Choudhary is India's first professional pharmaceutical blogger, author and founder of Pharmaceutical Guidelines, a widely-read pharmaceutical blog since 2008. Sign-up for the free email updates for your daily dose of pharmaceutical tips.
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