Explain reaction rate, activation energy, catalysts, concentration, temperature, surface area, and collision orientation using particle-level reasoning.
A lesson of Chemistry, in Equilibrium, Acids and Bases, and Redox, about 35 minutes.
By the end of this lesson, you will be able to say what a successful collision requires, explain each of the four ways to change a rate, and describe what a catalyst does and does not do.
Two Conditions for a Collision to Work
Reactions happen when particles collide. Most collisions do nothing at all, and
two conditions separate the productive ones.
Enough energy. The collision must supply at least the activation energy
$E_a$, because existing bonds have to break before new ones form, and breaking
costs energy.
Correct orientation. The right parts of the molecules must meet. Two complex
molecules colliding back-to-front bounce off unchanged however hard they hit.
$$\text{rate} \propto \text{collisions per second} \times \text{fraction that succeed}$$
Everything that changes a rate changes one of those two factors, and there is
no third mechanism. That makes kinetics unusually tidy: four practical levers, all
explained by one sentence.
Rate is a separate question from whether a reaction is favorable. Diamond
turning to graphite releases energy and takes longer than the age of the universe,
because its activation energy is enormous. Thermodynamics says which way; kinetics
says how fast.
Temperature: the Steepest Lever
Raising the temperature does two things, and one of them dominates.
Particles move faster, so they collide more often. True, and a fairly small
effect: a $10°C$ rise increases collision frequency by only a few percent.
Far more particles now exceed $E_a$. This is the big one. Molecular speeds are
spread across a distribution, and only the fast tail can react. Shifting the whole
distribution slightly moves a large fraction of molecules past the threshold,
because the tail is steep.
$$\text{a } 10°C \text{ rise typically DOUBLES the rate}$$
Doubling from a few percent more collisions is impossible, which is how you
know the energy effect is doing the work. It is the fraction that succeeds, not
the number of attempts.
That is why food keeps in a refrigerator: the spoilage reactions are the same
reactions, running several times slower. Every $10°C$ colder roughly halves them.
The Other Three Levers
Concentration. More particles per unit volume means more collisions per
second. Doubling a reactant's concentration typically increases the rate, though
not always by exactly double, because the relationship depends on the reaction's
mechanism.
Pressure, for gases, is the same lever wearing a different name: raising the
pressure pushes gas particles closer together, which is an increase in
concentration.
Surface area, for solids. A reaction between a solid and a liquid or gas
happens only at the surface, so a lump of magnesium reacts slowly and magnesium
powder reacts violently. Cutting a cube into smaller cubes multiplies the exposed
area while keeping the mass the same.
This is genuinely dangerous in industry. Fine dusts of flour, sugar, coal or
custard powder have so much surface area that they can explode when ignited in
air, and grain silo explosions kill people every year for exactly this reason.
Catalysts get their own section, because they work differently from all three
of these.
Sort It: Which Lever
Example 1: Explaining a Rate Change
Here is every step, worked all the way through.
Magnesium ribbon reacts slowly with acid. Magnesium powder of the same mass
reacts violently.
Has the amount of magnesium changed? Type yes or no no
How many of the four rate factors have been altered here? 1
What HAS changed? Type two words surface area
Does that change the number of collisions or the fraction that succeed? Type one word collisions
Catalysts Lower the Activation Energy
$$\textbf{a catalyst provides a different route with a lower } E_a$$
That is the entire mechanism, and everything else about catalysts follows.
A catalyst is not consumed. It takes part, forms an intermediate, and is
regenerated, so a tiny amount can process an enormous quantity of reactant
indefinitely.
A catalyst does NOT change $\Delta H$. The reactants and products are the same
substances at the same energies; only the hump between them is lower. It changes
how fast you get there and not where you end up.
And it speeds up the reverse reaction by exactly the same factor, because the
lower path is available in both directions. A catalyst can never shift a position
of equilibrium, only the speed of arriving at it.
$$\text{lower } E_a \Rightarrow \text{a larger fraction of collisions succeed}$$
Enzymes are biological catalysts, and they are extraordinary: some accelerate
reactions by a factor of $10^{17}$. Catalase, which breaks down hydrogen peroxide,
processes millions of molecules per second. Every reaction in your body runs at
body temperature only because an enzyme makes it possible; without them the same
chemistry would need temperatures that would kill you.
Industrially, about $90%$ of manufactured chemicals pass through a catalytic step.
A car's catalytic converter turns $\mathrm{CO}$ and unburnt fuel into
$\mathrm{CO_2}$ and water using platinum, rhodium and palladium, which is why
those metals are worth stealing.
Sort It: True of a Catalyst
Worked Example 1: What a Catalyst Changes
A reaction has $E_a = 80$ kJ/mol and $\Delta H = -50$ kJ/mol. A catalyst
lowers $E_a$ to $40$ kJ/mol.
Measuring a Rate
$$\text{rate} = \frac{\text{change in concentration}}{\text{time}}$$
In practice you measure whatever is easiest to follow:
Gas volume collected over time
Mass loss, if a gas escapes an open flask on a balance
Color change, followed with a light sensor
pH, if acid is consumed or produced
Rate is fastest at the start and slows as it goes, because reactant
concentration falls as the reaction proceeds, so collisions become less frequent.
A graph of product against time is steep at first and flattens toward a plateau.
The plateau is where a reactant ran out, and the height of the plateau depends
on the limiting reactant while the steepness depends on the rate factors. Two
experiments can reach the same plateau at very different speeds, or reach different
plateaus at the same speed, and reading which is which is the skill in these
graphs.
Worked Example 2: Reading a Rate Graph
Two experiments produce gas. Experiment B is steeper at the start but both
plateau at $50$ mL.
Worked Example 3: Combining Factors
A reaction is run at $20°C$ with $1$ M acid and a magnesium ribbon. It is then
repeated at $30°C$ with $2$ M acid and magnesium powder.
Common Mistakes
Mistake 1: Thinking a catalyst is consumed
It is regenerated, so a trace lasts indefinitely.
Mistake 2: Thinking a catalyst changes $\Delta H$
Only the barrier between reactants and products moves.
Mistake 3: Explaining temperature by collision frequency alone
The big effect is the fraction of collisions with enough energy.
Mistake 4: Confusing rate with extent
A fast reaction and a complete reaction are different claims.
Mistake 5: Expecting a rate factor to raise the plateau
Amount decides the plateau; rate decides the steepness.
Where This Goes Next
Most reactions do not happen in one step, and that is where kinetics gets its real
power.
The sequence of actual steps is the mechanism, and the slowest step is the
rate-determining step. The whole reaction can go no faster than its slowest
stage, exactly as a line moves at the speed of its slowest server.
That gives a way to find out something you cannot see directly. Measure how the
rate depends on each reactant's concentration, and the rate law that comes out
constrains which mechanisms are possible. A reactant that does not appear in the
rate law is not involved in the slow step at all, which is a genuine deduction
about invisible molecular events from a stopwatch and a burette.
The Arrhenius equation makes the temperature effect quantitative:
$$k = Ae^{-E_a/RT}$$
The exponential is why a modest temperature change has such a large effect, and
plotting $\ln k$ against $1/T$ gives a straight line whose slope yields $E_a$.
Measuring an activation energy is a graph, not a guess.
Kinetics and thermodynamics answer different questions, and both matter. A reaction
that is favorable and slow is useless, and a reaction that is fast and
unfavourable does not happen. Industrial chemistry is largely the business of
finding conditions where both are satisfied at once.
Check Your Understanding
Five of them, no instructions this time.
Summary
A collision works only with enough energy and the right orientation, and every
rate factor changes one of those two.
Temperature is the steepest lever, and it works mainly by pushing more
particles past $E_a$ rather than by speeding collisions up.
Concentration, pressure and surface area all increase collision frequency.
A catalyst lowers $E_a$ by offering a different route, is not consumed, does
not change $\Delta H$, and speeds both directions equally.
Rate is not extent. Steepness is rate; the plateau is amount.