Contents

- When to use integrated rate law
- What is integrated rate law
- How to use integrated rate law
- The integrated rate law equation
- The integrated rate law and half-life
- The integrated rate law and first-order reactions
- The integrated rate law and second-order reactions
- The integrated rate law and zero-order reactions
- The integrated rate law and pseudo-first-order reactions
- The integrated rate law and reactions with multiple steps

If you’re wondering when to use integrated rate law, you’re not alone. This is a common question for students studying chemistry. Keep reading to learn more about when to use integrated rate law and how it can help you understand chemical reactions.

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## When to use integrated rate law

In order to determine the rate of a chemical reaction, you need to know how concentration changes over time. The integrated rate law can be used to calculate the change in concentration of a reactant or product over time. The integrated rate law is based on the rate law equation, which states that the rate of a reaction is proportional to the concentrations of the reactants.

The integrated rate law can be used to determine the concentration of areactant or product at any given time. It can also be used to calculate the half-life of a reaction, which is the amount of time it takes for the concentration of a reactant or product to decrease by half.

If you know the initial concentrations of all reactants and products, as well as the rate constant for the reaction, you can use the integrated rate law to calculate the concentration of any reactant or product at any given time.

## What is integrated rate law

In general, a reaction rate can be described by the following formula:

rate = k[A]^x[B]^y

where k is the rate constant, [A] and [B] are the concentrations of reactants A and B, and x and y are the orders of reaction with respect to A and B. The integrated rate law is an equation that expresses the concentration of a reactant or product as a function of time. It can be used to determine the order of a reaction, the rate constant, or the half-life of a reaction.

The general form of the integrated rate law for a zero-order reaction is:

[A] = [A]_0 – kt

where [A]_0 is the initial concentration of A. For a first-order reaction, the integrated rate law is:

ln[A] = ln[A]_0 – kt

and for a second-order reaction, it is:

1/[A] = 1/[A]_0 + kt

## How to use integrated rate law

Integrated rate law is used to describe the change in concentration of a reactant over time. It is a differential equations method that considers all possible reaction rates to determine the rate of change of concentration for a given chemical reaction.

## The integrated rate law equation

The integrated rate law equation is used to determine the concentration of a reactant at a specific time during a reaction. The equation takes into account the fact that the rate of a reaction changes as the concentration of reactants changes. The integrated rate law equation can be used for any reaction, regardless of the order of the reaction.

To use the integrated rate law equation, you need to know the initial concentration of reactants, the time at which you want to know the concentration of reactants, and the rate constant for the reaction. The rate constant is a value that is specific to each reaction and cannot be determined from the other values in the equation. The units for the rate constant depend on the order of the reaction; for example, if the order of the reaction is two, then the units for the rate constant will be M-1s-1.

Once you have all of these values, you can plug them into the integrated rate law equation and solve for the concentration of reactants at your desired time.

## The integrated rate law and half-life

The integrated rate law is a mathematical way to describe how a reactant concentration changes over time during a chemical reaction. The half-life of a reaction is the amount of time it takes for the reactant concentration to decrease by half. The half-life is directly related to the integrated rate law constants.

## The integrated rate law and first-order reactions

An integrated rate law is a mathematical expression derived from the rate law that gives the concentration of a reactant as a function of time. It is usually first-order with respect to thereactant, but can also be zeroth-, second-, or third-order. The integrated rate law is obtained by integration of the rate law. The most common rate laws are those for second-order reactions and for zeroth-order reactions.

Integrated rate laws are only valid over a limited range of concentrations, typically less than 10% of the original reactant concentration. Higher concentrations can produce erroneous results due to side reactions or other effects not considered in deriving the integrated rate law.

## The integrated rate law and second-order reactions

In a second-order reaction, the rate of reaction is proportional to the concentration of each reactant raised to the power of its stoichiometric coefficient. The integrated rate law for a second-order reaction is:

[A]t = [A]0 * e^(-kt)

where k is the rate constant for the reaction and [A]0 is the concentration of reactant A at t=0. This equation can be integrated to give:

ln([A]t/[A]0) = -kt

and rearranged to solve for t:

t = 1/k * ln([A]t/[A]0)

## The integrated rate law and zero-order reactions

The integrated rate law is a differential equation that describes the changes in the concentration of a reactant with time during a chemical reaction. It can be used to determine the order of the reaction, the rate constant, and the half-life of the reaction.

The integrated rate law is only valid for reactions that are first-order or zeroth-order. First-order reactions are those that involve only one reactant, and zeroth-order reactions are those in which the concentration of the reactant does not change with time.

To determine the order of a reaction, you need to know the rate law. The rate law is an equation that describes how the rate of a reaction varies with the concentrations of each reactant.

The rate law for a first-order reaction is:

rate = k[A]

where k is the rate constant and [A] is the concentration of reactant A. The units for k are usually mol/L/s ormol/dm^3/s.mol/L/s means that when [A] is doubled, the rate doubles;mol/dm^3/s means that when [A] is doubled, the rate quadruples.

The integrated rate law for a first-order reaction is:

ln[A]t = -kt + ln[A]0 OR 1n[A] = -kt + 1n[A]0

where [A]t is the concentration at time t, [A]0 is the initial concentration, and k is the rate constant.

## The integrated rate law and pseudo-first-order reactions

In order to understand the integrated rate law, it is necessary to have a basic understanding of reaction order and how this influences the relationship between reactant concentration and time. The terms “first-order” and “second-order” are used to describe the relationship between reactant concentration and time for a chemical reaction. The order of a reaction is determined by experiments which measure the changes in reactant concentrations or product concentrations over time.

A first-order reaction is one in which the reactant concentration decreases by a constant percentage during each time period. The integrated rate law for a first-order reaction is:

[A]t= [A]0 x e-kt

where:

[A]t is the concentration of A at time t

[A]0 is the initial concentration of A

k is the first order rate constant

e is the natural logarithm base (2.71828)

t is time

The integrated rate law can be used to determine the half-life of a first-order reaction, which is defined as the time it takes for the reactant concentration to decrease by half. The half-life can be calculated from the equation:

t1/2 = 0.693/k

where:

t1/2 is the half-life

k is the first order rate constant

## The integrated rate law and reactions with multiple steps

In a chemical reaction, the integrated rate law is used to determine the concentration of a reactant at a specific time during the reaction. This law takes into account the fact that reactions can have multiple steps, and it is used to calculate the overall rate of the reaction.

The integrated rate law is derived from the rate laws for each individual step in the reaction. In a reaction with two steps, for example, the first step might be slower than the second step. The overall rate of the reaction would be determined by the slowest step. The integrated rate law takes this into account and provides a way to calculate the concentration of a reactant at any given time.

To use the integrated rate law, you need to know the order of the reaction and the activation energy for each step. The order of a reaction is determined by experiments, and it tells you how many reactants are involved in each step. The activation energy is a measure of how difficult it is for the reactants to overcome their attractions and form new bonds. It is usually expressed in terms of kilojoules per mole (kJ/mol).

Once you have these values, you can plug them into the equation:

[A]t = [A]0 e-kt

where [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration of reactant A, k is the overall rate constant for the reaction, and t is time.

This equation can be solved for any one of its variables if you know the values of all of the others. For example, if you know [A]0, k, and t, you can solve for [A]t. Or if you know [A], k, and [A]0, you can solve for t. This makes it possible to use the integrated rate law to answer questions about concentrations and times during a chemical reaction.