# Rate Equations - The Rate Constant

Chemical reactions occur at different rates depending on a variety of factors such as temperature, pressure, and concentration. The study of these rates is known as chemical kinetics, and one of the fundamental concepts in this field is the rate equation.

The rate equation is an expression that relates the rate of a chemical reaction to the concentration of reactants. The general form of the rate equation is:

rate = k[A]^m[B]^n

where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the orders of the reaction with respect to reactants A and B, respectively.

## The Rate Constant, k

The rate constant, k, is a proportionality constant that relates the rate of a reaction to the concentration of reactants. It is specific to a particular reaction and is independent of the initial concentrations of the reactants. In other words, k is a constant that remains the same for a given reaction, regardless of the initial concentrations of the reactants.

The rate constant is influenced by many factors such as temperature, pressure, and the presence of catalysts.

### How Rate Constant is Related to Rate of Reaction

The **rate constant**, **k**, is a number that connects the concentration of reactants in a reaction to the rate of that reaction. The rate constant is different for every reaction. The larger the value of ** k**, the faster the rate of reaction. The value of

**can be determined by**

*k***substituting**in the values of

**rate**and

**concentration of reactants**into the rate equation, and then rearranging.

The Arrhenius equation is a mathematical expression that relates the rate constant to temperature:

k = A * e^(-Ea/RT)

where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Therefore, the rate constant k increases with an increase in temperature, as the activation energy required for the reaction to occur decreases.

## The Units of the Rate Constant, k

The units of ** k** depend on the overall order of the reaction.

**Zero Order Reaction**

A zero order reaction, **rate = k**, the units of rate are **mol dm−³ s−¹**

*First Order Reaction*

First order – A first order reaction,** rate = k[A]**.

Rearrange the equation above, so we have **k = rate / [A]**

We know the **units of rate** are mol dm−³ s−¹ and the units of **concentration** are mol dm−³.

We now can cancel down to find the units of **k**.

Therefore the units of **k** for a **first order reaction** are **s−¹**.

### Second Order Reaction

A second order reaction, **rate = k[A][B]**

Rearrange the equation above so we have **k = rate / [A][B]**

Again, cancel down to find the units of **k**.

Therefore the units of k for a **second order reaction** are **mol−¹dm³s−¹**

### Third Order Reaction

A third order reaction, **rate = k[A][B]²**

Rearrange the equation above so we have** k = rate / [A][B]²**

Again, cancel down to find the units of **k**.

Therefore the units of **k** for a **third order reaction** are **mol−²dm ^{6}s−¹**

*Worked example:*

*Results to show the initial rate of reaction with initial concentration of CH3CHO*

*Calculate the value of the rate constant and its units.*

*The rate equation is: Rate = *

*Answer:*

*Substitute the value of rate and concentration into the rate equation.*

*To find the units, write the expression for k without any numbers, just with the units. Cancel common terms.*

## Importance of the Rate Constant

The rate constant is a crucial parameter in the rate equation, as it reflects the probability of the reactants colliding in the correct orientation and with sufficient energy to form the products. A larger rate constant corresponds to a faster reaction rate, while a smaller rate constant corresponds to a slower reaction rate.

By measuring the rate constant k, we can determine the order of the reaction with respect to each reactant and also predict the rate of the reaction under different conditions such as temperature and pressure.

## Rate Law

Rate law is a mathematical description of the relationship between the rate of a chemical reaction, its equilibrium constant and the concentrations of reactants. It is represented by an equation that relates these variables.

The rate law can be used to determine the rates at which reactions occur under different conditions.

## Reaction Mechanism

A reaction mechanism is a step-by-step description of how a chemical reaction proceeds. It shows how bonds are broken and formed, giving you an idea of what's happening at each stage in the process. Reaction mechanisms can be determined experimentally by studying the reactants and products under different conditions, or they can be predicted using quantum mechanics.

## Catalysts

A catalyst is a substance that speeds up the rate of a chemical reaction without being consumed by it. In other words, catalysts help reactions occur faster without adding any extra energy to the system.

The reason for this is simple: it takes energy to break bonds between atoms and molecules in order for them to combine into different compounds or elements (like when you burn wood). This means that if you want your reaction to happen faster, you need some way of reducing its activation energy so it can occur more easily and quickly--and that's where catalysts come in!

## Temperature and Concentration

Temperature and concentration are two factors that can be used to control the rate of a reaction.

The Arrhenius equation shows us how temperature affects the rate constant, k:

If T is raised by 10C, then k increases by about 2x10^-5 mol/s per degree Celsius (or 1/T). This means that if you double your temperature from 25C to 50C, then you will get four times as much product formed over time!

The Boltzmann distribution shows us how many particles there are at each energy level in an isolated system (like our reaction). As we increase T from 25C to 50C, we see more particles with higher energies and fewer with lower energies; this means that there will be more collisions between reactants or products at higher temperatures because they're moving faster relative to each other

## Enzymes

Enzymes are proteins that act as catalysts for chemical reactions. They speed up reactions by lowering the energy required to break bonds and form new ones.

For example, an enzyme called glucose-6-phosphate dehydrogenase converts glucose into 6-phosphogluconolactone. This reaction requires an input of energy in order to form a covalent bond between carbon and oxygen atoms (a double bond), so it's not spontaneous at room temperature. However, if we add the enzyme glucose-6-phosphate dehydrogenase to our system, then this reaction will proceed much more quickly because now there's less energy needed to break those double bonds!

## FAQs

**What is a rate equation?**

A rate equation is a mathematical expression that describes the rate of a chemical reaction as a function of the concentration of the reactants.

**What is the rate constant?**

The rate constant, also known as the reaction rate constant, is a measure of the speed of a chemical reaction. It is expressed as a constant value in units of reciprocal time (e.g., 1/seconds).

**How is the rate constant determined?**

The rate constant is determined by measuring the reaction rate at various concentrations of reactants and fitting the data to a rate equation.

**How does the rate constant relate to the rate of a chemical reaction?**

The rate constant is related to the rate of a chemical reaction by the rate equation. The higher the value of the rate constant, the faster the reaction will proceed.

**What factors can affect the value of the rate constant?**

The value of the rate constant can be affected by factors such as temperature, pressure, and the presence of catalysts or inhibitors.

**Can the rate constant change during a chemical reaction?**

Yes, the rate constant can change during a chemical reaction, for example, due to changes in temperature or the presence of catalysts or inhibitors.

**How is the rate constant used in A-Level Chemistry?**

In A-Level Chemistry, the rate constant is used to describe the speed of chemical reactions and to understand the factors that influence the reaction rate.

**What is the importance of understanding the rate constant in A-Level Chemistry?**

Understanding the rate constant is important in A-Level Chemistry as it provides a quantitative measure of the reaction rate and helps to predict the rate of chemical reactions under different conditions. This information is useful in understanding the mechanism of chemical reactions and in the design of chemical processes.