Chemistry 102

Rate of reaction

change in the amount of reactant or product per unit of time

rate expression formula (measuring reactant)

- change in concentration of reactant / time interval

What is chemical kinetics?

The study of reaction rates, factors affecting rates, and reaction mechanisms.

What is the rate of a chemical reaction?

The change in reactant or product concentration per unit time.

What are the usual units of reaction rate?

M/s, M/min, or another concentration-per-time unit

How is the average rate of disappearance of A calculated?

Rate of disappearance = −Δ[A]/Δt.

How is the average rate of formation of a product P calculated?

Rate of formation = Δ[P]/Δt.

Why is there a negative sign in the reactant rate expression?

Reactant concentration decreases, so the negative sign makes its disappearance rate positive.

What is the difference between average and instantaneous rate?

Average rate spans a time interval; instantaneous rate is the slope at one instant.

What is the initial reaction rate?

The instantaneous rate at t = 0, before substantial reactant depletion.

Why does reaction rate often decrease as time passes?

Reactant concentrations usually decrease, reducing the frequency of productive collisions.

What five factors commonly affect reaction rate?

Chemical nature, surface area, temperature, concentration, and catalysts.

How does increasing concentration usually affect reaction rate?

It often increases rate, but the dependence is determined experimentally.

Why can powdered solids react faster than large lumps?

Powders expose more surface area for contact and reaction.

How does increasing temperature usually affect reaction rate?

More molecules can overcome the activation-energy barrier, usually increasing rate.

What is a rate law?

An experimentally determined equation relating reaction rate to reactant concentrations.

What is the general rate law for aA + bB → products?

Rate = k[A]^m[B]^n.

What does k represent in a rate law?

The rate constant at a specified temperature for the stated reaction and rate law.

Can rate-law exponents be read from an overall balanced equation?

No. They must be determined experimentally unless the equation describes an elementary step.

What is the reaction order with respect to A?

The exponent m in the rate law, Rate = k[A]^m[B]^n

What is the overall reaction order?

The sum of all reactant exponents in the rate law, m + n.

What does zero order in A mean?

Changing [A] alone does not change the rate under the stated conditions.

What does first order in A mean?

Rate is directly proportional to [A], with other concentrations fixed.

What does second order in A mean?

Rate is proportional to [A]^2, with other concentrations fixed.

If [A] doubles for a first-order reaction, what happens to rate?

The rate doubles.

If [A] doubles for a second-order reaction, what happens to rate?

The rate increases by a factor of four.

If [A] doubles for a zero-order reaction, what happens to rate?

The rate remains unchanged, assuming zero-order behavior persists.

If [A] triples for a third-order dependence on A, what happens to rate?

The rate increases by a factor of 27.

How can initial-rate experiments determine reaction order?

Compare experiments where one reactant concentration changes while others remain constant.

For Rate = k[A]^m, how can m be found from two experiments?

m = ln(rate₂/rate₁) / ln([A]₂/[A]₁), if other factors are constant.

If doubling [A] quadruples the rate, what is the order in A?

Second order, because 2^m = 4 gives m = 2.

If doubling [A] leaves rate unchanged, what is the order in A?

Zero order, because 2^m = 1 gives m = 0.

How do you calculate k from a rate law?

Rearrange the experimentally determined rate law and substitute measured rates and concentrations.

Do product concentrations normally appear in a forward rate law?

Not when the measured rate is described by a forward reaction with negligible reverse contribution; reversible net rates may include products.

What is a differential rate law?

An equation showing how the instantaneous rate depends on concentrations.

What is an integrated rate law?

An equation relating reactant concentration to elapsed time.

How are differential and integrated rate laws related?

The integrated form is obtained by integrating the differential rate equation under its assumptions

What is the integrated rate law for a zero-order reaction?

[A]t = [A]₀ − kt

What is the integrated rate law for a first-order reaction?

ln[A]t = ln[A]₀ − kt, or [A]t = [A]₀e^(−kt).

What is the integrated rate law for a second-order reaction in A?

1/[A]t = 1/[A]₀ + kt.

Which plot is linear for a zero-order reaction?

[A] versus time; slope = −k.

Which plot is linear for a first-order reaction?

ln[A] versus time; slope = −k.

Which plot is linear for a second-order reaction in A?

1/[A] versus time; slope = +k.

How can a concentration-time graph identify reaction order?

Check which of [A], ln[A], or 1/[A] versus time gives a straight line

What is the y-intercept of a first-order ln[A] versus time plot?

ln[A]₀.

How do you calculate first-order k from two concentration measurements?

k = ln([A]₀/[A]t)/t.

How do you calculate zero-order k from two concentrations?

k = ([A]₀ − [A]t)/t.

How do you calculate second-order k from two concentrations?

k = (1/[A]t − 1/[A]₀)/t.

What are the units of k for a zero-order reaction?

Concentration/time, such as M·s⁻¹.

What are the units of k for a first-order reaction?

Time⁻¹, such as s⁻¹.

What are the units of k for a second-order reaction?

Concentration⁻¹·time⁻¹, such as M⁻¹·s⁻¹.

What is the general unit rule for k for an overall order n?

(Concentration)^(1−n) × time⁻¹, when rate units are concentration/time.

What is the half-life of a reaction?

The time required for a reactant concentration to fall to half its starting value.

What is the first-order half-life equation?

t₁/₂ = ln 2/k ≈ 0.693/k.

Does first-order half-life depend on initial concentration?

No. For a first-order reaction, half-life is independent of [A]₀.

What is the zero-order half-life equation?

t₁/₂ = [A]₀/(2k), provided the reaction remains zero order.

What is the second-order half-life equation for Rate = k[A]^2?

t₁/₂ = 1/(k[A]₀).

How does successive half-life behavior distinguish reaction orders?

First order: equal half-lives; zero order: half-lives shorten; second order: half-lives lengthen.

A first-order reaction has k = 0.20 s⁻¹. What is its half-life?

t₁/₂ = 0.693/0.20 = 3.47 s.

A first-order reaction has k = 0.10 min⁻¹. What fraction remains after 20 min?

[A]t/[A]₀ = e^(−kt) = e^(−2) ≈ 0.135, or 13.5%.

What does a reaction's rate constant tell you?

The proportionality between rate and concentration terms at a given temperature.

Does k change as reactant concentration changes?

For a given reaction under fixed conditions, k is independent of concentration; temperature and conditions can change it.

For a given reaction under fixed conditions, k is independent of concentration; temperature and conditions can change it.

The energy barrier reactants must overcome to reach the transition state.

What is the Arrhenius equation?

k = Ae^(−Ea/RT).

What does A represent in the Arrhenius equation?

The pre-exponential factor, reflecting collision frequency and other molecular factors.

What are the units of R in the Arrhenius equation?

Use 8.314 J·mol⁻¹·K⁻¹ when Ea is in J/mol.

Why must temperature be in kelvin in the Arrhenius equation?

The equation requires absolute temperature.

What is the linearized Arrhenius equation?

ln k = −(Ea/R)(1/T) + ln A.

What does an Arrhenius plot graph?

ln k on the y-axis against 1/T in K⁻¹ on the x-axis.

What is the slope of an Arrhenius plot?

−Ea/R.

How do you calculate Ea from an Arrhenius-plot slope?

Ea = −R × slope.

What is the y-intercept of an Arrhenius plot?

ln A.

What is the two-temperature Arrhenius equation?

ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂).

How does increasing temperature affect the Arrhenius rate constant?

It usually increases k because a larger fraction of molecules can overcome Ea.

What does e^(−Ea/RT) represent approximately?

The Boltzmann factor describing the energetic fraction associated with overcoming the barrier.

What is the effect of a larger activation energy at the same temperature?

The rate constant is generally smaller, assuming the pre-exponential factor is comparable.

If Ea = 0, what is the Arrhenius exponential factor?

e^0 = 1.

What is a reaction mechanism?

A proposed sequence of elementary steps that explains the overall chemical reaction.

What is an elementary step?

A single molecular event represented as one step in a reaction mechanism.

What is molecularity?

The number of reacting entities participating in one elementary step.

What is a unimolecular elementary step?

One reacting entity, such as A → products.

What is a bimolecular elementary step?

Two reacting entities, such as A + B → products or A + A → products.

Why are termolecular elementary steps rare?

Three particles simultaneously colliding with suitable energy and orientation is unlikely.

How is the rate law written for an elementary step?

Reactant concentration exponents match that step's stoichiometric coefficients.

Can the elementary-step rule be applied to the overall reaction?

No, unless the overall reaction itself is a single elementary step.

What two requirements must a valid mechanism satisfy?

Its steps must sum to the overall stoichiometry and agree with the experimental rate law.

What is an intermediate in a reaction mechanism?

A species formed in one step and consumed in a later step, absent from the net equation.

What is the rate-determining step?

The step that limits the overall reaction rate under the mechanism's conditions.

If the first elementary step is slow, how is the overall rate often estimated?

By the rate law of that slow step, if it directly controls the observed rate.

Why can a fast first step complicate a rate law?

A rapidly established pre-equilibrium may require expressing intermediate concentrations using equilibrium relationships.

What is the pre-equilibrium approximation?

Assuming a fast reversible step equilibrates before a slower subsequent step.

What is the steady-state approximation?

Assuming an intermediate's concentration changes very little because its formation and consumption nearly balance.

How do you obtain the net reaction from elementary steps?

Add the steps and cancel species appearing on both sides.

What is the difference between an intermediate and a catalyst?

An intermediate is formed then consumed; a catalyst is consumed in a step and regenerated later.

What does equilibrium mean for a reversible elementary step?

Forward and reverse rates are equal, so there is no net change in composition.

What is effective molecular orientation?

The alignment needed during a collision for bonds to break or form productively.

What is collision theory?

Reaction requires collisions with sufficient energy and suitable orientation.

What is the role of the orientation factor in collision theory?

It accounts for the fraction of collisions with productive molecular geometry.

How is the Arrhenius pre-exponential factor sometimes refined?

Collision theory often writes A = pZ, where Z is collision frequency and p is an orientation factor.

What is a catalyst?

A substance that increases reaction rate through an alternative pathway and is regenerated overall.