2.2.1

# Rate Equations (A2 Only)

Reading Rate Graphs

Reading Rate Graphs

Reaction rates can be measured over time. We plot this data on graphs, and you need to be able to read them.

Definition of a rate

Definition of a rate

- A rate of reaction is defined as the change in concentration of a reactant or product over time.
- This means that if you plot concentration against time, the rate is the gradient of the graph.

A simple graph

A simple graph

- The above graph is a straight line graph showing the concentration against time.
- To calculate the gradient of the graph (and the rate) you find the change in concentration divided by the change in time.
- In practice: pick two points and read off the x and y values.
- Calculate the differences in concentration values and the time, values and then divide the one by the other.

Curved graphs

Curved graphs

- Not all reaction rates are constant - a reaction may slow down or speed up with time.
- For reactions like this, you get a curved graph.

- You can calculate the rate at any point in time by calculating the gradient of a point on the graph.
- To do this, you need to draw a tangent on the graph at this point.

Drawing tangents

Drawing tangents

- A tangent is a straight line which just touches the curve in one place.
- To draw the tangent, choose your point and draw a straight line through it. You want to have an equal distance to the curve from the line on each side of the point.
- An example is above.

Rate Equations

Rate Equations

You can calculate rates of reactions by finding their rate equations. These link the concentration of each reactant to the rate of the equation.

Physical basis

Physical basis

- Reactions happen when molecules collide into one another.
- In a reaction between molecule A and B, the rate will be proportional to the number of collisions between A and B.

- If you double the concentration of B, you should have double the collisions between A and B.
- So, you would expect the reaction rate to double.

- In reality, this is an over-simplification because you have multiple steps in most reactions, which may or may not involve each molecule.

The rate equation

The rate equation

- A rate equation is always written of the form:
- Rate = k × [A]
^{m}[B]^{n}

- Rate = k × [A]
- k is called the rate constant.
- The numbers m and n tell you how the rate depends on the reactants.
- They are called the order of the reaction with respect to each reactant.

The order of reaction

The order of reaction

- Just as we define an order for the reactants, we define an overall order for the reaction.
- The overall order is given by m + n.
- You very rarely get any value above 2 for an order with respect to a reactant, or less than zero.

The rate constant

The rate constant

- The rate constant k has a few key features:
- It’s temperature dependent.
- It has different units for different reactions.

- The units of the reaction rate have to be concentration over time.
- But the units of the product of the reactants are never that, so you need to assign units to k to sort it out.
- The larger the rate constant, the faster the reaction.

Calculations of Rate Equations

Calculations of Rate Equations

You need to be able to do a whole bunch of calculations with rate equations.

Calculating the rate of reactions

Calculating the rate of reactions

- The rate of a reaction can be calculated if you know its rate constant, the reactant concentrations, and the order of the reaction with respect to each reactant.
- E.g. if a reaction obeys the equation:
- Rate = k[A][B], where the rate constant is 0.5dm
^{3}mol^{-1}t^{-1}, and the reactant concentrations are both 2moldm^{-3} - The rate is 2moldm
^{-3}× 2moldm^{-3}× 0.5dm^{3}mol^{-1}t^{-1}= 2moldm^{-3}t^{-1}

- Rate = k[A][B], where the rate constant is 0.5dm

Calculating the rate constant

Calculating the rate constant

- You can be given a rate equation and told to calculate the rate constant given some concentration data.
- E.g. the rate equation for the production of I-Cl is:
Rate = k[I
_{2}]^{1}[Cl_{2}]^{1}

- E.g. the rate equation for the production of I-Cl is:
Rate = k[I
- Given that the concentrations of I
_{2}and Cl_{2}are 1moldm^{-3}, and the rate of reaction is 40moldm^{-3}t^{-1}, what is the value of k?- k = 40moldm
^{-3}t^{-1}÷ (1moldm^{-3})^{2}= 40mol^{-1}dm^{3}t^{-1}

- k = 40moldm

1Physical Chemistry

1.1Atomic Structure

1.1.1Fundamental Particles

1.1.2Isotopes & Mass Number

1.1.3Mass Spectrometry

1.1.4Electron Shells, Sub-Shells & Orbitals

1.1.5Electron Configuration

1.1.6Ionisation Energy

1.1.7Factors Affecting Ionisation Energies

1.1.8Trends of Ionisation

1.1.9Specific Impacts on Ionisation Energies

1.1.10End of Topic Test - Atomic Structure

1.1.11A-A* (AO3/4) - Atomic Structure

1.2Amount of Substance

1.3Bonding

1.3.1Ionic Bonding

1.3.2Covalent & Dative Bonding

1.3.3Carbon Structures

1.3.4Metallic Bonding

1.3.5Physical Properties

1.3.6Shapes of Molecules

1.3.7Polarity

1.3.8Intermolecular Forces

1.3.9Intermolecular Forces 2

1.3.10End of Topic Test - Bonding

1.3.11Exam-Style Question - Shape of Molecules

1.3.12A-A* (AO3/4) - Bonding

1.4Energetics

1.5Kinetics

1.6Equilibria

2Physical Chemistry 2 (A2 Only)

2.1Thermodynamics (A2 Only)

2.2Rate Equations (A2 Only)

2.3The Equilibrium Constant Kp (A2 Only)

2.4Electrochemical Cells (A2 Only)

2.5Acids & Bases (A2 Only)

2.5.1Brønsted-Lowry Acids & Bases (A2 Only)

2.5.2pH (A2 Only)

2.5.3The Ionic Product of Water (A2 Only)

2.5.4Weak Acids & Bases (A2 Only)

2.5.5pH Curves & Titrations (A2 Only)

2.5.6pH Curves & Titrations 2 (A2 Only)

2.5.7Buffer Solutions (A2 Only)

2.5.8End of Topic Test - Acids & Bases

2.5.9Exam-Style Question - Weak Acids

2.5.10A-A* (AO3/4) - Acids & Bases

3Inorganic Chemistry

3.1Periodicity & Trends

4Inorganic Chemistry 2 (A2 Only)

4.1Period 3 (A2 Only)

4.2Transition Metals (A2 Only)

4.2.1General Properties (A2 Only)

4.2.2Substitution Reactions (A2 Only)

4.2.3Shapes of Complex Ions (A2 Only)

4.2.4Colours of Ions (A2 Only)

4.2.5Variable Oxidation States (A2 Only)

4.2.6Titrations (A2 Only)

4.2.7Homogeneous Catalysts (A2 Only)

4.2.8Heterogeneous Catalysts (A2 Only)

4.2.9End of Topic Test - Transition Metals

4.2.10A-A* (AO3/4) - Transition Metals

4.3Reactions of Ions in Aqueous Solutions (A2 Only)

5Organic Chemistry 1

5.1Introduction

5.2Alkanes

5.3Halogenoalkanes

5.4Alkenes

5.5Alcohols

5.6Organic Analysis

5.7A-A* (AO3/4) - Organic 1

6Organic Chemistry 2 (A2 Only)

6.1Optical Isomerism (A2 Only)

6.2Aldehydes & Ketones (A2 Only)

6.3Carboxylic Acids & Esters (A2 Only)

6.4Aromatic Chemistry (A2 Only)

6.5Amines (A2 Only)

6.6Polymers (A2 Only)

6.7Biological Organic (A2 Only)

6.8Organic Synthesis (A2 Only)

6.9NMR Spectroscopy (A2 Only)

6.10Chromatography (A2 Only)

6.11A-A* (AO3/4) - Organic 2

Jump to other topics

1Physical Chemistry

1.1Atomic Structure

1.1.1Fundamental Particles

1.1.2Isotopes & Mass Number

1.1.3Mass Spectrometry

1.1.4Electron Shells, Sub-Shells & Orbitals

1.1.5Electron Configuration

1.1.6Ionisation Energy

1.1.7Factors Affecting Ionisation Energies

1.1.8Trends of Ionisation

1.1.9Specific Impacts on Ionisation Energies

1.1.10End of Topic Test - Atomic Structure

1.1.11A-A* (AO3/4) - Atomic Structure

1.2Amount of Substance

1.3Bonding

1.3.1Ionic Bonding

1.3.2Covalent & Dative Bonding

1.3.3Carbon Structures

1.3.4Metallic Bonding

1.3.5Physical Properties

1.3.6Shapes of Molecules

1.3.7Polarity

1.3.8Intermolecular Forces

1.3.9Intermolecular Forces 2

1.3.10End of Topic Test - Bonding

1.3.11Exam-Style Question - Shape of Molecules

1.3.12A-A* (AO3/4) - Bonding

1.4Energetics

1.5Kinetics

1.6Equilibria

2Physical Chemistry 2 (A2 Only)

2.1Thermodynamics (A2 Only)

2.2Rate Equations (A2 Only)

2.3The Equilibrium Constant Kp (A2 Only)

2.4Electrochemical Cells (A2 Only)

2.5Acids & Bases (A2 Only)

2.5.1Brønsted-Lowry Acids & Bases (A2 Only)

2.5.2pH (A2 Only)

2.5.3The Ionic Product of Water (A2 Only)

2.5.4Weak Acids & Bases (A2 Only)

2.5.5pH Curves & Titrations (A2 Only)

2.5.6pH Curves & Titrations 2 (A2 Only)

2.5.7Buffer Solutions (A2 Only)

2.5.8End of Topic Test - Acids & Bases

2.5.9Exam-Style Question - Weak Acids

2.5.10A-A* (AO3/4) - Acids & Bases

3Inorganic Chemistry

3.1Periodicity & Trends

4Inorganic Chemistry 2 (A2 Only)

4.1Period 3 (A2 Only)

4.2Transition Metals (A2 Only)

4.2.1General Properties (A2 Only)

4.2.2Substitution Reactions (A2 Only)

4.2.3Shapes of Complex Ions (A2 Only)

4.2.4Colours of Ions (A2 Only)

4.2.5Variable Oxidation States (A2 Only)

4.2.6Titrations (A2 Only)

4.2.7Homogeneous Catalysts (A2 Only)

4.2.8Heterogeneous Catalysts (A2 Only)

4.2.9End of Topic Test - Transition Metals

4.2.10A-A* (AO3/4) - Transition Metals

4.3Reactions of Ions in Aqueous Solutions (A2 Only)

5Organic Chemistry 1

5.1Introduction

5.2Alkanes

5.3Halogenoalkanes

5.4Alkenes

5.5Alcohols

5.6Organic Analysis

5.7A-A* (AO3/4) - Organic 1

6Organic Chemistry 2 (A2 Only)

6.1Optical Isomerism (A2 Only)

6.2Aldehydes & Ketones (A2 Only)

6.3Carboxylic Acids & Esters (A2 Only)

6.4Aromatic Chemistry (A2 Only)

6.5Amines (A2 Only)

6.6Polymers (A2 Only)

6.7Biological Organic (A2 Only)

6.8Organic Synthesis (A2 Only)

6.9NMR Spectroscopy (A2 Only)

6.10Chromatography (A2 Only)

6.11A-A* (AO3/4) - Organic 2

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