Topic 5.1 Notes – Reaction Rates

1. What Reaction Rate Is

Kinetics is the study of reaction rates. A reaction rate tells you how quickly reactants are converted into products.

Quantitatively, rate is defined as change in concentration per unit time.

For a reactant:

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

For a product:

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

A few things to notice:

• The negative sign for reactants keeps the rate positive since reactant concentration decreases.
• Units are usually mol L⁻¹ s⁻¹ (M/s).
• Rate is about concentration, not moles. If volume changes, concentration changes too.

Quick example:

If $[\ce{NO2}]$ drops from 0.80 M to 0.65 M in 10.0 s:

$$\text{Rate} = -\frac{0.65 - 0.80}{10.0} = 0.015\ \text{M/s}$$

The negative inside cancels with the formula’s negative. Final rate is positive.

2. How Rate Appears on Graphs

Here’s a typical concentration vs. time graph for a reaction:

Concentration vs. time for a reactant and products

On this graph:

• The reactant ($\ce{N2O}$) slopes down as it is consumed.
• The products ($\ce{N2}$ and $\ce{O2}$) slope up as they form.
• The slope of any line represents the rate.

Average Rate

This is the slope between two points:

$$\text{Average rate} = \frac{\Delta[\ ]}{\Delta t}$$

It depends on the time interval you choose. Early in a reaction, it’s usually larger because concentrations are higher.

Instantaneous Rate

This is the slope of a tangent line at one point. It represents the rate at that exact moment.

On AP-style questions, if they give you two time points, you’re finding average rate. If they show a tangent line drawn at a point, that’s instantaneous rate.

As time passes, slopes get flatter. That means the reaction is slowing down because reactants are being used up.

3. Stoichiometry and Relative Reaction Rates

The balanced equation controls how the rates of different substances are related.

For a general reaction:

$$\ce{aA + bB -> cC + dD}$$

The rate relationships are:

$$\text{Rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = \frac{1}{c}\frac{\Delta[C]}{\Delta t} = \frac{1}{d}\frac{\Delta[D]}{\Delta t}$$

The coefficients act like conversion factors.

Example:

$$\ce{2H2(g) + O2(g) -> 2H2O(g)}$$

If $[\ce{H2}]$ decreases at 0.040 M/s, then:

• Hydrogen coefficient = 2
• Oxygen coefficient = 1

So oxygen is consumed at half the rate:

$$\text{Rate of } \ce{O2} = 0.020\ \text{M/s}$$

You’re using mole ratios, just like stoichiometry in Unit 4. If the equation isn’t balanced, the rate relationships will be wrong. That’s a common mistake on free-response questions.

4. Factors That Affect Reaction Rate

Reaction rate depends on how often particles collide and whether those collisions have enough energy.

Concentration

Higher concentration means:

• More particles in the same volume
• More frequent collisions
• Faster reaction

For gases, increasing pressure increases concentration, which increases rate.

Temperature

Temperature measures average kinetic energy.

When temperature increases:

• Particles move faster
• Collisions happen more often
• Collisions are more energetic

More collisions exceed activation energy, so rate increases. Temperature changes usually have the strongest effect in lab data.

Surface Area

For reactions involving solids:

• Powdered solid reacts faster than a chunk.
• More exposed surface means more collision sites.

This only matters when a solid is involved.

Catalysts

A catalyst:

• Increases rate
• Is not consumed
• Provides an alternative pathway
• Lowers activation energy

It does not change ΔH or the equilibrium position. It speeds up forward and reverse reactions equally.

Other Environmental Factors

• Nature of reactants. Ionic reactions in solution are often fast. Reactions breaking strong covalent bonds are slower.
• Solvent effects.
• Physical state. Gas-phase reactions tend to be faster than solid-phase ones.