Rate Equations

Chemical reactions are processes in which a set of reactants are converted into products as a result of changes to their structures. These structural changes can happen at different speeds, similar to how race cars can travel at different speeds. Just like how it's important to understand how the speed of a race car can be affected, understanding how the speed of chemical changes can be affected is an important part of physical chemistry.

Explore our app and discover over 50 million learning materials for free.

- Chemical Analysis
- Chemical Reactions
- Chemistry Branches
- Inorganic Chemistry
- Ionic and Molecular Compounds
- Kinetics
- Making Measurements
- Nuclear Chemistry
- Organic Chemistry
- Physical Chemistry
- Absolute Entropy And Entropy Change
- Acid Dissociation Constant
- Acid-Base Indicators
- Acid-Base Reactions and Buffers
- Acids and Bases
- Alkali Metals
- Allotropes of Carbon
- Amorphous Polymer
- Amount of Substance
- Application of Le Chatelier's Principle
- Arrhenius Equation
- Arrhenius Theory
- Atom Economy
- Atomic Structure
- Autoionization of Water
- Avogadro Constant
- Avogadro's Number and the Mole
- Beer-Lambert Law
- Bond Enthalpy
- Bonding
- Born Haber Cycles
- Born-Haber Cycles Calculations
- Boyle's Law
- Brønsted-Lowry Acids and Bases
- Buffer Capacity
- Buffer Solutions
- Buffers
- Buffers Preparation
- Calculating Enthalpy Change
- Calculating Equilibrium Constant
- Calorimetry
- Carbon Structures
- Cell Potential
- Cell Potential and Free Energy
- Chalcogens
- Chemical Calculations
- Chemical Equations
- Chemical Equilibrium
- Chemical Thermodynamics
- Closed Systems
- Colligative Properties
- Collision Theory
- Common-Ion Effect
- Composite Materials
- Composition of Mixture
- Constant Pressure Calorimetry
- Constant Volume Calorimetry
- Coordination Compounds
- Coupling Reactions
- Covalent Bond
- Covalent Network Solid
- Crystalline Polymer
- De Broglie Wavelength
- Determining Rate Constant
- Deviation From Ideal Gas Law
- Diagonal Relationship
- Diamond
- Dilution
- Dipole Chemistry
- Dipole Moment
- Dissociation Constant
- Distillation
- Dynamic Equilibrium
- Electric Fields Chemistry
- Electrochemical Cell
- Electrochemical Series
- Electrochemistry
- Electrode Potential
- Electrolysis
- Electrolytes
- Electromagnetic Spectrum
- Electron Affinity
- Electron Configuration
- Electron Shells
- Electronegativity
- Electronic Transitions
- Elemental Analysis
- Elemental Composition of Pure Substances
- Empirical and Molecular Formula
- Endothermic and Exothermic Processes
- Energetics
- Energy Diagrams
- Enthalpy Changes
- Enthalpy For Phase Changes
- Enthalpy of Formation
- Enthalpy of Reaction
- Enthalpy of Solution and Hydration
- Entropy
- Entropy Change
- Equilibrium Concentrations
- Equilibrium Constant Kp
- Equilibrium Constants
- Examples of Covalent Bonding
- Factors Affecting Reaction Rates
- Finding Ka
- Free Energy
- Free Energy Of Dissolution
- Free Energy and Equilibrium
- Free Energy of Formation
- Fullerenes
- Fundamental Particles
- Galvanic and Electrolytic Cells
- Gas Constant
- Gas Solubility
- Gay Lussacs Law
- Giant Covalent Structures
- Graham's Law
- Graphite
- Ground State
- Group 3A
- Group 4A
- Group 5A
- Half Equations
- Heating Curve for Water
- Heisenberg Uncertainty Principle
- Henderson-Hasselbalch Equation
- Hess' Law
- Hybrid Orbitals
- Hydrogen Bonds
- Ideal Gas Law
- Ideal and Real Gases
- Intermolecular Forces
- Introduction to Acids and Bases
- Ion And Atom Photoelectron Spectroscopy
- Ion dipole Forces
- Ionic Bonding
- Ionic Product of Water
- Ionic Solids
- Ionisation Energy
- Ions: Anions and Cations
- Isotopes
- Kinetic Molecular Theory
- Lattice Structures
- Law of Definite Proportions
- Le Chatelier's Principle
- Lewis Acid and Bases
- London Dispersion Forces
- Magnitude Of Equilibrium Constant
- Mass Spectrometry
- Mass Spectrometry of Elements
- Maxwell-Boltzmann Distribution
- Measuring EMF
- Mechanisms of Chemical Bonding
- Melting and Boiling Point
- Metallic Bonding
- Metallic Solids
- Metals Non-Metals and Metalloids
- Mixtures and Solutions
- Molar Mass Calculations
- Molarity
- Molecular Orbital Theory
- Molecular Solid
- Molecular Structures of Acids and Bases
- Moles and Molar Mass
- Nanoparticles
- Neutralisation Reaction
- Oxidation Number
- Partial Pressure
- Particulate Model
- Partition Coefficient
- Percentage Yield
- Periodic Table Organization
- Phase Changes
- Phase Diagram of Water
- Photoelectric Effect
- Photoelectron Spectroscopy
- Physical Properties
- Polarity
- Polyatomic Ions
- Polyprotic Acid Titration
- Prediction of Element Properties Based on Periodic Trends
- Pressure and Density
- Properties Of Equilibrium Constant
- Properties of Buffers
- Properties of Solids
- Properties of Water
- Quantitative Electrolysis
- Quantum Energy
- Quantum Numbers
- RICE Tables
- Rate Equations
- Rate of Reaction and Temperature
- Reacting Masses
- Reaction Quotient
- Reaction Quotient And Le Chateliers Principle
- Real Gas
- Redox
- Relative Atomic Mass
- Representations of Equilibrium
- Reversible Reaction
- SI units chemistry
- Saturated Unsaturated and Supersaturated
- Shapes of Molecules
- Shielding Effect
- Simple Molecules
- Solids Liquids and Gases
- Solubility
- Solubility Curve
- Solubility Equilibria
- Solubility Product
- Solubility Product Calculations
- Solutes Solvents and Solutions
- Solution Representations
- Solutions and Mixtures
- Specific Heat
- Spectroscopy
- Standard Potential
- States of Matter
- Stoichiometry In Reactions
- Strength of Intermolecular Forces
- The Laws of Thermodynamics
- The Molar Volume of a Gas
- Thermodynamically Favored
- Trends in Ionic Charge
- Trends in Ionisation Energy
- Types of Mixtures
- VSEPR Theory
- Valence Electrons
- Van der Waals Forces
- Vapor Pressure
- Water in Chemical Reactions
- Wave Mechanical Model
- Weak Acid and Base Equilibria
- Weak Acids and Bases
- Writing Chemical Formulae
- pH
- pH Change
- pH Curves and Titrations
- pH Scale
- pH and Solubility
- pH and pKa
- pH and pOH
- The Earths Atmosphere

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenChemical reactions are processes in which a set of reactants are converted into products as a result of changes to their structures. These structural changes can happen at different speeds, similar to how race cars can travel at different speeds. Just like how it's important to understand how the speed of a race car can be affected, understanding how the speed of chemical changes can be affected is an important part of physical chemistry.

The **rate equation** is an expression that links the rate of a reaction to the concentration of the species involved.

- We will be looking at the rate equation.
- We'll see what it tells us about the rate of a reaction.
- Finally, we'll explore the rate constant and reaction orders, and we'll briefly touch on methods used to determine the rate equation.

The rate of a reaction is how quickly a reaction occurs. But what does that mean and what does it tell us? Well, one way of looking at it is to think about how much product is made in a period of time, which will depend on how much reactant is used up. In essence, we can say that the rate of a reaction is the speed at which reactants are converted into products.

The **rate of reaction** is the change in concentration of reactants or products over time. It is typically measured in **mol dm ^{-3} s^{-1}**.

To calculate the rate of a reaction, we need to measure the **change in the amount of reactant/product** from the start of the reaction to the end.

We define the** rate of a reaction** as a measure of how much product is formed, or how much reactant is used, over a period of time.

We can measure this by observing things like colour change, pH change, volume of gas produced, or change in mass of a solid reactant. You should then be able to convert your data values into figures for concentration. This data is plotted on a line graph, with time on the x-axis and concentration on the y-axis. From the graph, we can find a value for the rate of reaction by working out the line's gradient. We either calculate an overall rate of reaction or an instantaneous rate of reaction. Both use the following equation:

$\mathrm{rate}\mathrm{of}\mathrm{reaction}=\frac{\mathrm{change}\mathrm{in}\mathrm{concentration}}{\mathrm{time}\mathrm{taken}}$

Calculating an overall rate of reaction is fairly straightforward. You divide the overall change in concentration of a reactant or product by the time taken. For a graph of concentration against time, this means dividing the change in y-values by the change in x-values. Here's an example.

Calculate the overall rate of reaction for the following graph.

To find the overall rate of reaction, we divide the change in concentration by the time taken.

It doesn't matter whether you measure the concentration of a product or reactant - both will give you a valid answer.

Here, the concentration starts at 40 mol dm^{-3} and ends at 8 mol dm^{-3}. This is a change of 40 - 8 = 32 mol dm^{-3}. The reaction takes 200 seconds. The rate of reaction is therefore $\frac{32}{200}=0.16\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}$.

Sometimes, finding an overall rate of reaction isn't that useful. You might instead want to know how the rate of reaction changes over time. To do this, you calculate** instantaneous rates of reaction**. This involves drawing a tangent to the curve at a particular point and finding its gradient. Again, this is given by the change in concentration divided by the time taken - in other words, the change in y-values divided by the change in x-values.

Calculate the instantaneous rate of reaction for the following graph at 60 seconds.

We first need to find the 60-second mark on the curve. We draw a tangent to the curve at this point.

Remember that a tangent is a straight line that *just* touches the curve at a specified point.

Next, we calculate the gradient of this tangent by dividing the change in concentration by the time taken. You do this by turning the tangent into a right-angled triangle.

Here, we can see from our right-angled triangle that the concentration starts at 22 mol dm^{-3} and ends at 6 mol dm^{-3}. This is an overall change of 16 mol dm^{-3}. This change in concentration takes place between 20 and 120 seconds, meaning it takes 100 seconds in total. The instantaneous rate of reaction is therefore $\frac{16}{100}=0.16\mathrm{mol}{\mathrm{dm}}^{-3}{\mathrm{s}}^{-1}$

Let's look at something different: the rate equation. The rate equation in chemistry is a formula that we can use to find the rate of a reaction using the concentration of species involved in the reaction. Here's what it looks like:

At first glance it certainly looks confusing, but once you understand what's going on it isn't all that bad.

- k is the rate constant.
- The letters A and B in the rate equation are used to represent species involved in the reaction. These could be reactants or catalysts.
- The square brackets around the letters represent concentration. So, [A] is used to show the concentration of species A.
- The letters m and n represent the
*order*of the reaction with respect to a certain species. They show the power that the concentration of that species is raised to in the rate equation. Overall, [A]^{m}represents the concentration of A, raised to the power of m. This means that A has the order m.

**k is the rate constant**. It is used in the rate equation to link the concentrations of certain species to the rate of that reaction. The value of k changes depending on the reaction and reaction conditions. However, k is always **constant for a certain reaction at a particular temperature**. If you were to carry out the exact same reaction at different temperatures, k would change, but if you carried it out at the same temperature, k would stay the same: after all, it is a constant!

To learn more about how the rate constant relates to temperature, read **The Arrhenius Equation**. And if you want to find out how to calculate the rate constant, alongside its units, head over to **Determining Rate Constant**.

In chemical reactions, reactants and catalysts (if there are any) have an **order of reaction****. **The sum of the individual orders of species in a reaction equals the overall order of the equation.

In the rate equation, the order of a reaction with respect to a species is shown using a power. For example, in the rate equation we looked at above, the order of A is represented by the letter m. The order of a reaction with respect to a species tells us how the concentration of that particular species affects the reaction rate. Some species don't affect the rate whatsoever, while other species affect it dramatically.

Any non-negative number can be an order, and species can also have fractional orders like 5/2. But for the purpose of your exams, you only need to know about zero, first and second-order reactants.

**The concentration of a zero-order reactant doesn't affect the rate of reaction.** If you double its concentration, the rate stays the same. This is because 2^{0} = 1. Because they have no effect on the rate of reaction, zero-order reactants don't appear in the rate equation.

**The concentration of first-order reactants is directly proportional to the rate of reaction**. If you double the concentration of a first-order reactant, the rate of reaction also doubles. This is because 2^{1} = 2.

If a reactant is first-order, it appears in the rate equation raised to the power of 1. However, we don't tend to write the number 1 because raising something to the power of 1 has no effect on its value. You'll see first-order reactants in the rate equation as [A], where A represents the species.

**The concentration of second-order reactants has an exponential effect on the rate of reaction**. Doubling the concentration of a second-order reactant causes the rate of reaction to quadruple. This is because 2^{2} = 4.

If a reactant is second-order then we put it in the rate equation raised to the power of 2; in other words, squared. You'll see it in the rate equation as [A]^{2}**.**

The overall **order of a reaction** is the **sum of all the individual reactant orders**. Remember that the order of a reactant is the power that it is raised to in the rate equation. If you're ever asked to find the overall order of reaction, simply add together all of the powers present in the equation and you'll reach your final answer.

Understanding orders of reaction is a bit tricky, so let's look at an example to help you understand.

**A reaction has the chemical equation and rate equation shown below.**

** $\mathrm{A}+\mathrm{B}+\mathrm{C}\to \mathrm{D}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{rate}=\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^{2}$**

**Describe the effect of doubling the concentrations of A, B, and C.**

First of all, looking at the rate equation, we can see that the only species present are A and B. C does not appear at all. It must therefore be zero-order. Hence, doubling the concentration of C will have no effect on the rate of reaction.

On the other hand, A does appear in the rate equation. It looks like [A] isn't raised to any power, but as we learnt above, [A] is the same as saying [A]^{1}. A is therefore first-order. Doubling the concentration of A will cause the rate of reaction to double, because 2^{1} = 2.

B also appears in the rate equation. It is raised to the power of 2, meaning that it is second-order. Doubling the concentration of B will cause the rate of reaction to quadruple, because 2^{2} = 4.

There are a few different methods we can use to determine the rate equation for a reaction. The basic principles come down to determining the species involved in the rate equation and then finding each of their orders. The main methods for doing this are:

- The initial rates method.
- Using rate-concentration graphs.
- Finding first-order reactants from their half-life.
- Inspecting the reaction mechanism.

We cover these methods in much more detail in **Determining Reaction Order**, but we'll explore them briefly now.

The **initial rates method** involves measuring the rate of the same reaction over several experiments, each with different starting concentrations of a particular reactant. This method allows us to see numerically how the concentration of the reactant affects the rate of the reaction. We do this for each reactant, and can use the information to determine the reactant's order.

Earlier in the article, we looked at how you use graphs showing concentration of a species against time to calculate rate of reaction at a specific instant. You can then take the values for instantaneous rate of reaction and plot them against concentration to make a **rate-concentration graph**. These take specific shapes, depending on the order of the species involved.

- A horizontal straight line shows that the rate of reaction is unaffected by the concentration of the species. The species is therefore zero-order.
- A sloping straight line through the origin shows that the rate is directly proportional to the concentration of the species. The species is therefore first-order.
- A curved line through the origin shows that the rate is exponentially proportional to the concentration of the species. The species is second-order or higher.

The **half-life**, ${\mathrm{t}}_{1/2}$, of a reactant is the time it takes for the concentration of that reactant to become half of what it was where you started measuring from. There's an interesting feature of first-order reactants: they have a **constant half-life.** This means that it takes the same amount of time to get from, say, a concentration of 1.0 to a concentration of 0.5 mol dm^{-3}, as it does to get from a concentration of 0.8 to 0.4 mol dm^{-3}. In both cases, the concentration has halved.

You can measure half-life using concentration-time graphs. Pick any point on the graph and look at the concentration for that time value. Then, see how long it takes to halve the concentration. Repeat this again to find multiple half-lives for a species. If all of the half-lives are the same, the species is first-order.

The half-life of a first-order reactant relates to the rate constant, k, using the following equation:

$\mathrm{k}=\frac{\mathrm{ln}\left(2\right)}{{\mathrm{t}}_{1/2}}$

This means that once you know the half-life of a first-order reactant, you can easily find k.

Reactions can have mechanisms with one step or multiple steps. Each step happens at a different speed, and the rate of reaction is determined by the **slowest step**. We call the slowest step in a reaction the **rate-determining step**, and it gives us an idea of what the rate equation is likely to look like. This is because the rate equation is only made up of reacting species found in the steps *up to and including* the rate-determining step. The number of moles of each species relates to its order.

If you know the reaction mechanism and the rate-determining step of a reaction, you can predict the rate equation!

The

**rate of a chemical reaction**is the change in concentration of reactants or products over time.Rate of reaction can be represented by a

**rate equation**. Rate equations are composed of a**rate constant (****k)**, and reactant concentrations raised to the power of their respective**order**.Rate constants are constant for a particular reaction at a certain temperature.

The

**order of a reaction with respect to a species**tells us how the rate of reaction depends on the concentration of that species.The concentration of zero-order reactants has no effect on the rate of reaction.

The concentration of first-order reactants is directly proportional to the rate of reaction.

The concentration of second-order reactants has an exponential effect on the rate of reaction.

The rate equation can be determined using the

**initial rates method**, by identifying the shapes of graphs, by calculating**half-lives**, and by inspecting the reaction mechanism.

^{m} [B]^{n}. The rate constant, k, is a value that is always constant for a particular reaction at a particular temperature. [A] represents the concentration of A, whilst the letter m represents the order of the reaction with respect to A. Overall, [A]^{m} means the concentration of A, raised to the power of m. To write a rate equation, you work out the rate constant and the orders of reaction with respect to each species involved, and write them in the form given above.

Why is the Arrhenius equation useful in chemistry?

It allows us to relate the temperature of a reaction with its rate

What does the letter A represent in the Arrhenius equation?

A is the Arrhenius constant

What information about a reaction can the value of e^{x} give us in the Arrhenius equation?

the number of reacting particles that have enough energy to react

Rearrange the Arrhenius equation into its logarithmic form.

ln(k) = ln(A) - E_{a}/RT

Given a graph showing an Arrhenius plot for a chemical reaction, how could you use the plotted data to determine activation energy and the rate constant for that reaction?

The activation energy would be equal to the gradient of the line.

The rate constant would be equal to the y-intercept.

When drawing an Arrhenius plot, what would you label your axis?

The *x-axis* would be *1/T*

The *y-axis* would be* l**n(K)*

Already have an account? Log in

Open in App
More about Rate Equations

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in

Already have an account? Log in

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up with Email

Already have an account? Log in