AP Chemistry 5.1: Reaction Rates and Unit 5 Review

Kinetics is the study of how fast chemical reactions occur and why some reactions happen much faster than others. In earlier units, you mainly focused on what substances are made of and how much product can form. Kinetics asks a different question:

• How quickly does the reaction happen?
• Two reactions can both be chemically possible but occur at completely different speeds. Combustion reactions can happen extremely quickly once started, while other reactions may take hours, days, or even years.
• The major ideas in Unit 5 all connect. Reaction rates measure how quickly concentrations change. Rate laws show how reactant concentration affects reaction speed. Integrated rate laws connect concentration and time. Reaction mechanisms describe the individual steps that actually occur. Collision theory and activation energy explain why reactions need successful collisions, and catalysts speed reactions up by providing a different pathway with a lower activation-energy barrier.

The reaction rate tells us how quickly reactants are consumed or products are formed. Because chemical reactions involve reactants disappearing and products appearing, reaction rate can usually be measured by following how the concentration of one substance changes over time.

• For a simple reaction:
• A → B
• the concentration of A decreases as time passes, while the concentration of B increases.
• If [A] changes from 1.00 M to 0.70 M over 10 seconds, the change in concentration is:
• Δ[A] = 0.70 − 1.00 = −0.30 M
• The negative sign means A was consumed.
• The average change in concentration per unit time is:
• Δ[A] / Δt = −0.30 M / 10 s = −0.030 M/s
• However, reaction rate is normally reported as a positive quantity, so for a reactant we place a negative sign in front:
• Rate = −Δ[A]/Δt
• Therefore:
• Rate = 0.030 M/s

For a product, concentration increases, so:

• Rate = +Δ[B]/Δt

A typical rate unit is:

• M/s
• which means molarity per second.

For a reaction with coefficients other than 1, different substances do not necessarily change concentration at the same numerical rate.

• Consider:
• 2A → B
• For every 2 mol of A consumed, only 1 mol of B forms.
• Therefore A disappears twice as fast as B appears.

To define one consistent reaction rate, divide each concentration change by its stoichiometric coefficient:

• Rate = −(1/2)(Δ[A]/Δt) = Δ[B]/Δt

For the general reaction:

• aA + bB → cC + dD
• the reaction rate can be written as:
• Rate = −(1/a)(Δ[A]/Δt) = −(1/b)(Δ[B]/Δt) = (1/c)(Δ[C]/Δt) = (1/d)(Δ[D]/Δt)
• Reactants get negative signs because their concentrations decrease. Products get positive signs because their concentrations increase.

Consider:

• 2NO₂ → 2NO + O₂
• Suppose O₂ forms at:
• 0.020 M/s
• According to the coefficients, 2 mol NO form for every 1 mol O₂.
• Therefore NO forms at:
• 0.040 M/s
• NO₂ is consumed at the same magnitude:
• 0.040 M/s

But the overall reaction rate is:

• 0.020 M/s
• because we divide the NO₂ or NO concentration change by their coefficient of 2.
• This distinction between rate of concentration change and overall reaction rate is important.

An average reaction rate measures the change over a time interval.

• For example:
• Rate = −Δ[A]/Δt
• from 10 seconds to 20 seconds.

An instantaneous rate describes the rate at one specific moment. Graphically, it corresponds to the slope of the tangent line to a concentration-vs-time curve at that moment.

• You do not always need calculus to understand the idea. Think of average rate like the average speed during an entire car trip, while instantaneous rate is like what the speedometer shows at one particular moment.

For many reactions, the reaction is fastest near the beginning and becomes slower as time passes.

• This happens because reactants are gradually consumed. As their concentrations decrease, there are fewer reactant particles in a given volume, so successful collisions generally occur less frequently.
• A graph of reactant concentration against time therefore often starts steep and becomes flatter as the reaction progresses.

Several major factors can change reaction speed.

Increasing the concentration of a reactant usually increases reaction rate if that reactant appears in the rate law.

• A higher concentration means more reactant particles occupy the same volume. This generally increases the frequency of collisions between particles.
• However, the exact mathematical effect of concentration must be determined from the rate law, which is covered in Topic 2.

For gases, decreasing the container volume increases pressure and effectively increases the number of gas particles per unit volume. This can increase collision frequency and therefore increase reaction rate.

• The effect is similar to increasing concentration in solution.

Increasing temperature generally increases reaction rate.

• Higher temperature gives particles a greater average kinetic energy. They move faster, collisions occur more frequently, and—most importantly—a larger fraction of collisions have enough energy to overcome the activation energy barrier.
• This is why heating a reaction mixture often causes the reaction to happen much faster.

Surface area matters when a solid reactant is involved.

• Suppose a solid reacts with a solution. Only particles at the exposed surface can directly collide with the solution particles.
• Breaking the solid into smaller pieces increases its total exposed surface area.
• Therefore:
• powdered solid generally reacts faster than one large chunk of the same mass
• because more particles are exposed for collisions.

A catalyst increases reaction rate by providing a different reaction pathway with a lower activation energy.

• The catalyst is not consumed in the overall reaction.
• Catalysis is covered in detail later in this unit.

If a graph shows reactant concentration vs. time, the concentration generally decreases.

• A steep downward slope means a relatively fast disappearance of the reactant.
• A flatter slope means the reaction is occurring more slowly.

For products, concentration usually increases, so the graph slopes upward.

• Always pay attention to whether the graph is showing a reactant or product.

Do not forget that reactant concentration changes are negative, but reaction rate is normally reported as positive.

Do not assume every species changes concentration at the same numerical rate. Use the coefficients in the balanced equation.

Do not confuse reaction rate with the rate constant k. They are related, but they are not the same thing.

Reaction rate answers:

• “How fast are reactants disappearing or products appearing?”
• For a reactant:
• Rate = negative concentration change / time
• For a product:
• Rate = positive concentration change / time

Unit 5 makes much more sense when you connect all six topics instead of memorizing them separately.

• Start with:
• Reaction rate
• which tells you how quickly concentration changes.
• Then:
• Rate law
• tells you how concentration affects that rate.
• Then:
• Integrated rate law
• connects concentration to time.
• Next:
• Reaction mechanism
• explains the actual elementary steps causing the observed reaction.
• Then:
• Collision theory and activation energy
• explain why some collisions succeed while others fail.
• Finally:
• Catalysis
• shows how changing the reaction pathway can lower activation energy and make the reaction faster.
• The overall chain is:
• particle collisions
• → some have enough energy and correct orientation
• → elementary reaction steps occur
• → mechanism produces overall reaction
• → concentrations change with time
• → rate law describes how fast

Reaction rates: Remember to divide concentration changes by stoichiometric coefficients when calculating the overall reaction rate.

Reactant signs: Reactant concentrations decrease, so the negative sign is used to make the reaction rate positive.

Rate law: Do not use coefficients from the overall balanced equation as exponents unless the reaction is specifically an elementary step.

Reaction order: Overall order is the sum of the exponents.

Concentration effects: A second-order reactant doubling in concentration makes its contribution to the rate increase by 4×, not 2×.

Rate constant: k is not the same as rate and its units depend on overall reaction order.

Temperature: Changing temperature changes k.

Integrated laws: Zero order uses [A], first uses ln[A], second uses 1/[A] for linear plots.

Graph slopes: Zero and first order have slope −k; second order has slope +k.

Half-life: The equation t½ = 0.693/k is specifically for first-order processes.

Radioactive decay: Radioactive decay follows first-order kinetics.

Mechanisms: A valid mechanism must add to the overall reaction and agree with the experimental rate law.

Intermediates: Formed during one step and consumed later.

Catalysts: Consumed early and regenerated later.

Rate-determining step: The slow step can control the observed rate law.

Activation energy: Do not confuse Eₐ with the overall reaction energy change.

Temperature: Higher temperature does not normally lower Eₐ; it increases the fraction of particles with enough energy to overcome Eₐ.

Catalysts: Catalysts lower the activation-energy pathway but do not change the energies of the initial reactants or final products.

Maxwell–Boltzmann: Higher temperature changes the energy distribution. A catalyst lowers the Eₐ threshold without changing that distribution at fixed temperature.

Before taking a Unit 5 test, you should be able to calculate an average reaction rate from concentration and time data and relate the disappearance of reactants to the appearance of products using stoichiometric coefficients. You should understand why reaction rates can change when concentration, temperature, surface area, pressure, or catalysts change.

You should be able to interpret a rate law such as Rate = k[A]²[B], determine individual and overall reaction orders, predict how changing concentration changes the reaction rate, determine a rate law from an initial-rate table, calculate k, and identify the correct units of k.

You should know the zero-, first-, and second-order integrated rate laws and recognize which concentration transformation produces a linear graph. You should be able to obtain k from a graph's slope, calculate concentrations after a certain time, and use t½ = 0.693/k for first-order reactions. You should also understand why radioactive decay follows first-order kinetics.

For mechanisms, you should be able to identify elementary steps, intermediates, catalysts, and the rate-determining step. You should be able to add elementary reactions to obtain the overall reaction and determine whether a proposed mechanism agrees with an experimentally measured rate law.

For activation energy, you should understand collision theory, successful vs. unsuccessful collisions, activation energy, transition states, reaction-energy diagrams, forward and reverse activation energies, and the effect of temperature on reaction rate. You should also be able to interpret Maxwell–Boltzmann distributions and understand the Arrhenius equation.

Finally, you should understand exactly what a catalyst does: it provides an alternative reaction mechanism with a lower activation-energy barrier. It speeds up the reaction without being consumed overall and without changing the energy difference between reactants and products.

If you can connect rate laws, concentration-time data, mechanisms, energy diagrams, and particle collisions instead of treating them as separate memorization topics, you understand the main logic behind AP Chemistry Unit 5.