Chemical Kinetics: Reaction Rates and Rate Laws

What is chemical kinetics?

The area of chemistry concerned with reaction rates and the sequence of steps by which reactions occur.

How is reaction rate defined?

Either the increase in the concentration of a product per unit time or the decrease in the concentration of a reactant per unit time.

What factors affect reaction rates?

Concentration of reactants, physical state of reactants, temperature, and presence of a catalyst.

What is the average reaction rate?

The change in measured concentrations in any particular time period.

How does the time interval affect average reaction rates?

The larger the time interval, the more the average rate deviates from the instantaneous rate.

What are relative reaction rates?

The rates of consumption of reactants and formation of products based on stoichiometry.

What is the instantaneous rate?

The change in concentration at any one particular time, determined by the slope of a tangent line to the curve.

How can the instantaneous rate be calculated?

By taking the slope of a line tangent to the curve at that particular point, equivalent to the first derivative of the function.

What is a rate law?

An equation that relates the rate of a reaction to the concentration of reactants, including the rate constant and the order of the reaction.

What is the significance of the rate order in a rate law?

It indicates how the rate of reaction is affected by the concentration of each reactant.

How can the order of a reaction be determined?

Using the method of initial rates from a table of concentration and initial rates.

What is the Arrhenius Equation?

An equation that shows how the rate constant of a reaction depends on temperature and activation energy.

What is the general form of the rate of reaction?

Rate = -Δ[Reactant]/Δt or Rate = Δ[Product]/Δt.

What is the relationship between concentration and reaction rates?

Higher concentrations of reactants generally lead to higher reaction rates.

What is the role of a catalyst in a chemical reaction?

A catalyst increases the rate of a reaction without being consumed in the process.

How can average rates be calculated from concentration data?

By measuring the change in concentration over a specific time interval.

What is the difference between average and instantaneous rates?

Average rates are calculated over a time interval, while instantaneous rates are measured at a specific moment.

What is the formula for calculating relative reaction rates?

Relative rates are based on stoichiometric coefficients from the balanced chemical equation.

What is the effect of temperature on reaction rates?

Increasing temperature generally increases reaction rates due to higher kinetic energy of molecules.

How can a plot of concentration versus time be used in kinetics?

It can be used to determine average and instantaneous rates of reaction.

What is the significance of the slope in a concentration versus time graph?

The slope at a specific point represents the instantaneous rate of reaction at that time.

What is the rate law?

An equation that defines the experimentally determined relationship between reactant concentrations and the rate of the reaction, expressed as Rate = k [A]m [B]n.

What do the variables m and n represent in the rate law?

m and n are the reaction orders with respect to reactants A and B.

How is the overall order of a reaction determined?

The overall order is the sum of the exponents for the concentration terms in the rate law.

What effect does increasing reactant concentration have on reaction rates?

Increasing concentrations increases collisions between reactants, leading to a higher rate of product formation.

What is the initial rate of a reaction?

The initial rate is the rate of a reaction at t = 0, immediately after the reactants are mixed.

What is the purpose of the Initial Rate Method?

To determine the rate law by measuring initial rates under different conditions.

What is the rate constant (k)?

A proportionality constant that relates the rate of a reaction to the concentration of reactants.

How can the rate constant k be calculated?

By substituting the initial concentrations and measured rates into the rate law.

What is the significance of the exponent m in the rate law?

It indicates the order of the reaction with respect to reactant A.

In the reaction 2NO(g) + O2(g) → 2NO2(g), what is the rate law?

Rate = k[NO]m[O2]n, where m and n are determined experimentally.

What does a second order reaction in N2O5 imply about the rate increase?

If the rate increases by a factor of (2.5)² = 6.25, the reaction is second order in N2O5.

What is the relationship between the initial concentration and the rate for a first-order reaction?

If the initial concentration increases, the rate will increase proportionally.

How can you verify the units of the rate constant k?

By checking that the units of k correspond to the expected units for the reaction order, such as 1/s for first-order reactions.

What is the initial concentration of N2O5 used in the worked example?

0.030 M.

What happens to the decomposition rate of N2O5 if its concentration is increased by a factor of 3/2?

The decomposition rate will increase by a factor of 3/2.

What is the significance of the overall order of a reaction?

It provides insight into the relationship between reactant concentrations and the rate of the reaction.

What does the term 'instantaneous rate' refer to?

The rate of a reaction at a specific moment in time, not necessarily at the start.

How is the rate law determined?

The rate law must be determined experimentally by changing the initial concentration of reactants and measuring the effect on the initial rate.

What is an example of a rate law for a reaction involving NO and O3?

Rate = k[NO][O3].

What does a first-order reaction mean in terms of concentration change?

The rate is directly proportional to the concentration of the reactant.

What is a common method for determining reaction orders?

By comparing initial rates from experiments with varying concentrations.

What is the relationship between the second-order integrated rate law and a plot of inverse reactant concentration versus time?

A plot of the inverse reactant concentration versus time is linear for a second-order reaction.

How can the rate constant be determined from a plot of inverse reactant concentration versus time for a second-order reaction?

The rate constant can be determined from the slope of the plot.

What is the purpose of the second-order integrated rate law?

It is used to find the reactant concentration at a given time or the time elapsed for a given concentration change.

What is the relationship between the zero-order integrated rate law and a plot of reactant concentration versus time?

A plot of the reactant concentration versus time is linear for a zero-order reaction.

How can the rate constant be determined from a plot of reactant concentration versus time for a zero-order reaction?

The rate constant can be determined from the slope of the plot.

What is half-life in the context of chemical reactions?

Half-life is the time during which the concentration of a reactant decreases by half.

How can half-life be identified from a plot of reactant concentration versus time?

It can be identified by observing the time it takes for the concentration to reduce to half its initial value.

How do you calculate the half-life for first-order reactions?

The half-life for first-order reactions is constant and can be calculated using the integrated rate law.

What is the half-life for second-order reactions?

The half-life for second-order reactions depends on the initial concentration, with each successive half-life being twice as long as the previous one.

How long does it take for 95.0% of a sample of 32P to decay if its half-life is 14.3 days?

It takes approximately 57.2 days for 95.0% of a sample of 32P to decay.

What percentage of carbon-14 remains after 16,230 years if its half-life is 5,715 years?

Approximately 25% of carbon-14 remains after 16,230 years.

For the reaction A + B → AB, if the reaction is first-order in A with a rate constant of 6.3 x 10^-6 s^-1 and an initial concentration of 0.100 M, what is its molarity after 10.0 hours?

The molarity of A after 10.0 hours is approximately 0.025 M.

How many hours are required for the concentration of A to reach 0.025 M in the reaction A + B → AB?

It takes approximately 10.0 hours for the concentration of A to reach 0.025 M.

For the reaction 2 NO2(g) → 2 NO(g) + O2(g), what does the integrated rate law indicate about the plot of 1/[NO2] versus time?

The plot of 1/[NO2] versus time is a straight line, indicating a second-order reaction.

What is the slope of the plot of 1/[NO2] versus time for the reaction 2 NO2(g) → 2 NO(g) + O2(g)?

The slope of the plot is equal to the rate constant (k).

What is the initial concentration of C4H6 in the reaction 2C4H6(g) → C8H12(g) if the rate constant is 4.0 x 10^-2 M^-1s^-1?

The initial concentration of C4H6 is 0.020 M.

How can the molarity of C4H6 be determined after a reaction time of 1.00 h in the reaction 2C4H6(g) → C8H12(g)?

The molarity can be calculated using the second-order integrated rate law.

What is the time in hours when the C4H6 concentration reaches a value of 0.0020 M in the reaction 2C4H6(g) → C8H12(g)?

The time can be calculated using the second-order integrated rate law.

What is a pseudo-first-order reaction?

A reaction where all reactants except one are at high concentrations, so their concentrations do not significantly decrease, and the reaction rate is controlled by the limiting reactant.

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

The integrated rate law is [A] = -kt + [A]o, where t1/2 = [A]o/2k.

What is the rate of a zero-order reaction?

Rate = k[NH3]0 = k, indicating that the rate is independent of the concentration of the reactant.

What is the significance of the activation energy (Ea) in a chemical reaction?

Activation energy is the minimum energy required for molecular collisions to break bonds in reactants, leading to product formation.

How does temperature affect reaction rates?

Increased temperature raises the kinetic energy of molecules, leading to more frequent and energetic molecular collisions.

What does the slope of a plot of ln(k) versus 1/T represent?

The slope is equal to -Ea/R, where Ea is the activation energy and R is the universal gas constant.

What is the frequency factor (A) in the Arrhenius equation?

The frequency factor is the product of molecular collisions and a factor that expresses the probability of the correct orientation for a reaction.

What is an activated complex?

An activated complex is a short-lived, high-energy transition state formed during a chemical reaction.

What is the relationship between activation energy and the rate constant (k)?

A low activation energy (Ea) results in a large rate constant (k), indicating a fast forward reaction, while a high Ea results in a small k, indicating a slow reverse reaction.

What is the role of reaction intermediates in a reaction mechanism?

Reaction intermediates are species formed in one elementary step and consumed in another, contributing to the overall reaction.

What is the difference between unimolecular and bimolecular reactions?

Unimolecular reactions involve a single reactant molecule, while bimolecular reactions involve two reactant molecules.

How can the activation energy be mathematically determined from rate constants at different temperatures?

By using the Arrhenius equation and comparing rate constants at two different temperatures, activation energy can be calculated.

What is a potential energy diagram?

A potential energy diagram is a plot of energy versus reaction progress, illustrating the energy changes during a reaction.

What does a high activation energy indicate about a reaction's rate?

A high activation energy indicates a slower reaction rate due to fewer molecules having sufficient energy to overcome the barrier.

What is the significance of the rate-determining step in a reaction mechanism?

The rate-determining step is the slowest step in the mechanism that determines the overall rate law for the reaction.

How can you determine if a reaction is exothermic or endothermic from an energy profile?

If the products have lower energy than the reactants, the reaction is exothermic; if the products have higher energy, it is endothermic.

What is the activation energy for the reaction NO(g) + F2(g) → NOF(g) + F(g) given Ea = 6.3 kJ/mol?

The activation energy for this reaction is 6.3 kJ/mol.

What are the rate constants for the decomposition of dinitrogen pentoxide at two different temperatures?

At 25°C, the rate constant is 3.7 x 10^-5 s^-1, and at 55°C, it is 1.7 x 10^-3 s^-1.

What is the effect of temperature on the rate of a forward reaction with low activation energy?

A low activation energy leads to a fast forward reaction, especially as temperature increases.

What is the effect of temperature on the rate of a reverse reaction with high activation energy?

A high activation energy results in a slow reverse reaction, particularly at lower temperatures.

What is a reaction mechanism?

A set of steps that describe how a reaction occurs at the molecular level, consistent with the rate law for the reaction.

Define an elementary step in a reaction mechanism.

A molecular-level view of a single process taking place in a chemical reaction.

What does molecularity refer to in a reaction?

The number of ions, atoms, or molecules involved in an elementary step in a reaction.

What is a reaction intermediate?

A species produced in one step of a reaction and consumed in a subsequent step, not appearing in the net equation.

What is the rate-determining step (RDS) in a reaction mechanism?

The slowest step in the mechanism that limits the overall rate of the reaction.

For the reaction 2 NO2 (g) → 2 NO(g) + O2(g), what is the observed rate law?

Rate = k[NO2]2.

In the proposed mechanism for 2 NO2 (g) → 2 NO(g) + O2(g), what is the slow step?

2 NO2(g) → NO(g) + NO3(g) with Rate = k1[NO2]2.

What is the overall equation for the reaction NO2(g) + CO(g) → NO(g) + CO2(g)?

NO2(g) + CO(g) → NO(g) + CO2(g).

In the two-step mechanism for 2NO2 (g) + O3 (g) → N2O5 (g) + O2 (g), what is the first step?

NO2 (g) + O3 (g) → NO3 (g) + O2 (g).

What is the reaction intermediate in the mechanism for 2NO2 (g) + O3 (g) → N2O5 (g) + O2 (g)?

NO3 (g).

What is a catalyst?

A substance added to a reaction that increases the rate of the reaction but is not consumed in the process.

Differentiate between homogeneous and heterogeneous catalysts.

Homogeneous catalysts are in the same phase as the reactants, while heterogeneous catalysts are in a different phase.

What is the role of enzymes in biological reactions?

Enzymes are biological catalysts that speed up reactions by adsorbing substrate reactants onto an active site.

What is the lock and key mechanism in enzymatic reactions?

A model describing how enzymes and substrates fit together to catalyze a reaction.

In the enzymatic hydrolysis of sucrose, which step is the rate-determining step?

The conversion of the enzyme-substrate complex (ES) to enzyme and product (E + P).

What is the activation energy (Ea) for the slow step in the natural photodecomposition of ozone?

17.7 kJ/mol.

What is the activation energy for the Cl-catalyzed reaction in ozone decomposition?

2.2 kJ/mol.

What is the significance of the rate law in a reaction mechanism?

It reflects the relationship between the rate of reaction and the concentration of reactants, derived from the rate-determining step.

What is the overall equation for the reaction involving H2(g) and ICl(g)?

H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g).

In the proposed mechanism for H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g), what is the slow step?

H2(g) + ICl(g) → HCl(g) + HI(g).