# Integrated Rate Law Definition5 min read

The integrated rate law is a mathematical equation used to calculate the rate of a chemical reaction at any given point in time. It takes into account the initial concentrations of the reactants and the rate of the reaction at the time the equation is calculated. This law is particularly useful for reactions that occur in a closed system, where the concentration of the reactants remains constant.

## What is the definition of integrated rate equation?

The integrated rate equation (IRE) is a mathematical formula used to calculate the change in a quantity over time. The IRE is particularly useful for calculating the rate of change of a population, or how a population changes over time.

The IRE is a derived equation, meaning that it is based on a variety of other equations. In order to understand the IRE, it is important to first understand the individual equations that it is based on. The most important of these equations is the law of mass action, which states that the rate at which a reaction proceeds is proportional to the product of the concentrations of the reactants.

The IRE is used to calculate the change in a population over time by taking into account the law of mass action, as well as the first and second laws of thermodynamics. The first law of thermodynamics states that the change in the internal energy of a system is equal to the sum of the heat flows into and out of the system, while the second law of thermodynamics states that the entropy (a measure of disorder) of a system always increases over time.

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By incorporating these three equations into a single equation, the IRE is able to calculate the change in population over time. This equation takes into account the fact that the rate of reaction is proportional to the product of the concentrations of the reactants, that the change in internal energy is equal to the sum of the heat flows into and out of the system, and that the entropy of a system always increases over time.

## What is the difference between rate law and integrated rate law?

Rate law and integrated rate law are two important aspects of chemical kinetics. Rate law governs the rate of a reaction at a given instant, while integrated rate law governs the overall reaction rate.

The rate law is a mathematical equation that describes the rate of a chemical reaction as a function of the concentrations of the reactants. It is usually expressed in terms of the rate constant, k. The rate law can be determined experimentally by measuring the reaction rate at different concentrations of the reactants.

The integrated rate law is a mathematical equation that describes the reaction rate as a function of the concentrations of the reactants and the time. It is usually expressed in terms of the integrated rate constant, k. The integrated rate law can be determined experimentally by measuring the reaction rate at different concentrations of the reactants and different time intervals.

The difference between rate law and integrated rate law is that the rate law describes the instantaneous reaction rate, while the integrated rate law describes the overall reaction rate.

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## What is the purpose of an integrated rate law?

The purpose of an integrated rate law is to mathematically model the change in concentration of a reactant or product over time. This information can be used to optimize reaction conditions and improve process efficiency.

## How do you derive the integrated rate law?

The integrated rate law is a mathematical equation used to calculate the rate of a reaction at any given time. It is derived from the rate law, which is a mathematical equation that calculates the rate of a reaction at any given point in time. The integrated rate law can be used to determine the rate of a reaction at any point in time, as well as the amount of product that has been produced at any given point in time.

## What is the integrated rate law of first order reaction?

The integrated rate law of a first order reaction is a mathematical equation that describes the rate of a reaction as a function of time. The equation can be used to predict the rate of a reaction at any point in time.

The integrated rate law of a first order reaction is expressed as follows:

d[A]/dt = k[A]

where [A] is the concentration of the reactant A, and k is the rate constant for the reaction.

The integrated rate law can be used to predict the rate of a reaction at any point in time. To do this, the equation is integrated over the time interval of interest. The resulting equation can be used to calculate the rate of the reaction at any point in time.

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## What is the integrated rate law of first-order reaction?

The integrated rate law of a first-order reaction is a mathematical equation that describes how the reaction rate changes with time. The equation takes into account the initial reaction rate and the reaction’s half-life.

The integrated rate law of a first-order reaction is written as follows:

d[reactant]/dt = k[reactant]

Where k is the reaction rate constant and [reactant] is the concentration of the reactant.

The equation can be used to calculate the reaction rate at any point in time. It also allows for the determination of the half-life of a reaction. The half-life is the amount of time it takes for the reaction rate to decline to half of its initial value.

## What is the unit of rate constant?

What is the unit of rate constant?

The rate constant is a dimensionless quantity that has the units of reciprocal time (s-1).