Reaction Kinetics (AS & A Level 9701) Study Notes

Welcome to Reaction Kinetics! This is a fascinating chapter because it moves beyond just what reactions happen (which you learned in stoichiometry and energetics) to how fast they happen and why. Understanding kinetics is vital for chemists and engineers—it helps us speed up slow reactions (like industrial processes) or slow down fast, dangerous ones (like explosions or food spoilage).

Don't worry if the calculations look complex at first. We will build up the concepts step by step, starting with the fundamentals you need for AS, and then moving into the A Level quantitative concepts.

1. Defining and Measuring Reaction Rate (AS Level Fundamentals)

1.1 What is the Rate of Reaction?

The rate of reaction is simply how fast the concentration of a reactant decreases or the concentration of a product increases over time.

Definition: The change in concentration of a reactant or product per unit time.

Units: The standard unit is usually $\text{mol dm}^{-3}\text{s}^{-1}$.

We can express the rate mathematically as:

$$ \text{Rate} = \frac{\Delta [\text{Reactant or Product}]}{\Delta t} $$

(Note: We usually look at the disappearance of reactants, which gives a negative slope on a graph, so we often ignore the negative sign to express the rate as a positive value.)

1.2 Measuring the Rate Experimentally

To calculate the rate, you need experimental data (how concentration changes over time). You typically follow the reaction by measuring a property that changes as the reaction progresses.

Methods to monitor a reaction include:

  • Change in Volume/Pressure: If a gas is produced (e.g., $\text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_{2} + \text{H}_{2}$).
  • Change in Mass: If a gas is lost (by placing the reaction on a balance).
  • Change in Colour: If a reactant or product is coloured (measured using a colorimeter).
  • Change in pH: If an acid or alkali is consumed or produced.
  • Change in Conductivity: If there is a change in the number or type of ions.

Calculating Rate from Graphs:

When you plot concentration (or volume/mass) against time, the rate at any specific point is given by the gradient (slope) of the tangent drawn at that point.

  • Initial Rate: Find the gradient of the tangent at $t = 0$. This is the fastest rate.
  • Rate decreases over time because the concentration of reactants decreases, leading to fewer collisions.
Key Takeaway:

The rate of reaction is the speed at which concentrations change. Experimentally, we measure this by monitoring a changing physical property, and graphically, the rate is the steepness of the concentration-time curve.

2. The Collision Theory: Why Reactions Happen

The Collision Theory explains that for reactants to turn into products, the reactant particles must collide with each other.

2.1 Fundamental Concepts

For a collision to be effective (meaning it actually results in a reaction), two conditions must be met:

  1. Sufficient Energy (Activation Energy): The particles must collide with energy equal to or greater than the activation energy (\(E_a\)).
  2. Correct Orientation: The particles must collide facing the correct way so that the necessary bonds can break and new bonds can form.

Effective Collisions lead to product formation.
Non-effective Collisions are collisions that happen but do not lead to a reaction (either because of low energy or wrong orientation).

The reaction rate depends directly on the frequency of effective collisions.

Analogy: The Car Crash

Imagine a chemical reaction is a car crash that results in new, rearranged parts (products).

  • Collision: The cars must physically hit each other.
  • Correct Orientation: They must hit bumper-to-bumper (the necessary bonds must align). If they just scrape fenders (wrong orientation), the crash isn't effective.
  • Sufficient Energy (\(E_a\)): They must be travelling fast enough. If they only bump lightly (low energy), nothing changes. They need enough speed to cause significant damage (reaction).

Key Takeaway:

Rate depends on effective collisions, which require particles to meet with enough energy (>$E_a$) and in the right orientation.

3. Factors Affecting Reaction Rate (Qualitative Explanation)

The following factors increase the rate by increasing the frequency of effective collisions:

3.1 Concentration of Reactants (or Pressure for Gases)

Increasing the concentration of reactants (or increasing the pressure for gaseous reactants) increases the reaction rate.

  • Why? More particles are packed into the same volume.
  • Result: This leads to a higher frequency of collisions overall, and therefore a higher frequency of effective collisions per unit time.

3.2 Surface Area (for Solid Reactants)

Increasing the surface area of a solid reactant (e.g., using powder instead of chunks) increases the reaction rate.

  • Why? Reactions involving solids can only occur at the surface of the solid.
  • Result: Breaking the solid into smaller pieces exposes more surface area to the other reactants, increasing the sites available for collision, and thus increasing the frequency of effective collisions.

3.3 Intensity of Light

For photochemical reactions (reactions initiated by light), increasing the intensity of light increases the rate.

  • Why? Light provides the energy needed to break bonds and initiate the reaction mechanism (often involving free radicals).
Quick Review Box:

Concentration, pressure, and surface area increase the rate primarily by making particles collide MORE OFTEN.

4. Temperature and Activation Energy

This is arguably the most crucial area of AS kinetics. We use the Boltzmann Distribution to explain the effect of temperature and activation energy.

4.1 Activation Energy (\(E_a\))

Definition: The activation energy (\(E_a\)) is the minimum energy required for a collision to be effective.

Recall the reaction pathway diagram from Chemical Energetics (Topic 5):

(Imagine a sketch here: An energy profile graph with reactants, a transition state peak, and products. \(E_a\) is the height from the reactants to the peak.)

  • All collisions must overcome this "energy barrier" to react.

4.2 The Boltzmann Distribution

The Boltzmann Distribution curve shows the distribution of kinetic energies among the molecules in a sample at a given temperature.

Features of the Distribution:

  1. The area under the curve represents the total number of molecules.
  2. Only a small fraction of molecules possess energy greater than or equal to \(E_a\).

(Imagine a sketch: A graph showing Number of molecules (Y-axis) vs. Kinetic Energy (X-axis). The curve peaks and tails off. \(E_a\) is marked far down the x-axis.)

4.3 Effect of Temperature

When the temperature is increased (from $T_1$ to $T_2$):

  • The curve flattens and shifts slightly to the right.
  • The average kinetic energy of the molecules increases.

The Big Explanation:

A small increase in temperature results in a disproportionately large increase in the fraction of molecules that possess energy greater than or equal to \(E_a\). This larger shaded area under the curve means many more molecules are able to react upon collision.

This increases the frequency of effective collisions dramatically, explaining why reaction rates often double for every 10 °C rise in temperature.

Common Mistake Alert!

Students often think increasing temperature only increases collision frequency. While this is true, the main reason for the massive rate increase is the large rise in the proportion of molecules that possess $E_a$.

Key Takeaway:

Temperature increases the rate primarily by increasing the proportion of particles with energy $\ge E_a$, as shown by the shift in the Boltzmann distribution curve.

5. The Role of Catalysis (AS & A Level)

A catalyst is a substance that increases the rate of a chemical reaction without being consumed by the reaction itself.

5.1 How Catalysts Work

Catalysts provide an alternative reaction pathway that has a lower activation energy (\(E_a\)).

In terms of the Boltzmann Distribution:

  • When a catalyst is added, the \(E_a\) line shifts significantly to the left (to a lower energy value).
  • Even though the distribution of kinetic energies remains the same, a much larger fraction of molecules now have energy $\ge$ the new, lower \(E_a\).
  • The frequency of effective collisions increases dramatically, speeding up the reaction.

In terms of the Reaction Pathway Diagram:

(Imagine a sketch: The original high peak (\(E_a\) uncatalysed) is replaced by a lower peak (\(E_a\) catalysed) which starts and ends at the same enthalpy levels.)

  • A catalyst does not change the overall enthalpy change ($\Delta H$) of the reaction.
  • A catalyst does not change the position of equilibrium (Topic 7.1), although it allows equilibrium to be reached faster.

Did You Know?

The human body is full of biological catalysts called enzymes, which allow complex reactions to occur rapidly at body temperature (around 37 °C) that would otherwise require dangerously high temperatures or pressures.

5.2 Types of Catalysis (A Level Focus)

Catalysis is divided into two main categories based on the physical states of the reactants and the catalyst.

5.2.1 Heterogeneous Catalysis (Different State)

The catalyst is in a different physical state from the reactants (usually a solid catalyst and gaseous reactants).

Mechanism (Action): The process generally involves three steps:

  1. Adsorption: Reactant molecules stick to the surface of the solid catalyst. This concentrates the reactants.
  2. Reaction (Bond Weakening): Adsorption weakens the bonds within the reactant molecules, allowing them to react with a lower \(E_a\).
  3. Desorption: The product molecules detach from the catalyst surface.

Examples (Syllabus Specific):

  • Iron (Fe) catalyst in the Haber process (\(\text{N}_{2} + 3\text{H}_{2} \rightleftharpoons 2\text{NH}_{3}\)).
  • Palladium (Pd), Platinum (Pt), and Rhodium (Rh) in car catalytic converters, which remove pollutants like oxides of nitrogen (\(\text{NO}_x\)).
5.2.2 Homogeneous Catalysis (Same State)

The catalyst is in the same physical state as the reactants (usually liquid/aqueous solution).

Mechanism (Action): The catalyst reacts in one step to form an intermediate, and is then reformed in a subsequent step. This creates a two-step pathway with lower \(E_a\) for both steps.

Example (Syllabus Specific):

  • Catalysis using $\text{Fe}^{2+}$ or $\text{Fe}^{3+}$ ions in the reaction between $\text{I}^{-}$ and peroxodisulfate ions ($\text{S}_{2}\text{O}_{8}^{2-}$):

Step 1 (Catalyst used):
$$ \text{S}_{2}\text{O}_{8}^{2-} (aq) + 2\text{Fe}^{2+} (aq) \rightarrow 2\text{SO}_{4}^{2-} (aq) + 2\text{Fe}^{3+} (aq) $$

Step 2 (Catalyst reformed):
$$ 2\text{I}^{-} (aq) + 2\text{Fe}^{3+} (aq) \rightarrow \text{I}_{2} (aq) + 2\text{Fe}^{2+} (aq) $$

The $\text{Fe}^{2+}$ is used in Step 1 and reformed in Step 2, acting as a true catalyst. Transition metals like iron are often good homogeneous catalysts because they can easily change oxidation states.

Key Takeaway:

Catalysts speed up reactions by lowering $E_a$ (providing a new mechanism). Heterogeneous catalysts work via surface adsorption; homogeneous catalysts work by forming and regenerating an intermediate.

6. Advanced Kinetics: Rate Equations, Order, and Mechanism (A Level)

While the AS content explains the qualitative effect of factors, A Level kinetics deals with the precise, quantitative relationship between reactant concentration and rate.

6.1 Rate Equations and Order of Reaction

For a general reaction: $$ a\text{A} + b\text{B} \rightarrow \text{Products} $$

The relationship between concentration and rate is given by the rate equation, which can only be determined by experiment:

$$ \text{Rate} = k [\text{A}]^m [\text{B}]^n $$

Key Terms:

  • Rate Constant ($k$): This is the constant of proportionality in the rate equation. It depends only on temperature and the presence of a catalyst.
  • Order of Reaction (m or n): The power to which the concentration of a reactant is raised in the rate equation. It is determined experimentally, NOT from the balanced stoichiometric equation (a and b).
  • Overall Order of Reaction: The sum of the individual orders (\(m + n\)).

6.2 Understanding Reaction Orders (m, n = 0, 1, or 2)

The order tells you how the rate changes when you change that reactant’s concentration.

Order Definition Effect on Rate (when [A] is doubled)
Zero Order (m=0) Rate $\propto [\text{A}]^0$ (Rate is independent of [A]) Rate does not change.
First Order (m=1) Rate $\propto [\text{A}]^1$ (Rate is directly proportional to [A]) Rate doubles.
Second Order (m=2) Rate $\propto [\text{A}]^2$ (Rate is proportional to the square of [A]) Rate quadruples ($\times 4$).

6.3 Determining the Units of the Rate Constant ($k$)

The units of $k$ depend on the overall order of the reaction. To find the units, rearrange the rate equation:

$$ k = \frac{\text{Rate}}{[\text{A}]^m [\text{B}]^n} $$

Substitute the units: \(\text{Rate} = \text{mol dm}^{-3}\text{s}^{-1}\) and \([\text{Concentration}] = \text{mol dm}^{-3}\).

Example: If the overall order is 2 (e.g., $m=1, n=1$):

$$ k = \frac{\text{mol dm}^{-3}\text{s}^{-1}}{(\text{mol dm}^{-3})(\text{mol dm}^{-3})} = \frac{\text{mol dm}^{-3}\text{s}^{-1}}{\text{mol}^2 \text{dm}^{-6}} = \text{mol}^{-1} \text{dm}^{3} \text{s}^{-1} $$

6.4 The Half-Life ($t_{1/2}$) Method

The half-life ($t_{1/2}$) is the time taken for the concentration of a reactant to fall to half of its initial value.

  • First-Order Reactions: The half-life is independent of concentration. This is the hallmark of a first-order reaction. If you double the initial concentration, the time taken for it to halve remains the same.
  • Calculation (First Order only): We can relate the half-life and the rate constant $k$: $$ k = \frac{0.693}{t_{1/2}} $$

6.5 Reaction Mechanism and the Rate-Determining Step (RDS)

Most reactions occur in a sequence of elementary steps, called the reaction mechanism.

  • Intermediate: A species that is formed in one step and used up in a subsequent step.
  • Rate-Determining Step (RDS): This is the slowest step in the reaction mechanism. Like a traffic bottleneck, the overall rate of the reaction can never be faster than the rate of this slowest step.

Crucial Rule: The species involved in the rate-determining step are the ones that appear in the rate equation (and their powers correspond to their stoichiometric coefficients in the RDS).

Example: If the proposed mechanism is:

Step 1 (Slow): $\text{A} + \text{B} \rightarrow \text{Intermediate}$
Step 2 (Fast): $\text{Intermediate} + \text{C} \rightarrow \text{Product}$

  • The RDS is Step 1.
  • The rate equation must be: $\text{Rate} = k [\text{A}]^1 [\text{B}]^1$. (First order with respect to A and B, overall second order.)

Note: If the rate equation determined by experiment matches the stoichiometry of the proposed RDS, it suggests that the proposed mechanism is chemically plausible.

Key Takeaway:

A Level kinetics uses the Rate Equation ($\text{Rate} = k [\text{A}]^m [\text{B}]^n$) to quantify rate. The order (m, n) determines how concentration affects rate and must be found experimentally. The RDS governs the overall rate and dictates the species that appear in the rate equation.