Effect of Concentration, Temperature and Catalysts on Reaction Rate

The previous chapter built collision theory from first principles: a reaction needs a collision with sufficient energy and the correct orientation, and the Maxwell-Boltzmann distribution showed why temperature affects the energetic fraction so strongly. This chapter puts that machinery to work on the three variables an experimenter can actually control — concentration, temperature and the presence of a catalyst — and explains, qualitatively and semi-quantitatively, exactly how and why each one changes the rate of a reaction. The next chapter then turns these qualitative trends into the precise mathematical language of a rate law.

You should already be fluent with the two requirements of an effective collision and the shape of the Maxwell-Boltzmann distribution from the previous chapter; everything here is a direct application of that model.

1. Concentration: More Particles, More Collisions

Increasing the concentration of a reactant in solution packs more particles into the same volume of solvent. With more particles occupying a given space, the average distance between particles falls, and particles of different reactants encounter each other more frequently. Collision theory predicts, directly from this, that the collision frequency rises in proportion to the concentrations of the reacting species.

Key mechanism. Raising concentration increases the frequency of collisions. It does not change the activation energy, the shape of the Maxwell-Boltzmann distribution, or the fraction of collisions that are correctly oriented — those are properties of the reaction and the temperature, not of how much reactant happens to be present.

Because the fraction of collisions that are effective stays the same (both the energy and orientation requirements are unaffected by concentration), the rate of effective collisions rises in the same proportion as the collision frequency — which, for the simplest reactions, means rate rises in direct proportion to concentration. (The precise mathematical form of this proportionality, which is not always a simple direct one, is the subject of the next chapter's rate laws.)

Worked example 1. A reaction's initial rate is measured as $4.0\times 10^{-3}~\text{mol}\,\text{dm}^{-3}\,\text{s}^{-1}$ at $[\text{A}] = 0.20~\text{mol}\,\text{dm}^{-3}$. If doubling $[\text{A}]$ to $0.40~\text{mol}\,\text{dm}^{-3}$ is found experimentally to double the rate, the new rate is

This doubling behaviour — rate directly proportional to $[\text{A}]$ — is one common pattern, examined rigorously as "first order in $\text{A}$" in the next chapter; it is not the only possible pattern, and must be established experimentally for a given reaction rather than assumed.

For gas-phase reactions, increasing pressure at constant temperature has the identical effect: compressing a fixed amount of gas into a smaller volume raises its concentration, increasing collision frequency in exactly the same way as increasing concentration does in solution.

2. Temperature: Reshaping the Energy Distribution

Chapter 2 already derived the central result: raising temperature shifts the Maxwell-Boltzmann distribution's peak to higher energy and flattens it, so that a disproportionately larger fraction of collisions now exceed $E_a$. This section makes the comparison with concentration explicit, since the two effects are frequently confused.

Key distinction. Concentration changes the collision frequency without touching the energetic fraction. Temperature changes the energetic fraction (via the reshaped distribution) far more than it changes the collision frequency, which rises only weakly (roughly as $\sqrt{T}$). The two variables speed up a reaction through almost entirely different mechanisms.

Worked example 2. At $300~\text{K}$, a reaction has a rate of $1.0\times 10^{-4}~\text{mol}\,\text{dm}^{-3}\,\text{s}^{-1}$. Experimentally, raising the temperature to $310~\text{K}$ — a rise of only $10~\text{K}$, or about $3\%$ — is found to double the rate:

Compare this with concentration: doubling $[\text{A}]$ (a $100\%$ increase in concentration) was needed to double the rate in Worked example 1, whereas here a mere $3\%$ rise in absolute temperature achieves the same doubling. This enormous difference in sensitivity is exactly what the reshaping Maxwell-Boltzmann tail, rather than any change in collision frequency, explains: collision frequency itself rises by only a percent or two over this temperature range, nowhere near enough to double the rate on its own.

The precise quantitative relationship between rate constant and temperature — allowing $E_a$ itself to be measured from experimental data — is the Arrhenius equation, developed later in this block; this chapter establishes only the qualitative mechanism behind the trend.

3. Catalysts: An Alternative, Lower-Energy Pathway

A catalyst is a substance that increases the rate of a reaction without itself being permanently consumed, by providing an alternative reaction pathway with a lower activation energy. The catalyst participates in intermediate steps of the mechanism but is fully regenerated by the end of the overall reaction, so it does not appear in the overall balanced equation and its own mass is unchanged once the reaction is complete.

Definition. A catalyst lowers $E_a$ by opening a different route from reactants to products — often via temporary bonding to a catalyst surface or the formation of a reactive intermediate — without altering $\Delta H$ for the overall reaction, since $\Delta H$ depends only on the fixed energies of the reactants and products, not on the pathway taken between them.

On an energy profile diagram, a catalysed pathway is drawn with the same reactant and product energy levels as the uncatalysed pathway, but with a lower transition-state peak (or, for a multi-step catalytic mechanism, a lower highest peak among several smaller humps). Because the peak is lower for both directions simultaneously, a catalyst speeds up the forward and reverse reactions by the same factor — an idea returned to when chemical equilibrium is developed later in this block.

Worked example 3. An uncatalysed reaction has $E_a = 95~\text{kJ}\,\text{mol}^{-1}$; a catalysed pathway for the same reaction has $E_a = 55~\text{kJ}\,\text{mol}^{-1}$. $\Delta H = -30~\text{kJ}\,\text{mol}^{-1}$ in both cases, since the reactants and products are chemically identical regardless of which pathway is taken. The effect on rate is explained exactly as in Section 2: lowering $E_a$ moves the threshold line on the (unchanged) Maxwell-Boltzmann distribution further to the left, so a much larger fraction of existing collisions — at the same temperature — now exceed the smaller barrier.

3.1 Homogeneous and heterogeneous catalysis

A catalyst is homogeneous when it is in the same phase as the reactants (typically all dissolved in the same solution), reacting with a reactant to form a reactive intermediate that subsequently reacts further, regenerating the catalyst. A catalyst is heterogeneous when it is in a different phase from the reactants — most commonly a solid catalysing a reaction between gases or between species in solution — with the reaction proceeding at the catalyst's surface via adsorption of reactants, reaction on the surface, and desorption of products. Industrial examples include the iron catalyst of the Haber process (heterogeneous) and acid catalysis of ester hydrolysis (homogeneous).

Key distinction. A homogeneous catalyst forms a genuine chemical intermediate with a reactant, detectable in principle; a heterogeneous catalyst instead provides a surface on which reactant bonds are weakened by adsorption, lowering the energy needed to break them, without the catalyst entering a distinct dissolved intermediate species.

4. Why Catalysts Do Not Change Equilibrium Position

Since a catalyst lowers $E_{a,\text{forward}}$ and $E_{a,\text{reverse}}$ by an identical amount (both pass through the same lowered transition-state peak), it speeds up the forward and reverse reactions equally. The system reaches its final (equilibrium) state faster, but that final state — the equilibrium position, developed fully in a later chapter — is unaffected, because both the forward and reverse rate constants increase by the same factor, so their ratio $K = k_{\text{f}}/k_{\text{r}}$ is unchanged.

Common Exam Pitfalls

• Attributing a faster rate at higher concentration to "more energy" or "a lower $E_a$." Concentration affects only collision frequency; $E_a$ and the energy distribution are untouched.
• Attributing a faster rate at higher temperature mainly to "more frequent collisions." The dominant cause is the disproportionate growth of the fraction of collisions exceeding $E_a$, not the comparatively small rise in collision frequency itself.
• Saying a catalyst "provides more energy" to the reacting particles. A catalyst does not add energy to the system; it lowers the energy required by providing an alternative, less demanding pathway.
• Claiming a catalyst changes $\Delta H$. $\Delta H$ depends only on the reactants' and products' energies, which are fixed regardless of pathway; only $E_a$ changes with a catalyst.
• Believing a catalyst shifts the position of equilibrium. A catalyst speeds up the forward and reverse reactions equally, reaching the same equilibrium position faster — it never favours one direction over the other.
• Confusing the mild sensitivity of rate to concentration with the strong sensitivity of rate to temperature, and using the wrong explanation (collision frequency vs energy distribution) for the wrong variable.

Summary

• Concentration (or pressure, for gases) increases rate by increasing collision frequency; $E_a$, the energy distribution and the orientation fraction are unaffected.
• Temperature increases rate mainly by reshaping the Maxwell-Boltzmann distribution, disproportionately increasing the fraction of collisions exceeding $E_a$; the accompanying rise in collision frequency (roughly $\sqrt{T}$) is comparatively minor.
• A catalyst provides an alternative pathway of lower activation energy without changing $\Delta H$, increasing the fraction of existing collisions (at the same temperature) able to react.
• Catalysts are classified as homogeneous (same phase as reactants, via a reactive intermediate) or heterogeneous (different phase, typically a solid surface via adsorption, reaction and desorption).
• A catalyst speeds up the forward and reverse reactions by the same factor, reaching equilibrium faster without shifting the equilibrium position, because both rate constants increase by the same factor, so $K = k_{\text{f}}/k_{\text{r}}$ is unchanged.
• The precise mathematical relationships underlying these qualitative trends (the rate law's dependence on concentration, and the Arrhenius equation's dependence on temperature) are developed in the next chapters of this block.