Leave a can of fizzy drink open and it goes flat, but the bubbles do not all escape: some carbon dioxide stays dissolved, and if you reseal the bottle the fizz partly returns. A kettle's limescale builds up over months, and a splash of vinegar dissolves it in minutes. A pot of milk goes off in days on the counter and in weeks in the fridge. In each case a chemical change is running in both directions, and in each case two separate questions are being asked at once.
The first question is how far: when the change has finished, what does the mixture look like? The second is how fast: how long until it gets there? A graduate in this course keeps them apart so automatically that it is hard to remember they were ever confused. The first is equilibrium. The second is kinetics. The most useful single sentence in this course is that they have almost nothing to do with each other.
- Who takes it
- Chemistry, biochemistry, chemical engineering, materials and environmental students, usually in year 2 in the American Chemical Society pattern and often in year 1 in the UK and Europe. Some programmes teach equilibrium inside General Chemistry and kinetics inside Physical Chemistry; others give them a course of their own.
- What it is for
- Predicting how far a reaction will go, how quickly, and what to change (temperature, pressure, a catalyst, a concentration) to move either.
- Comes after
- General Chemistry (35/36) and Calculus I (34/01); the rate equations are small differential equations.
- Leads to
- Organic Chemistry: Structure & Mechanism (35/38), Physical Chemistry (35/40), Analytical Chemistry & Spectroscopy (35/42) and Biochemistry (35/43).
- What this piece gives you
- You will not be able to derive an integrated rate law for a three-step mechanism. You will see why a fuel does not burn until you light it, why a buffer resists pH changes, and why a catalyst cannot make a hopeless reaction go. Easier first reads: The Science of Bread (14/07) and Entropy (13/12); the free-energy side of this story is in Thermodynamics (34/14).
Reactions run both ways, and K is the score
Take a simple change, A turning into B. Molecules of A turn into B at a rate proportional to how much A there is. But B also turns back into A, at a rate proportional to how much B there is. Early on there is only A, so the forward traffic dominates. As B builds, the reverse traffic grows. Eventually the two rates are equal: A is still turning into B and B back into A, but at the same speed, so the totals stop changing. That is dynamic equilibrium. Nothing has stopped; the traffic in each direction has matched.
For a general reaction aA + bB ⇌ cC + dD, K is [C]c[D]d ÷ [A]a[B]b measured at equilibrium. A large K means the products dominate; a small K, the reactants. Halfway through a reaction you can compute the same fraction with the current amounts, and call it Q, the reaction quotient. Q is where the mixture is; K is where it is going. If Q < K the reaction runs forward, if Q > K it runs back, and if Q = K it is done. Q versus K is the compass of this whole course.
A ⇌ B, first-order both ways, start with 1 M A. A(t) = Aeq + (1 − Aeq)e−(kf+kr)t. Notice that the time axis changes with the rate constants but the final split depends only on their ratio.
Try the four presets. "Fast, far" and "Slow, far" end at the same split, since K is 10 in both, and differ only in how long the journey takes. Keep that picture for the end of this piece. Also notice what K does not contain: no mention of time.
Le Chatelier: push a mixture and it pushes back
In 1884 Henri Le Chatelier gave the working rule: if you disturb a system at equilibrium, it shifts in the direction that partly undoes the disturbance. Add reactant and the mixture eats some of it. Squeeze a gas mixture and it moves toward the side with fewer gas molecules. Heat it and it moves in the direction that absorbs heat. The rule is a shorthand for comparing Q with K. Change a concentration or pressure and you change Q away from K; change the temperature and you change K itself.
The great example is the Haber process: N₂ + 3H₂ ⇌ 2NH₃. Fritz Haber showed it working in the laboratory in 1909, and Carl Bosch scaled it up at BASF's Oppau plant, which opened in 1913. Today the process produces on the order of 230 million tonnes of ammonia a year (a 2018 figure), most of it for nitrogen fertiliser. The reaction releases heat (ΔH = −92.28 kJ per mole of N₂) and shrinks four gas molecules to two. So Le Chatelier says: low temperature and high pressure favour ammonia. And the catch is that low temperature also makes the reaction painfully slow. Haber's legacy is double. He won the 1918 Nobel Prize in Chemistry (received in 1919) for the process that feeds a large part of humanity, and he also led Germany's chemical-weapons effort in the First World War, including the first large chlorine gas attack at Ypres in 1915. Both are true.
Kp = exp(−(ΔH − TΔS)/RT) with ΔH = −92.28 kJ and ΔS = −198.1 J/K per mole N₂, treated as constant; ideal gases; start from 1 N₂ : 3 H₂. At 200 bar real gases deviate (the ideal model overstates the yield), and plants run the loop with recycle and a catalyst, 300 to 500 °C and roughly 60 to 180 bar. The numbers show the trend, not a plant design.
Pin the state at 450 °C, then drag the temperature down: Q for the pinned mixture falls below the new, larger K, and the mixture shifts toward ammonia. Raise the pressure: Q falls again, same direction. Le Chatelier's rule is just that comparison made visible.
Acid–base equilibria and buffers
The weak acid of General Chemistry is an equilibrium: HA ⇌ H⁺ + A⁻, with Ka = [H⁺][A⁻] ÷ [HA]. A strong base added to a weak acid converts HA to A⁻ step by step, and the pH traces out a curve with a long flat stretch. That flat stretch is a buffer: a mixture of a weak acid and its conjugate base, which absorbs added acid (A⁻ takes the proton) or added base (HA gives one) with only a small shift in pH. Blood is buffered, so are cells, so is swimming-pool water, and so is a bottle of eye-drops.
The equation is an approximation and graduates know exactly where it breaks. It assumes the acid and its conjugate base are present in about their nominal amounts. That fails in very dilute solutions (the water supplies its own H⁺ and OH⁻) and near the very start or end of a titration. The tool below solves the full charge balance for the pH, so you can watch the two answers disagree.
Exact pH from the charge balance [Na+] + [H+] = [A-] + [OH-] at 25 °C, Kw = 10-14, ideal solution. Buffer capacity β = ln 10 ·([H+] + [OH-] + C·Ka[H+]/(Ka + [H+])²). The tool is a model of the calculation, not a laboratory procedure. pKa values are standard textbook figures (acetic 4.756).
Look at the half-way point (12.5 mL) for acetic acid at 0.1 M: the exact pH is 4.76, equal to the pKa, because exactly half the acid has become A⁻. Now drop the concentration to 0.001 M and move to 1 mL of base: Henderson–Hasselbalch says 3.38 and the true answer is 3.99. This is the first time you meet a rule that works in the textbook and fails in a real, dilute system.
Solubility: a salt's equilibrium with its own ions
A "insoluble" salt is really a very small K. Silver chloride in water is the standard example: AgCl(s) ⇌ Ag⁺ + Cl⁻. The equilibrium constant for dissolving a solid is the solubility product Ksp = [Ag⁺][Cl⁻] (the solid itself does not appear). With Ksp = 1.77 × 10⁻¹⁰ at 25 °C, a litre of water holds only 1.33 × 10⁻⁵ mole of AgCl, about 2 mg. The same logic runs the scale in a kettle (calcium carbonate), the shells of sea creatures, and why a tooth enamel dissolves slowly when the mouth turns acidic.
The new idea is the common-ion effect. Add chloride from another source and the product [Ag⁺][Cl⁻] would exceed Ksp, so the solid reforms and the dissolved silver drops. Le Chatelier again. At 0.1 M extra chloride, the AgCl that dissolves falls from 1.3 × 10⁻⁵ to 1.8 × 10⁻⁹ mol/L, thousands of times less.
Ksp at 25 °C: AgCl 1.77 × 10⁻¹⁰, BaSO₄ 1.1 × 10⁻¹⁰, CaF₂ 3.9 × 10⁻¹¹, PbI₂ 9.8 × 10⁻⁹ (published tables differ by tens of percent). Solved exactly: s(s + c) = Ksp for AgCl and BaSO₄; s(2s + c)² = Ksp for CaF₂ and PbI₂. Ideal solutions; complex ions and activity are ignored. Lead and barium salts are toxic: this is arithmetic, not a recipe.
Rate laws: what the speed depends on
Now the other question. The rate law says how the speed of a reaction depends on concentrations, and you find it by measurement, not by reading the balanced equation. In a first-order reaction the rate is proportional to the amount present: rate = k[A]. Bleach fading a stain, a drug being cleared from blood, a radioactive nucleus decaying: all first order, and all share a signature, a half-life that does not depend on how much you start with. In a second-order reaction the rate goes with the square: rate = k[A]². Here the half-life grows as the reactant thins out, because molecules must find each other. In a zero-order reaction the rate does not depend on concentration at all, as when a catalyst surface or an enzyme is saturated.
Integrated rate laws with k in the units each order needs (M/s, 1/s, 1/(M·s)); the time axis rescales to show about four half-lives (zero order: until it runs out).
The practical use: plot the data three ways. If ln[A] against time is a straight line, the reaction is first order. If 1/[A] against time is straight, it is second order. If [A] itself is straight, zero order. A graduate reads a rate from a graph the way you read a speed from a speedometer.
Activation energy, Arrhenius and catalysts
Why do reactions that are strongly favoured still take time? Because molecules must pass over an energy barrier on the way from reactants to products: bonds must start breaking before new ones pay back. The barrier height is the activation energy Ea. Most molecules at room temperature do not have enough energy; the few in the high tail of the energy distribution do. In 1889 Svante Arrhenius (Nobel Prize in Chemistry 1903, for his theory of electrolytic dissociation), building on van 't Hoff's 1884 work, wrote down how the rate constant depends on temperature.
The exponential is brutal. For Ea = 50 kJ/mol, warming from 25 °C by just 10 K multiplies the rate by about 1.9, the origin of the "rate doubles every ten degrees" rule of thumb, which is true only for barriers of this size. For a higher barrier, the multiplier is larger. And a catalyst works by offering a different path with a lower barrier. Dropping Ea from 75 to 50 kJ/mol at 298 K multiplies the rate by about 24,000. It does this without being used up and, crucially, without touching the start and end points. The experimental window on all this opened in the 1980s and 1990s: Ahmed Zewail, who received the 1999 Nobel Prize in Chemistry for his work on femtochemistry, used ultrashort laser flashes to watch molecules while they pass through the "transition state" at the top of the barrier, in real time.
k = A·exp(−Ea/RT) with an illustrative A = 1013 s-1 (typical for a unimolecular step); half-life for a first-order step. The curve is a schematic of the barrier and its lowered version, drawn to scale in height only. Catalyst floor is 5 kJ/mol.
Fast and far are different questions
Put the two halves together and you get a 2 × 2 table. A reaction can be far and fast (acid meets base), far and slow (iron rusting in dry air, or a diamond turning into graphite, which is thermodynamically downhill by about 3 kJ/mol and so slow it is immeasurable), not far and fast (a mixture that flicks to a small equilibrium in a blink), or not far and slow (nothing to see). K tells you where the arrow ends. Ea tells you how long the trip takes. A catalyst changes only the second. Heat changes both, which is why industry has to compromise.
Pick an answer; the explanation follows. Diamond to graphite: ΔG ≈ −2.9 kJ/mol at 25 °C and 1 bar (standard textbook tables).
What a graduate just sees
- Every reaction is a two-way road; "complete" really means K is huge.
- Compare Q with K and you know which way the mixture will move.
- K says how far and the rate law says how fast; neither predicts the other.
- A catalyst speeds up the road in both directions and never changes where it ends.
- Warming a reaction speeds it up exponentially; if it is exothermic, it also lowers the yield at equilibrium.
- A buffer is a weak acid and its partner in balance; it works best at pH ≈ pKa.
- "Insoluble" means a very small Ksp; adding a shared ion pushes the solid back out.
- The order of a reaction is measured, not read off the equation; a first-order half-life is constant.
Where it shows up next
- Organic Chemistry (35/38): SN1 is first order and SN2 second order, and that difference in rate law is how chemists first proved the mechanisms differ.
- Physical Chemistry (35/40): K is derived from free energy, and the Arrhenius A and Ea from collision and transition-state theory.
- Analytical Chemistry (35/42): titrations, buffers and Ksp are the analyst's everyday tools.
- Biochemistry (35/43): enzymes are catalysts that lower barriers by a factor of millions; blood pH and the buffer systems of cells are this piece applied.
- In the world: fertiliser plants, drug shelf-life, water treatment, the cooling of ocean-acidified shells, and the choice between a fridge and a freezer.
If you want to go deeper
- 📘 Free textbook. OpenStax, Chemistry 2e, chapters on kinetics, equilibrium and acid–base. openstax.org
- 📘 Textbook. Brown et al., Chemistry: The Central Science (Pearson), or Atkins and de Paula's Physical Chemistry when you want the thermodynamic derivation behind K.
- 📘 Gentler. Peter Atkins, Reactions: The Private Life of Atoms (Oxford, 2011): a book-length tour of why reactions go.
- 🌐 Free course. MIT OpenCourseWare 5.60 Thermodynamics & Kinetics (Spring 2008).
Every reaction asks two independent questions. The equilibrium constant says where the mixture ends up; the rate law and the energy barrier say how soon it gets there. Compare Q with K to know the direction; remember that a catalyst changes only the speed.
Try this: this week, notice one thing that is "favoured but slow" in your kitchen (an apple browning, bread going stale, sugar sitting unburnt in a bowl) and one thing a cold fridge slows down (milk). The first is a barrier; the second is Arrhenius.
Sources. Equilibrium, Le Chatelier (1884), Ksp, the Henderson–Hasselbalch equation and rate laws are standard textbook chemistry (OpenStax Chemistry 2e). The Arrhenius equation was proposed in 1889 (Wikipedia, Arrhenius equation); Arrhenius's Nobel Prize in Chemistry was in 1903. Haber process: demonstrated 1909, first industrial plant 1913, ΔH = −92.28 kJ/mol, ~230 million tonnes of ammonia in 2018 (Wikipedia, Haber process); Haber's Nobel Prize in Chemistry for 1918 was awarded in 1919 (Wikipedia, Fritz Haber). Zewail: 1999 Nobel Prize in Chemistry for femtochemistry (nobelprize.org via Wikipedia). Ksp values vary between tables (Wikipedia Solubility equilibrium; Engineering Toolbox; University of Wisconsin tables). Not laboratory instruction.
- 🌐 OpenStax Chemistry 2e
- 🌐 MIT OCW 5.60 Thermodynamics & Kinetics
- 📘 Peter Atkins, Reactions: The Private Life of Atoms