What Is Reaction Rate?
Reaction rate is defined as the change in concentration of a reactant (or product) per unit time. As a reaction proceeds, reactants are consumed and products are formed.
Rate = Δ[concentration] / Δt (units: mol·L−1·s−1)
Rate can also be measured experimentally by:
- Volume of gas produced per unit time (cm³·s−1)
- Change in mass per unit time (g·s−1) — when a gas escapes from the reaction mixture
- Change in colour intensity (colorimetry)
- Change in conductivity or turbidity
There are two types of rate:
- Average rate: total change in concentration over a time interval: Δ[c]/Δt
- Instantaneous rate: the rate at a specific moment — found from the gradient (slope) of the tangent to the concentration vs. time curve at that point
Why does rate decrease over time? As reactants are consumed, there are fewer reactant particles per unit volume. This reduces the frequency of collisions, which reduces the rate. On a concentration-time graph, the curve becomes less steep as time passes.
Collision Theory
Collision theory explains why and how reactions occur at the particle level. For a reaction to occur, particles must:
- Actually collide with each other
- Collide with sufficient energy (energy ≥ activation energy Ea)
- Collide with the correct orientation (the reactive parts of the molecules must face each other)
A collision that meets both energy and orientation requirements is called an effective collision. Only effective collisions lead to a reaction. The rate of reaction is proportional to the frequency of effective collisions.
Rate ∝ frequency of effective collisions = frequency of collisions × fraction with E ≥ Ea × fraction with correct orientation
Factors Affecting Reaction Rate
1. Concentration (solutions)
Increasing the concentration of a dissolved reactant increases the number of particles per unit volume. This leads to more frequent collisions per second, and therefore more effective collisions per second, increasing the rate.
- Higher concentration → more particles per volume → more frequent collisions → higher rate
- As the reaction proceeds and reactants are consumed, concentration decreases → rate decreases over time
2. Pressure (gases)
For reactions involving gases, increasing pressure compresses the gas into a smaller volume. This increases the number of gas particles per unit volume — the same effect as increasing concentration. Higher pressure → more frequent collisions → higher rate.
3. Surface Area (solids)
Reactions between a solid and a liquid (or gas) can only occur at the surface of the solid. Breaking a solid into smaller pieces (e.g., powder vs. lumps) increases the total surface area exposed to the reactant, so more particles are available to collide. This increases the rate.
- Marble powder reacts much faster with HCl than a single marble chip of the same mass
- The total amount of solid (moles) is unchanged — only the rate changes
Explosion risk: Fine dust (coal dust, flour dust) has enormous surface area and can react extremely rapidly with oxygen — leading to explosions. This is why dust in mines and mills is a serious safety hazard.
4. Temperature
Increasing temperature has two effects that both increase the reaction rate:
- Particles move faster → more frequent collisions
- A greater fraction of particles has kinetic energy ≥ Ea → more effective collisions per collision
The second effect (more particles exceeding Ea) is the dominant one. As a rough rule of thumb, reaction rate approximately doubles for every 10°C rise in temperature for many reactions.
5. Catalysts
A catalyst is a substance that increases the rate of a reaction without being consumed in the process. It provides an alternative reaction pathway with a lower activation energy.
- More particles have energy ≥ the lower Ea → more effective collisions → higher rate
- The catalyst is not consumed — it is regenerated and can be used repeatedly
- Homogeneous catalyst: same phase as reactants (e.g., H²SO₄ catalysing esterification in solution)
- Heterogeneous catalyst: different phase from reactants (e.g., Fe(s) catalysing the Haber process for N₂(g) + H₂(g))
Maxwell-Boltzmann Distribution
The Maxwell-Boltzmann distribution is a graph showing the distribution of kinetic energies among particles in a gas at a given temperature. Key features:
- The curve starts at the origin (no particles have zero energy)
- It rises to a peak (the most probable energy) then falls away asymptotically
- The area under the whole curve represents the total number of particles (constant)
- The vertical line at Ea divides the graph: particles to the right of Ea have sufficient energy to react
- The shaded area to the right of Ea represents the fraction of particles that can undergo effective collisions
Effect of temperature increase:
- The curve shifts to the right and becomes flatter and broader
- The peak moves to a higher energy value
- The area to the right of Ea (shaded region) becomes significantly larger
- This means a much larger fraction of particles can react → rate increases
The Ea line stays fixed when temperature changes. The catalyst lowers the Ea line (shifts it left), increasing the shaded area without changing the curve shape.
Rate-Time and Concentration-Time Graphs
| Graph type | Reactant | Product | Key interpretation |
|---|
| Concentration vs time | Decreasing concave curve | Increasing concave curve (flattens) | Gradient at any point = instantaneous rate |
| Rate vs time | Starts high, decreases to near zero | Same shape | Rate is always positive; decreases as reactants consumed |
| Volume of gas vs time | N/A | Increasing curve, levels off | Initial gradient = initial rate; final volume = when reactant exhausted |
⭐ IEB Extension — Rate Law and Reaction Order
The rate law (or rate equation) expresses the rate as a function of reactant concentrations:
rate = k[A]m[B]n
- k = rate constant (depends on temperature; determined experimentally)
- m, n = orders of reaction with respect to A and B (must be determined from experiment, not from stoichiometry)
- Overall order = m + n
To determine orders from experimental data: compare experiments where one concentration is changed while the other is kept constant. If doubling [A] doubles the rate: first order (m=1). If doubling [A] quadruples the rate: second order (m=2).
⭐ IEB Extension — Half-Life and Arrhenius Equation
For a first-order reaction, the half-life t½ is constant and independent of initial concentration:
t½ = 0.693 / k
The Arrhenius equation relates the rate constant k to temperature T (in Kelvin) and activation energy Ea:
k = Ae(−Ea/RT)
Where A is the pre-exponential (frequency) factor and R = 8.314 J·mol−1·K−1. As T increases, k increases — confirming that rate increases with temperature. A catalyst lowers Ea, which increases k at the same temperature.