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• Chemical kinetics is the study of reaction rates and the factors influencing them, like temperature.
• The reaction rate refers to the pace at which a chemical reaction occurs.
• The reaction rate measures how quickly reactants form products or are consumed.
• Controlling reaction speed is important.
• Reaction rates vary significantly; some reactions are very fast (explosions), while others are very slow (rusting).

Defining Rate

• Rate quantifies the change in a quantity over a specific time period.
• The units for the rate of a car's speed is measured in miles per hour (mi/hr).

Defining Reaction Rate

• Reaction rate measures reactant concentration decrease or product concentration increase over time.
• A negative sign precedes the definition for reactants to indicate decreasing concentration.
• For the reaction H2(g) + l2(g) → 2 Hl(g) the rate is expressed as Rate = - (Δ[H2] / Δt) = - ([H2]t2 - [H2]t₁) / (t2-t1).
• Δ signifies "change in".
• [] denotes molar concentration.
• t represents time.
• The rate of a reaction is positive and negative numbers regarding products and reactants, respectively.
• Reaction rates decrease with time due to decreasing reactant concentrations.
• For a reactant, a negative sign is included to denote a concentration decrease and ensure a positive rate value.
• As a reaction progresses, its rate typically slows due to decreasing reactant concentrations.
• Reactions end as reactants are used up or the system reaches equilibrium.

Reaction Rate and Stoichiometry

• Reaction rates relate to changes in reactant or product concentration over time.
• For a reaction aA + bB → cC + dD, change in concentration for each substance is multiplied by 1/coefficient.
• The equation Rate = - (1/a)(Δ[A]/Δt) = - (1/b)(Δ[B]/Δt) = (1/c)(Δ[C]/Δt) = (1/d)(Δ[D]/Δt) expresses this relationship.
• Given the reaction 5H2O2 (aq) + 2MnO4 (aq) + 6H+(aq) → 2Mn2+ (aq) + 8H2O(1) + 5O2(g), the rate of appearance of O2(g) is 1.0x10-3 mol/(L⋅s).
• The simultaneous rate of disappearance of MnO4 is calculated using −(1/2)(Δ[MnO4-]/Δt) = (1/5)(Δ[O2]/Δt).
• The rate of disappearance of MnO4- at the same time is -4.0x10-4 mol/(L⋅s).

Factors Affecting Reaction Rate: Reactant Concentration

• Reaction rate often depends on reactant molecule concentrations.
• Rate law is an equation that relates the rate to the concentrations of reactions, assuming no reverse reaction.
• The rate of a reaction directly correlates with the concentration of each reactant raised to a power.
• For the reaction A → products, the rate law is Rate = k[A]n.
• "n" defines the reaction order and determines the rate’s concentration dependence.
• "k" is the rate constant.
• Reaction order, "m" and "n" is determined for each reactant using experimental data.
• The law Rate = k[A]m[B]n shows reaction rate depends products of reactant concentrations [A] and [B], raised to orders m and n.
• The overall order sums all reactant orders.
• The exponent applied to each reactant in the rate law indicates the reaction order with respect to that reactant.
• The order of the reaction indicates the sum of the exponents on the reactants.
• Given Rate = k[NO]2[O2], substance [NO] is second order, [O2] is first order, and the overall reaction is third order.

Reaction Order and Rate

• If the reaction is zero order, Rate = k[A]0 = k, and [A] has no effect on the reaction rate.
• Doubling [A] will have no effect on the reaction rate in a zero order reaction.
• If the reaction is first order, with rate = k[A]1 = k[A], doubling [A] will double the rate of the reaction given as rate = k[A]¹ = k[A].
• With a second order reaction, Rate = k[A]2, doubling [A] will quadruple the rate, because the rate relies on the concentration square, given as Rate = k[A]2.
• When A → products, a doubling of [A] doubles the rate, indicating the reaction is first order.

Determining Order and Rate Constant Example

• In the reaction NO2(g) + CO(g) → NO(g) + CO2(g), the concentration of NO2 doubles, the CO stays constant, and the rate quadruples to suggest that the reaction is second order in NO2.
• In the reaction NO2(g) + CO(g) → NO(g) + CO2(g), the concentration of CO doubles, the NO2 stays constant, and the rate stays constant to suggest that the reaction is zero order in CO
• The overall rate expression would be Rate = k[NO2]2[CO]0 = k[NO2]2

Determining the Order of a Reaction

• Determining the rate law needs experimental data.
• The "method of initial rates" compares rates from experiments, varying one concentration at a time.
• The impact of a single reactant's concentration change is assessed by comparing different experiments.
• The rate law (Rate = k[A]2[B]) indicates compound B is first order because, with A constant, doubling B doubles the rate.
• Doubling A, while B remains constant, multiplies the rate by four, indicating a second order dependence on A.

Integrated Rate Laws

• Rate law shows rate and concentration relationship.
• Equations linking concentration and time are useful.
• Calculus helps derive the "integrated rate law" expressing the relationship between [A] and time.

Determining Rate Law with Multiple Reactants

• The rate of the reaction is affected when each reactant changes.
• The concentration effect of each reactant on the rate can be found by changing one reactant's initial concentration at a time.
• Comparing rate differences in reactions reveals the rate law.
• Rate = k[A]m[B]n shows the reaction order with respect to A is "m" while the reaction order with respect to B is "n"

Half-Life

• The half-life (t1/2) is the time it takes for the reactant concentration to halve.
• Reaction order influences half-life.

First-Order Reactions

• First-order reactions are very common.
• Examples of first order reactions include the hydrolysis of aspirin and anticancer drugs, SO2CI2 → CI2 + SO2, 2N2O5 → O2 + 4NO2, and 2H2O2 → 2H2O + O2.
• The rate of the reaction in a first-order reaction is directly proportional to the concentration of one reactant, often in the form A → products.
• The equation rate = -Δ[A]/Δt = k[A] expresses the differential rate for a first-order reaction.
• The rate law for a first-order reaction is expressed rate = k[A]¹ = k[A].
• The integrated rate law is expressed as ln[A] = −kt + ln[A]initial or ln([A]/[A]initial) = -kt.
• Half life is quantified as t1/2 = 0.693 / k, where rate is in M/sec and k is in s-1
• In a straight line graph of ln[A] over time, slope gives "-k", the rate constant, and y-intercept represents I[A]initial.
• Graphing In[A] versus time yields a straight line to determine the rate constant in a first-order integrated rate law.

Second-Order Reactions

• Reactions in which two monomers combine to form a dimer, with the decomposition of NO2 to NO and O2, and HI to I2 and H2 as examples.
• Second-order reactions are those that have a rate proportional to the square of one reactant's concentration, often in the form 2A → products.
• Second-order reactions involve a rate proportional to the concentrations product of two reactants, often in the form A + B → products.
• The equation Rate = k[A]2 represents a second-order reaction.
• The relationship is 1/[A] = kt + 1/[A]initial.
• The slope of 1/[A] versus time graph is "k", with "1/[A]initial" as the y-intercept to determine the rate constant.
• The half life is given by t1/2 = 1 / (k[A]initial)
• When Rate = M/sec, k = M-1⋅s-1.

Zero-Order Reactions

• Examples include photochemical reactions (hydrogen and chlorine), N2O decomposition (hot platinum surface), and NH3 decomposition (molybdenum or tungsten).
• The oxidation of ethanol, catalyzed by alcohol dehydrogenase, is a zero-order reaction in the human liver.
• The rate equals the constant k, expressed Rate = k[A]° = k.
• Constant rate reactions follow the formula [A] = −kt + [A]initial.
• The graph of [A] versus time shows a straight line with slope of -k and y-intercept of [A]initial.
• During these reactions the half life is [Ainitial] / 2k, where Rate = M/sec, and k = M/sec