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Chemistry
KINETICS

The study of chemical kinetics examines the speed at which reactants are converted into products. Different reactant and product concentrations change at different speeds relative to each other based on their molar coefficients.  This is generally called the rate of a chemical reaction.  A solid understanding of solution stoichiometry  is needed to determine the molarities needed for rate law calculations.

I NEED HELP WITH THE RELATIONSHIP BETWEEN CONCENTRATION AND TIME

Factor Affecting the Rate of a Reaction

Nature of Reactants

The chemical composition and structure of reactants play a crucial role in determining reaction rates. Reactants with weaker chemical bonds tend to react more readily than those with stronger bonds. Additionally, the presence of functional groups or substituents can affect the reactivity of molecules.

Concentration of Reactants

The concentration of reactant molecules affects the frequency of collisions and, consequently, the reaction rate.  Generally, an increase in the concentration of reactants leads to a higher collision frequency, thus accelerating the reaction rate.  This relationship is described by the collision theory, which states that the rate of a chemical reaction is proportional to the number of effective collisions per unit time. Effective collisions are those that occur with sufficient energy and proper orientation to result in product formation.

Temperature

Temperature has a significant impact on reaction rates.  The warmer particles are, the faster they will move.  According to the Arrhenius equation, an increase in temperature leads to a greater number of reactant molecules possessing energy equal to or greater than the activation energy. Consequently, the reaction rate typically increases with temperature due to the higher frequency of effective collisions.

Pressure

In gas-phase reactions, pressure can influence reaction rates by altering the concentration of gas molecules. Increasing pressure  increases the rate of reactions involving gases, as it compresses gasses leading to a higher concentration of reactant molecules and more frequent collisions.  Remember that changes in volume are inverse changes in pressure.  For example, increasing the volume of a reaction vessel decreases the pressure, which in turn decreases the frequency of collisions.  In other words, increasing volume generally decreases the reaction rate.

Surface Area

In heterogeneous reactions involving solid reactants, the surface area of the solid can affect reaction rates. Increasing the surface area exposes more reactant particles to potential collisions, thereby enhancing the reaction rate. This is particularly important in catalytic reactions where the catalyst is often in the form of a finely ground solid powder.  

Presence of Catalysts

Catalysts are substances that facilitate chemical reactions by providing an alternative reaction pathway with a lower activation energy. They increase reaction rates by lowering the energy barrier for the reaction to occur. Catalysts remain unchanged at the end of the reaction and can be reused multiple times.

Rate Law Expressions

A rate law expression is a mathematical equation that tells the reactants involved in determining the rate, and the extent to which they do so.  The general form of a rate law expression for a reaction involving multiple reactants is:

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

K is the rate constant, which is specific to a particular reaction at a given temperature.  [A] and [B] are the concentrations of reactants A and B, respectively.  Finally, m and n are the reaction orders with respect to reactants A and B. These values are the exponents to which the concentration of each reactant is raised in the rate law expression.

The values of m and n, as well as the rate constant k, are determined experimentally by studying the reaction under various conditions, such as changing the concentrations of reactants or altering the temperature. By measuring the reaction rate under these conditions, scientists can derive the rate law expression and determine the reaction orders and rate constant.

Reaction Orders

An order describes the relationship between the rate of a chemical reaction and the concentration of reactants.  It reflects how changes in the concentration of a particular reactant affect the rate of the reaction, and is the exponent to which the concentration of a reactant is raised in the rate law expression.  For example, if a reaction is first-order with respect to reactant A, doubling the concentration of A will double the rate of the reaction.  If a reaction is second-order with respect to a particular reactant, doubling the concentration of that reactant will quadruple the rate of the reaction.  The overall order of the reaction is the sum of the individual reaction orders for each reactant involved. It represents the combined effect of all reactants on the reaction rate.

 

K – The Reaction Rate Constant

A reaction rate constant, denoted by the symbol k, describes the speed of a chemical reaction, and is specific to a particular reaction at a given temperature. It is a proportionality constant that relates the rate of the reaction to the concentrations of the reactants. Essentially, it indicates how quickly reactants are transformed into products under specific conditions. Additionally, the temperature dependence of the rate constant can be described by the Arrhenius equation, which relates the rate constant to the temperature and the activation energy of the reaction, providing further insights into reaction mechanisms and thermodynamics.

 

Determining Rate Laws Using the Method of Initial Rates

The method of initial rates is technique used in the lab to determine the rate law and order of a chemical reaction by measuring the initial rates of the reaction under different initial concentrations of reactants. By systematically varying the concentrations of reactants and analyzing the resulting rate data, the orders with respect to each reactant as well as the overall order can be determined.  To perform the method of initial rates, the reaction is initiated holding all concentrations constant with the exception of one.  The concentration of this one is then changed and effects on the rate are observed.  Separate trials are performed changing only one concentration at a time.  In this way the concentration effects of each individual reactant can be determined.  If there is no change in the speed of a reaction when a concentration is changed, the order with respect to the reactant whose concentration was changed is zero.  If the speed of the reaction doubles when the concentration of a single reactant doubles, the order with respect to that reactant is one, and so on.  It is important to remember that orders are exponential relationships which describe the extent to which reactants affect the rate.  Additionally, the overall order of a reaction is the sum of the individual orders.  Once all of the orders are determined, use the rate and concentration values from one experiment only to solve for K

 

Integrated Rate Laws

Rate Laws tell only which reactants are responsible for changing the speed of a reaction and the extent to which they do so.  Integrated rate laws though, include the value of time.  They provide a way to directly relate the amount of  reactant consumed or product formed to a given time frame.  Conversely, if initial and final concentrations are known, the amount of time that the reaction has progressed can be determined using an integrated rate law.  There are several types of integrated rate laws, each corresponding to different reaction orders and rate expressions. The most common integrated rate laws are for zeroth, first, and second-order reactions.  Each have their own value for K, graph, and accompanying half-life equation.

Collision Theory

At its core, a chemical reaction involves the breaking and formation of chemical bonds between atoms and molecules. For a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation to overcome the activation energy barrier which is the minimum amount of energy required for a reaction to proceed. Collisions between reactant molecules that possess energy greater than the activation energy lead to successful reactions and product formation.  The collision theory posits that not all collisions between reactant molecules lead to the formation of products; only those collisions with enough kinetic energy to overcome the activation energy barrier result in a successful reaction. Reactant molecules must collide in a specific orientation that allows the necessary chemical bonds to be broken and formed during the reaction process.

Reaction Rate Mechanisms

Reaction rate mechanisms, also known as reaction mechanisms, describe the step-by-step sequence of elementary reactions that occur during a chemical reaction. These mechanisms provide a detailed molecular-level understanding of how reactants are transformed into products and the intermediates formed along the reaction pathway.

Elementary reactions are individual molecular processes that occur during the reaction, each involving a specific set of reactant molecules and resulting in the formation of products. You can think of them as individual steps of an overall reaction. Elementary reactions are characterized by their molecularity, which refers to the number of reactant molecules involved in the reaction.  For example, unimolecular (involving one molecule), bimolecular (involving two molecules), and termolecular (involving three molecules) reactions.

Intermediates are transient species that are formed in one step and consumed in another during the overall course of the reaction.  Because they are not part of the original reactants or final products, they do not appear in the overall balanced equation for the reaction. Reaction intermediates are typically unstable and have short lifetimes, making them difficult to detect experimentally. However, their existence can often be inferred from experimental observations, such as the presence of reaction products or kinetic data.

The rate-determining step, also known as the rate-limiting step, is the slowest step in the reaction mechanism and governs the overall rate of the reaction. It is typically characterized by a high activation energy barrier and determines the kinetics of the reaction. The rate law for the overall reaction is often based on the rate-determining step of the mechanism.

Catalysts are substances that facilitate chemical reactions by providing an alternative reaction pathway with a lower activation energy. Unlike intermediates, catalysts are present in both the original reactants and final products. They participate in intermediate steps of the reaction and are regenerated at the end of the process. This allows them to catalyze multiple reaction cycles without being consumed themselves.

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