Kinetics: How Fast Do Reactions Go?
Welcome to Kinetics! In chemistry, thermodynamics tells us if a reaction can happen, but kinetics tells us how fast it actually happens. From the slow rusting of an old bicycle to the instant explosion of fireworks, reaction speeds vary hugely.
In this chapter, we will explore why some reactions are lightning-fast while others take years, how molecules interact during collisions, and how we can control and speed up reactions in the laboratory and in industry.
1. What is the Rate of Reaction?
The rate of reaction is defined as the change in concentration of a reactant or a product per unit time.
\(\text{Rate} = \frac{\text{change in concentration}}{\text{time taken}}\)
The standard units for rate of reaction are \(\text{mol dm}^{-3}\text{s}^{-1}\) (moles per cubic decimetre per second).
Did you know? At the start of a reaction, the rate is at its highest because the concentration of reactant particles is at its maximum. As reactants are used up, the reaction slows down and eventually stops when a limiting reactant runs out.
Key Takeaway
Rate measures how quickly reactants disappear or products appear. Fast reactions have a high rate; slow reactions have a low rate.
2. Collision Theory: Making Reactions Happen
For a chemical reaction to occur, particles must collide with each other. However, simply bumping into each other is not enough! Most collisions bounce apart without reacting.
According to Collision Theory, for a collision to be successful (or effective), two conditions must be met:
• Sufficient Energy: The colliding particles must possess energy equal to or greater than the activation energy (\(E_a\)).
• Correct Orientation: The particles must collide with the correct alignment so that the reactive parts of the molecules come into contact.
What is Activation Energy (\(E_a\))?
Activation energy (\(E_a\)) is the minimum amount of kinetic energy that colliding particles must have for a chemical reaction to take place.
Analogy: Imagine trying to kick a football over a tall wall. If you do not kick the ball with enough energy, it hits the wall and bounces back. The height of the wall is like the activation energy — only kicks with equal or greater energy will clear the wall!
Key Takeaway
Not every collision produces a reaction. A collision is only successful if particles collide with energy \(\ge E_a\) and the correct orientation.
3. The Maxwell-Boltzmann Distribution
In any gas or liquid at a given temperature, not all particles move at the same speed. Some move slowly with low energy, many move at intermediate speeds, and a few move very fast with high energy.
The Maxwell-Boltzmann distribution is a graph showing the spread of molecular energies in a sample of gas at a specific temperature.
Key Features of the Maxwell-Boltzmann Curve
• Starts at \((0,0)\): No molecules have zero energy.
• Peak of the curve: Represents the most probable energy (\(E_{mp}\)), which is the energy possessed by the greatest number of molecules.
• Mean energy (\(\bar{E}\)): Located slightly to the right of the peak because the curve is asymmetrical.
• Asymptotic tail: The curve approaches the horizontal axis at high energies but never touches it, because there is no theoretical maximum energy.
• Total area under the curve: Equal to the total number of particles in the sample.
• Area to the right of \(E_a\): Represents the fraction of molecules that have energy equal to or greater than the activation energy (\(E \ge E_a\)). Only these molecules can react upon colliding.
Effect of Increasing Temperature
When you increase the temperature of a reaction mixture:
• The average kinetic energy of the particles increases.
• The curve flattens and broadens.
• The peak shifts to the right (higher energy) and downwards (lower height).
• The total area under the curve remains constant because the number of particles has not changed.
• Crucially: The area under the curve to the right of \(E_a\) increases significantly! A much larger fraction of particles now possesses \(E \ge E_a\).
Why does a small increase in temperature cause a huge increase in rate?
A small temperature rise (e.g., \(10\text{ K}\)) slightly increases the speed of particles, leading to slightly more frequent collisions. However, its main effect is that it greatly increases the fraction of particles with energy \(\ge E_a\), leading to a massive increase in the frequency of successful collisions.
Key Takeaway
Increasing temperature flattens and shifts the Maxwell-Boltzmann curve to the right. This significantly increases the proportion of particles with energy \(\ge E_a\).
4. Factors Affecting the Rate of Reaction
There are four main factors that influence the rate of a chemical reaction:
1. Concentration (and Pressure in Gases)
• What happens: Increasing concentration (or pressure for gases) means there are more particles per unit volume.
• Why rate increases: Particles are packed closer together, so they collide more frequently. This increases the frequency of successful collisions.
• Note: The activation energy (\(E_a\)) and the average energy of the particles do not change.
2. Temperature
• What happens: Particles gain kinetic energy and move faster.
• Why rate increases: While collisions occur slightly more frequently, the dominant factor is that a much larger fraction of particles has \(E \ge E_a\), resulting in a much higher frequency of successful collisions.
3. Surface Area (for Solids)
• What happens: Breaking a solid into smaller pieces (or using a fine powder) increases the total surface area exposed to the other reactant.
• Why rate increases: More reactant particles are exposed on the surface, leading to more frequent collisions.
4. Presence of a Catalyst
• What happens: A catalyst provides an alternative reaction route with a lower activation energy.
• Why rate increases: More particles have energy \(\ge\) the new lower activation energy (\(E_{\text{cat}}\)), leading to more frequent successful collisions.
Key Takeaway
To speed up a reaction, you either increase how often particles collide (concentration, pressure, surface area) or increase the proportion of collisions that are successful (temperature, catalyst).
5. Catalysts
A catalyst is a substance that increases the rate of a chemical reaction without being used up itself. It remains chemically unchanged at the end of the reaction.
How Does a Catalyst Work?
A catalyst provides an alternative reaction pathway that has a lower activation energy (\(E_a\)) than the uncatalysed pathway.
On a Maxwell-Boltzmann distribution curve, adding a catalyst does not change the shape of the curve. Instead, it shifts the activation energy line to the left (from \(E_a\) to \(E_{\text{cat}}\)). As a result, a much larger area of the curve lies to the right of this new threshold, meaning many more particles possess the required energy to react successfully.
Types of Catalysts
1. Homogeneous Catalysts
• A catalyst that is in the same physical state (phase) as the reactants.
• Example: Aqueous acid (\(\text{H}^+\text{(aq)}\)) catalysing the esterification of liquid carboxylic acids and alcohols.
• Mechanism: They usually work by forming an intermediate compound with the reactants, which then breaks down to give the products and regenerates the catalyst.
2. Heterogeneous Catalysts
• A catalyst that is in a different physical state (phase) from the reactants. It is typically a solid catalyst used with gaseous or aqueous reactants.
• Example 1: Solid iron (\(\text{Fe}\)) in the Haber Process: \(\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}\)
• Example 2: Solid vanadium(V) oxide (\(\text{V}_2\text{O}_5\)) in the Contact Process: \(2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\text{SO}_3\text{(g)}\)
• Example 3: Platinum (\(\text{Pt}\)), Palladium (\(\text{Pd}\)), or Rhodium (\(\text{Rh}\)) in catalytic converters in car exhausts.
How Heterogeneous Catalysts Work (Adsorption & Desorption)
Solid heterogeneous catalysts work in three main steps:
1. Adsorption: Reactant molecules form weak bonds with the surface of the solid catalyst at active sites. This weakens the covalent bonds within the reactant molecules and holds them in a favourable orientation.
2. Reaction: The reactant molecules react together on the surface to form product molecules.
3. Desorption: The product molecules detach and leave the surface of the catalyst, freeing up active sites for new reactant molecules.
Economic and Environmental Importance of Catalysts
• Energy Savings: Catalysts allow industrial processes to operate at lower temperatures and pressures, saving enormous amounts of fuel and electricity.
• Reduced Carbon Footprint: Burning less fossil fuel to heat industrial reactors reduces \(\text{CO}_2\) emissions.
• Higher Atom Economy / Better Yield per Hour: Reactions run faster and with fewer unwanted side products.
Key Takeaway
Catalysts lower \(E_a\) without being consumed. Homogeneous catalysts share the same phase as reactants; heterogeneous catalysts are in a different phase and operate via surface adsorption and desorption.
6. Measuring Reaction Rates Experimentally
To measure the rate of a reaction in the lab, we monitor how a measurable property changes over time.
Common Experimental Methods
1. Collection of a Gas (Gas Syringe or Inverted Cylinder)
• When to use: When a gas is produced in a reaction involving liquids or solids.
• Example: Reaction of magnesium with hydrochloric acid:
\(\text{Mg(s)} + 2\text{HCl(aq)} \rightarrow \text{MgCl}_2\text{(aq)} + \text{H}_2\text{(g)}\)
• How: Connect a gas syringe to the reaction flask and record the volume of gas collected at regular time intervals (e.g., every \(10\text{ seconds}\)).
2. Mass Loss Method (Using a Balance)
• When to use: When a dense gas (such as \(\text{CO}_2\)) is evolved.
• Example: Reaction of calcium carbonate with hydrochloric acid:
\(\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}\)
• How: Place the flask on a mass balance with a cotton wool plug in the neck (to prevent acid spray from escaping). Record the decrease in mass over time as \(\text{CO}_2\) escapes.
• Note: This method is not suitable for light gases like hydrogen (\(\text{H}_2\)) because the mass change is too small to measure accurately.
3. Disappearing Cross Method (Turbidity / Precipitation)
• When to use: When a reaction produces an insoluble solid (precipitate) that makes the solution cloudy.
• Example: Reaction of sodium thiosulfate with hydrochloric acid:
\(\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + 2\text{HCl(aq)} \rightarrow 2\text{NaCl(aq)} + \text{SO}_2\text{(g)} + \text{S(s)} + \text{H}_2\text{O(l)}\)
• How: Place the beaker over a piece of paper with a black 'X' drawn on it. Time how long it takes for the solid sulfur (\(\text{S}\)) to make the solution opaque so that the cross is no longer visible. Rate is proportional to \(\frac{1}{\text{time}}\).
4. Colorimetry
• When to use: When a reactant or product is coloured (e.g., iodine, \(\text{I}_2\), which is brown/yellow in solution).
• How: A colorimeter measures the absorbance of light passing through the solution over time as the colour changes.
Key Takeaway
Choose an experimental method based on what changes during the reaction: gas volume for gases, mass loss for heavy gases, disappearing cross for precipitates, or colorimetry for coloured substances.
Common Mistakes to Avoid in Kinetics Exams
• Mistake 1: Saying that a catalyst "gives particles more energy".
Correction: Catalysts do not increase molecular energy! They provide a pathway with a lower activation energy.
• Mistake 2: Drawing the Maxwell-Boltzmann curve touching the energy axis at high energy.
Correction: The curve is asymptotic — it must never touch or cross the horizontal axis at the high-energy end.
• Mistake 3: Starting the Maxwell-Boltzmann curve above the origin.
Correction: The curve must start at \((0,0)\) because zero molecules have zero energy.
• Mistake 4: Saying temperature increases rate solely because particles collide more often.
Correction: Although collision frequency increases slightly, the main reason is that a much greater proportion of molecules has \(E \ge E_a\).
Quick Chapter Summary Checklist
• Rate of reaction: Change in concentration per unit time (units: \(\text{mol dm}^{-3}\text{s}^{-1}\)).
• Collision theory: Collisions require energy \(\ge E_a\) and correct orientation.
• Maxwell-Boltzmann curve: Represents energy distribution; area under curve = total particles; area \(\ge E_a\) = reacting particles.
• Temperature effect: Flattens curve, shifts peak right, massively increases particles with \(E \ge E_a\).
• Concentration/Pressure/Surface Area: Increase collision frequency.
• Catalyst: Lowers \(E_a\) by providing an alternative pathway; unchanged at the end.
• Homogeneous vs. Heterogeneous: Same phase vs. different phase (heterogeneous works via adsorption/desorption).