Kinetics

This is Unit Nine of Chemistry, Part One: rates, rate laws and integrated rate laws. Every unit so far has asked what a reaction produces or how far it goes. This one asks how fast, which turns out to be a separate question with separate machinery. The through-line is that speed cannot be read off a balanced equation. The equation tells you what reacts and in what proportion; it tells you nothing about how quickly, and the central correction of this unit is that a rate law's exponents have to be measured rather than copied from the coefficients sitting right there. By the end you will be able to say why a reaction rate is reported positive; say where a rate law's exponents come from; say what the method of initial rates requires of its trials; say how the three integrated rate laws are told apart; and say which order has a constant half-life.

Four entries. The definition and a sign convention that looks like a fudge and is not, how the rates of different substances in one reaction relate to each other, and three different things the word "rate" can mean.

Change over time.

Chem 1601 Reaction Rate Defined

A reaction rate is a reactant's or product's concentration change divided by elapsed time, reported as a positive quantity. A reactant's concentration falls as the reaction runs, so its change is negative — and the rate definition flips that sign deliberately, so every rate for one reaction comes out positive and comparable.

Tied by coefficients.

Chem 1604 Relative Reaction Rates from Stoichiometry

In one reaction, every substance's rate of change relates to every other's through the balanced equation's stoichiometric coefficients. Two substances in the same reaction rarely change concentration at equal rates — only equal coefficients produce equal rates, and a substance with a coefficient of two changes twice as fast as one with a coefficient of one.

One shared value.

Chem 1607 Writing Relative Rate Expressions from a Balanced Equation

Writing a reaction's relative rate expressions means dividing each substance's concentration-change rate by its own stoichiometric coefficient, with reactant terms carrying a negative sign, so that every resulting term equals the same positive overall rate. Forgetting the negative sign on a reactant, or dividing by another substance's coefficient, produces a term that does not match the others.

Three kinds.

Chem 1610 Average, Instantaneous, and Initial Rate

An average rate spans a measured interval, an instantaneous rate holds at one moment, and an initial rate is the instantaneous rate at the very start. An average rate over a long interval can differ substantially from the initial rate, since reactions slow as their reactants are consumed.

Five entries, five factors. What the substances are, what physical state they are in, how hot they are, how concentrated they are, and whether anything is present to help — that last one previewed here and taken up properly in Part Two.

What is reacting.

Chem 1615 Reactant Identity and Reaction Rate

Two reactions that look structurally similar can proceed at very different rates, because rate depends on the chemical identity of the specific substances involved. Predicting that sodium and iron react at comparable rates in air, both being a metal reacting with oxygen, ignores how differently reactive the two metals are.

Where they meet.

Chem 1618 Physical State and Surface Area

A reaction between different phases occurs only at the interface where they meet, so dividing a solid into smaller pieces speeds it up by exposing more of that interface. More surface area speeds a heterogeneous reaction only where the phases actually meet — total mass does not itself set the rate.

Warmer, faster.

Chem 1621 Temperature and Reaction Rate

A reaction's rate rises as temperature rises, because more reactant molecules gain enough energy to react as the sample warms. How much a given reaction speeds up per degree is specific to that reaction, not a fixed factor every reaction shares — which is what Part Two's activation-energy material quantifies.

More crowded.

Chem 1624 Concentration and Reaction Rate

Raising a reactant's concentration usually raises a reaction's rate, since more particles per unit volume means more collisions between them. The word "usually" is carrying weight: exactly how a rate responds to concentration is a separate, experimentally determined question, which the next topic takes up.

Helped along.

Chem 1627 Catalysis Previewed as a Rate Factor

A catalyst is a substance that increases a reaction's rate without itself being permanently consumed. It can appear to be consumed partway through, since it often participates in an intermediate step, but a true catalyst always reappears unchanged once the reaction completes. Part Two takes up how it works.

Six entries, and the centre of the unit. The equation relating rate to concentration, what its exponents are called, the correction this unit exists to deliver about where those exponents come from, and the experimental method that actually produces them.

Rate from concentration.

Chem 1632 The Rate Law and Reaction Order

A rate law expresses a reaction's rate as its rate constant multiplied by each reactant's concentration raised to that reactant's reaction order. An order is usually a small positive integer, but nothing guarantees that — it can be a fraction, zero, or even negative, and which it is has to be established rather than assumed.

Add the exponents.

Chem 1635 Overall Reaction Order

A reaction's overall order is the sum of the individual orders of every reactant appearing in its rate law. The sum uses the exponents actually written: a reactant absent from the rate law contributes zero to the overall order, not one, since its concentration does not affect the rate at all.

Measured, not read off.

Chem 1638 Rate Laws Come From Experiment, Not Stoichiometric Coefficients

A rate law's reaction orders are determined by experiment and never predicted from a balanced equation's stoichiometric coefficients. Where an order does happen to match its coefficient in an overall equation, that is coincidence — only experiment establishes what the order actually is.

The tempting shortcut.

Chem 1641 The Stoichiometric-Coefficient Misreading of a Rate Law

Copying a balanced equation's coefficients into a rate law's exponents is an error, because only an elementary step — a single collision event — works that way. The shortcut fails for most reactions, which proceed through a sequence of elementary steps that an overall equation cannot reveal.

Vary one, hold the rest.

Chem 1644 Determining a Rate Law by the Method of Initial Rates

Determining a rate law by the method of initial rates means comparing trials in which one reactant's concentration changes while the others are held constant, using the ratio of rates against the ratio of concentrations to solve for each order, then substituting one full trial back to find the rate constant. Comparing two trials where more than one concentration changed makes the order impossible to isolate — only a pair differing in exactly one reactant works.

The constant's units.

Chem 1649 Rate Constant Units Vary With Overall Order

A rate constant's units depend on the reaction's overall order, because the constant is what converts the concentration terms into a rate — and different orders leave different powers of concentration to convert. Quoting a rate constant without its units leaves it ambiguous, since the same number could describe reactions of different orders.

Six entries. A rate law says how fast a reaction is going right now; an integrated rate law says how much is left after a given time. There is one for each order, and each is identified by which plot of the data comes out straight.

Concentration against time.

Chem 1654 The Integrated Rate Law

An integrated rate law relates a reactant's concentration directly to elapsed time, which lets either a concentration or a time be calculated from the other. A rate law and its integrated form answer two different questions about one reaction — how fast it is going, against how much remains.

A log plot.

Chem 1657 The First-Order Integrated Rate Law

For a first-order reaction, the natural log of concentration falls linearly with time, so plotting ln of concentration against time gives a straight line. A curved plot rules first order out — it does not merely weaken the case, since linearity here is the defining test.

Which fraction.

Chem 1660 Solving the First-Order Integrated Rate Law for Time or Concentration

Solving the first-order law for an unknown time or concentration means substituting the rate constant and both concentration values into the logarithmic form, then rearranging for whichever is unknown, with both concentrations in the same unit before the log is taken. Substituting the fraction decomposed instead of the fraction remaining inverts the ratio inside the logarithm and gives a wrong time.

A reciprocal plot.

Chem 1663 The Second-Order Integrated Rate Law

For a reaction second order in one reactant, the reciprocal of concentration rises linearly with time, so plotting one over concentration against time gives a straight line. Checking only one order's plot risks a false match — comparing both plots is what actually distinguishes first order from second.

Add to the reciprocal.

Chem 1666 Solving the Second-Order Integrated Rate Law

Solving the second-order law for a later concentration means substituting the initial concentration, the rate constant and the elapsed time into the reciprocal form, then taking the reciprocal of the result to recover the concentration itself. Adding the rate-constant term to the concentration rather than to its reciprocal is the step most often reversed — this law is linear in one over concentration, never in concentration.

A straight fall.

Chem 1669 The Zero-Order Integrated Rate Law

For a zero-order reaction, concentration falls linearly with time at a constant rate, independent of how much reactant remains — so the plot of concentration itself against time is the straight one. A constant rate is not an unlimited one: a zero-order reaction still stops once its reactant is consumed.

Three entries closing the part. The interval it takes for half the reactant to disappear, why that interval behaves differently for different orders, and the shortcut that follows for one order only.

Down to half.

Chem 1672 Half-Life Defined

A reaction's half-life is the interval over which the reactant concentration drops to one-half of its value. Each half-life removes half of whatever remains at its start, not half of the original starting amount — which is why two half-lives leave a quarter rather than nothing.

Constant, or not.

Chem 1675 Half-Life's Order Dependence

A first-order half-life stays constant throughout a reaction, so it takes the same time to go from full to half as from half to a quarter. Second- and zero-order half-lives change as concentration falls. Assuming every half-life is constant, by analogy with the first-order case, gives a wrong answer for the other orders.

One shortcut.

Chem 1678 Calculating a First-Order Rate Constant From a Measured Half-Life

Calculating a first-order rate constant from a measured half-life means substituting that half-life into k equals 0.693 over the half-life, where 0.693 is the natural log of two. The shortcut holds for first-order reactions only — applying it to a second- or zero-order half-life produces a rate constant with no correct meaning.

Five things to carry out of this part. A reaction rate is reported positive by convention: a reactant's concentration falls, so its change is negative, and the definition flips that sign so every substance's rate in one reaction comes out positive and comparable once divided by its own coefficient. A rate law's exponents come from experiment and nowhere else — they are not the balanced equation's coefficients, and copying those coefficients into the exponents works only for an elementary step, a single collision event, which most reactions are not. The method of initial rates requires trials that differ in exactly one reactant's concentration: comparing two trials where more than one concentration changed leaves the orders impossible to separate. The three integrated rate laws are told apart by which plot of the data is straight — concentration against time for zero order, the natural log of concentration for first order, and the reciprocal of concentration for second — and comparing the plots rather than checking one is what distinguishes them. And the constant half-life belongs to first order alone: it takes the same time to fall from full to half as from half to a quarter, while second- and zero-order half-lives change as concentration falls. Part Two takes up why reactions have rates at all — collision theory, activation energy, mechanisms and catalysis.