Some reactions take a split second, others take centuries
An explosion is over in an instant, iron takes days or years to rust, and rocks take thousands of years to weather. Chapter 2.10 asked how much energy a reaction releases or absorbs. This chapter asks how fast reactions go, and why some are fast and others slow.
Reaction rate
The reaction rate化学反应速率 is how fast the concentration of a reactant falls or a product rises:
The minus sign makes the rate positive for a reactant, whose concentration is falling. Units are usually M/s (mol/(L·s)). Calculated over a time interval, this is an average rate.
In one reaction, different substances change at different rates, in the ratio of their coefficients. In N₂ + 3H₂ ⇌ 2NH₃, H₂ is used up three times as fast as N₂, and NH₃ forms twice as fast as N₂ is used up.
Collision theory
To react, molecules must first collide. But gas molecules collide billions of times per second; if every collision led to reaction, every gas reaction would be over instantly. In fact most collisions just bounce the molecules apart. A collision that does lead to reaction is an effective collision有效碰撞, and it needs two things:
- Enough energy: the molecules must collide hard enough to start breaking the old bonds.
- The right orientation: they must hit so that the parts that react come into contact.
The minimum energy needed for an effective collision is the activation energy活化能, Ea. The larger Ea is, the smaller the fraction of molecules with enough energy, and the slower the reaction.
As you saw in 2.8.7, at any temperature molecules have a range of speeds and energies. Only the most energetic few can get over the activation-energy barrier.
In the model below, change the temperature, the activation energy, and the number of particles, and watch how often collisions happen and how many are effective. “Skip ahead 10 s” jumps straight to the result:
Reaction energy diagrams
A reaction energy diagram shows how the energy of the system changes during a reaction. The reactants rise to a high-energy, unstable arrangement called the transition state过渡态 (or activated complex), then fall to the products.
- The rise from the reactants to the transition state is the forward activation energy, Ea.
- The rise from the products to the transition state is the reverse activation energy.
- Their difference is the enthalpy change from 2.10: ΔH = Ea(forward) − Ea(reverse).
Activation energy controls how fast a reaction goes. ΔH controls whether it releases or absorbs heat. They are different quantities.
Drag the sliders to change the activation energy and ΔH, then add a catalyst (lesson 2.11.2) to compare:
How Chinese textbooks differ
- Chinese textbooks define activation energy as the difference between the average energy of the “activated molecules” (活化分子, molecules energetic enough to react) and the average energy of all the reactant molecules. US textbooks call it the minimum energy needed to react. At this level both mean the height from reactants to the transition state on the energy diagram.
- Chinese textbooks label the forward and reverse activation energies E₁ and E₂ and write ΔH = E₁ − E₂.
- Chinese textbooks write rates as v(NH₃) in mol/(L·s) or mol/(L·min), always positive, without the minus sign.
Example 1: calculating rates
In a 2.0 L container, N₂ + 3H₂ ⇌ 2NH₃ forms 0.80 mol of NH₃ in 2.0 min. Find the average rate of formation of NH₃, and the rates at which N₂ and H₂ are used up.
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The definition. Average rate = Δ[concentration] ÷ Δt. It uses the change in molarity, not in moles, so divide by the volume first.
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Change in [NH₃].
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Rate of formation of NH₃.
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Use the coefficients. In one reaction, the rates of the species are in the ratio of their coefficients, N₂ : H₂ : NH₃ = 1 : 3 : 2:
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Think about it. Three different numbers describe how fast the same reaction goes, so always say which substance a rate refers to.
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A common mistake. Skipping the volume: 0.80 mol ÷ 2.0 min = 0.40 mol/min is not a rate in M/min.
Example 2: reading an energy diagram
A reaction has a forward activation energy of 120 kJ/mol and ΔH = −60 kJ/mol. (a) What is the reverse activation energy? (b) Is the reaction exothermic or endothermic? (c) How does a catalyst change Ea and ΔH?
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What the diagram shows. The forward barrier is the climb from the reactants to the peak; the reverse barrier is the climb from the products to the same peak. Their difference is the energy gap between reactants and products: ΔH = Ea(forward) − Ea(reverse).
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Reverse activation energy. Rearranging:
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Exothermic or endothermic. ΔH < 0: the products are lower in energy than the reactants, so it is exothermic. The reverse barrier is higher than the forward one.
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Catalyst. A catalyst provides a different pathway that lowers both barriers, but it doesn’t change the energies of the reactants and products, so ΔH stays the same.
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Check. 120 − 180 = −60 kJ/mol, which is ΔH.
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A common mistake. Writing Ea(reverse) = 120 + (−60) = 60 kJ/mol. For an exothermic reaction the products sit lower, so the climb back up is longer, not shorter.
- N₂ + 3H₂ ⇌ 2NH₃: N₂ is used up at 0.1. How fast is H₂ used up?
H₂ : N₂ = 3 : 1, so 0.3.
- Same reaction: how fast does NH₃ form?
NH₃ : N₂ = 2 : 1, so 0.2.
- N₂ + 3H₂ ⇌ 2NH₃: NH₃ forms at 0.4. How fast is H₂ used up?
H₂ : NH₃ = 3 : 2, so 0.4 × 3/2 = 0.6.
- 2SO₂ + O₂ ⇌ 2SO₃: SO₂ is used up at 0.2. How fast is O₂ used up?
SO₂ : O₂ = 2 : 1, so 0.1.
- 2SO₂ + O₂ ⇌ 2SO₃: SO₃ forms at 0.1. How fast is O₂ used up?
SO₃ : O₂ = 2 : 1, so 0.05.
- In a 2 L flask, 0.8 mol of A is used up in 2 min. Rate for A?
Δ[A] = 0.4 M, and 0.4 ÷ 2 = 0.2.
- In a 0.5 L flask, 0.15 mol of B forms in 1 min. Rate for B?
Δ[B] = 0.15 ÷ 0.5 = 0.3 M, and 0.3 ÷ 1 = 0.3.
- A + 3B ⇌ 2C: B is used up at 0.6. How fast is A used up?
A : B = 1 : 3, so 0.2.
Common mistakes
Mistake 1: “Every collision between reactant molecules leads to a reaction.” Most collisions are ineffective. Only collisions with enough energy and the right orientation react.
Mistake 2: “A higher activation energy means the reaction releases more heat.” Activation energy is the barrier on the energy diagram and controls the rate. ΔH is the energy difference between reactants and products. The two aren’t directly related.
Mistake 3: “A reaction has one rate, whichever substance you measure.” The rate depends on which substance you follow: in N₂ + 3H₂ ⇌ 2NH₃, H₂ is used up three times as fast as N₂. Always say which substance a rate refers to.
Quick check
Which statement about effective collisions is correct?
An effective collision is one that leads to reaction. Even energetic molecules must collide with the right orientation.
A reaction has a forward activation energy of 80 kJ/mol and a reverse activation energy of 200 kJ/mol. What is ΔH?
ΔH = Ea(forward) − Ea(reverse) = 80 − 200 = −120 kJ/mol. ΔH < 0, so the reaction is exothermic.
Summary
- Reaction rate is the change in concentration per unit time, in M/s or M/min. In one reaction, the rates for different substances are in the ratio of their coefficients.
- An effective collision needs enough energy and the right orientation. Activation energy is the minimum energy needed; the higher it is, the slower the reaction.
- On an energy diagram, ΔH = Ea(forward) − Ea(reverse). Ea controls the rate, ΔH the heat.
On to AP (for later)
AP topic 5.1 defines rate from concentration changes over time and relates the rates of different species through coefficients. The collision model in topic 5.5 asks for both conditions, enough energy and correct orientation. Topic 5.6 asks you to draw or read a reaction energy profile and label Ea and ΔH. Later in Unit 5 come rate laws and reaction mechanisms, which build on this lesson.