Chem Unit 11 - Kinetics

Increasing reactant concentration may or may not affect rate depending on order x

0 order reactant means changing the concentration will have no affect 1 order reactant means changing the concentration will have an effect 2 order reactant means changing the concentration will have a significant effect

Differences in chemical reactivity can be attributed to

1. Factors that affect the breaking and forming of chemical bonds, ionization energy, electronegativity, ionic and molecular polarity, size, and complexity of structure are some of these factors. 2. The state of the reacting species may also play a role

Increasing temperature will increase the rate of a reaction for two reasons:

1. More frequent collisions 2 More forceful/energetic collisions.

Collision theory

1. The reacting species (ions, atoms, or molecules) must collide. The rate of reaction is proportional to the rate of reactant collisions. 2. The reacting species must collide in proper orientation that allows contact between the atoms that will become bonded together in the product 3. The collision must occur with adequate energy to permit mutual penetration of the reacting species valence shells so that the electrons can rearrange and form new bonds (and new chemical species)

Rates of chemical reactions play important roles for understanding the processes that involve chemical changes. Three questions are typically posed when planning to carry out a chemical reaction:

1.Will the reaction being proposed produce the desired products in useful quantities? 2. How rapidly will the reaction occur? 3.What molecular level processes take place as the reaction occurs?

half life of a second order reaction

1/(.5[a]) = k(t(.5))+1/[A]0

second order integrated rate law

1/[A]t = kt + 1/[A]0

Determining rate laws from experimental data

A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carries out using different initial reactant concentrations. Then, comparing the measured rates for these trials permits thej determination of the reaction orders and subsequently the rate (constant (k)) which together are used to formulate a rate law.

Using a rate as a conversion factor

A derived Unit is a unit that consists of two or more other units. A quantity expressed with a derived unit may be used to convert a unit that measures one thing into a unit that measures something else completely. One of the most common examples is the use of a rate to convert between distance and time. The keys to this type of problem are: Determining which form of the conversion factor to use, and deciding where to start

integrated rate laws

A mathematical expression for reactant concentration as a function of time

Determining the validity of a reaction mechanis,m

A valid reaction mechanism for a particular chemical reaction must meet three criteria 1. Each elementary step is most commonly unimolecular or bimolecular because the chance of more than two reacting particles colliding at once with sufficient energy and proper orientations to produce products is infinitesimally small. Mechanisms involving termolecular steps are usually not valid. 2. Elementary steps of a proposed mechanism must algebraically sum to the overall balanced equation. The rate law of the mechanism that is the rate law of the slow step. must correlate with the experimentally determined rate law (determined using method of initial rates or [reactants] vs time)

Effect of temperature on reaction rates

According to the kinetic molecular theory the temperature of matter is a measure of the average kinetic energy of its constituent atoms or molecules. A higher temperature results in a correspondingly higher rate of collisions and a greater fraction of collisions possessing sufficient energy to over come the activation barrier. This yields a greater value for the rate constant k, and a correspondingly faster reaction rate. For slow reactions at temperature near 25degrees C an increase in 10degrees C will approximately double the number of reacting particles that have enough energy to react. At temperature much higher than that, increasing temperature leads to smaller and smaller increases in the number of successful collisions.

effects of a catalyst on a reaction

Adding a catalyst lowers Ea so the lower energy collisions that normally do not produce activated complexes and products will now produce products. In other words at any temperature using a catalyst will result in a greater percentage of collisions producing products.

Reaction energy diagrams and catalysis

An increase in temperature or concentration of reactants allows for many more collisions to attain the activation energy Ea and hence react successfully. In contrast a catalyst provides an alternative reaction pathway in which a different lower energy activated complex can form. Reaction pathways are called mechanisms reaction mechanisms and the roles catalysts play in them will be covered in section VI of this unit. Catalysts provide an additional reaction mechanism (path) that has a lower activation energy which results in an increased reaction rate. The catalyst is neither consumed nor changed following the reaction. Catalysts must be consumed in one step of a mechanism and be regenerated in a later step. This is why we say catalysts are neither consumed nor changed as a chemical reaction occurs , a consequence of this is that more than one activated complex is formed. This leads to more than one peak in the potential energy diagram for most catalyzed reactions Potential energy profiles for catalyzed reactions will usually involve the formation of more than one activated complex and hence more than one peak in the diagram.

Molecularity of elementary reactions

As mentioned above each step in a reaction mechanism is called and elementary reaction the molecularity of each elementary process is defined as the number of reactant species that must collide t o produce the reaction indicated by that step. A reaction involving one molecule is called a unimolecular step. A reaction involving the collisions of two species is called a bimolecular step, and a reaction involving the collisions of three species is called a termolecular step Unlike balanced equations representing an overall reaction the equations for elementary reactions are explicit representations of the chemical change taking place. The reactants in an elementary reactions equation undergo only the bond breaking and or making events depicted to yield the products. For this reason, the rate law for an elementary reaction may be derived directly form the balanced chemical equation describing the reaction. This is not the case for typical chemical reactions, for which the rate laws mar be reliably determined only via experimentation.

Catalysts in a mechanism

As we described briefly in earlier sections a catalyst functions by providing an alternate lower energy pathway for a reaction to follow. We know this "alternate pathway" is actually a different reaction mechanism, In essence most catalysts function by allowing the assembly of a different lower, energy activated complex than would have been formed if the catalyst was not present. Since catalysts are present before and after a reaction is compete they must be used to facilitate the formation of a lower energy activated complex in one step and then reformed in some later step. A catalyst is consumed in an early step and regenerated in a subsequent or later step.

Calculation of the activation energy for a multistep mechanism

Calculation of the activation energy for a multistep mechanism can be challenging. The activation energy for any step is simple, the potential energy change from the reactants for the elementary step to the activated complex for that step. Consequently the rate determining step with the highest activation energy. This value however is not necessarily the overall activation for the reaction. Rather the overall activation energy is the difference between potential energy of the activated complex with the highest energy and the potential energy of the reactants for the reaction as a whole.

presence of a catalyst - rate of reaction

Catalysts are substances that increase the rates of chemical reactions without being used up in the reaction. Catalysts remain in the same quantities and forms when a reaction starts and ends. The formulas of catalysts are not included in a chemical reaction. Sometimes the formula of a catalyst is shown above the arrow between products and reactants to show its presence.

Homogenous catalysts

Catalysts can be classified as one of two types, heterogeneous or homogenous. Many reactions are catalyzed in the presence of an acid, In such a case the hydrogen ions from the acid react with and somehow modify the structure of the reactant to make it more susceptible to reaction with another reactant. Catalysts such as this exist in the same phase (aqueous) as the rest of the reaction system are sometimes called homogenous catalysts.

In summary we see for a reversible potential energy diagram the following points are always true:

Change in H for reverse reactions have the same magnitude and opposite signs No matter the direction an activated complex must be formed. Ea is always smaller in the exothermic direction Altering reaction conditions of temperature, Concentration, pressure or surface area will have no effect on the potential energy diagram. The only thing that will alter the diagram is the addition of a catalyst.

Reaction mechanisms

Chemical reactions very often occur in a stepwise fashion, involving two or more distinct reactions taking place in sequence. A balanced equation indicates what is reacting (reactants) and what is produced (products) but it reveals no details about how the reaction actually takes place. The reaction mechanism (or reaction path) provides details regarding a precise step by step process by which a reaction occurs. Each of the steps in a reaction mechanism is an elementary reaction. These elementary reactions occur precisely as represented in the step equations; they must sum to yield the balanced chemical equation representing the overall reaction Species produced in an early step of a mechanism and consumed in a later step are called intermediates. A reaction mechanism is a series of steps (simple reactions) that may be added together to give an overall reaction In section 5 we learned that a successful collisions between reacting species require sufficient energy (Ea) and appropriate orientation. Consequently the simultaneous collisions of more than two reactant molecules with good geometry and Ean. is highly unlikely. It is not surprising that reactants having more that two reactant particles almost always involve more than one step in their reaction mechanism,.

collision frequency

Collision theory explains why most reaction rates increase as concentrations increase. With an increase in the concentration or partial pressure of any reacting substance, the change for collisions between molecules are increased because there are more molecules per unit of volume. More collisions mean a faster reaction rate assuming the energy of the collisions is adequate.

Orientation of collisions

Consider the reaction of carbon monoxide with oxygen Carbon Monoxide is a pollutant produced by the combustion of hydrocarbon fuels To reduce this pollutant automobiles have catalytic converters that use a catalyst to carry out this reaction, minimizing the release of carbon monoxide into our atmosphere If carbon monoxide and oxygen are present in sufficient amounts the reaction occurs at high temperatures and pressure.

Reaction Mechanisms and PE diagrams

Even though many reactions involve only two reacting species, studies show that the majority of chemical changes occur by mechanisms that involve at least two steps. Often one step is much slower than the other(s). The overall reaction rate cannot exceed the rate of the slowest step in a mechanism. Because the slow step limits the overall reaction rate it is called the rate determining step. A variety of conditions may cause a particular step to limit the overall reaction rate, these include -Complex collisions geometry -High activation energy -Low concentration of reactants -A termolecular collision Adding reactants to a reaction that appears in a non rate determining step of a mechanism, will have no effect on the reactions overall reaction state To increase the rate of a reaction it is necessary to increase the concentration of reactants in the rate determining step. Each step in a reaction mechanism: Involves different reacting species with different bonding arrangements and hence different potential energies and enthalpies Has its own rate law, rate constant, and its own Activation energy, depending on the activated complex formed for that step Consequently the potential energy diagram for a reaction will have the same number of peaks as there are steps in the reaction mechanism

Nature of reactants effects on rate of reaction

Fundamental differences in chemical reactivity are a major factor in determining the rate of a chemical reaction. For instance, Zinc metal oxidizes quickly when exposed to air and moisture, while iron reacts much more slowly under the same conditions. For this reason, Zinc is used to protect the integrity of the iron beneath it in galvanized nails. Generally reactions between simple monoatomic ions in a precipitation reaction such as Ag+ and Cl- are almost instantaneous. This is due to ions being extremely mobile, in close proximity to one another, having opposite charges, and requiring no bond rearrangement to react. However, more complicated ionic species react more slowly than those that are monoatomic

Heterogeneous catalysts

Heterogeneous catalysts are those in which reactions are limited to their surface only, most heterogeneous catalysts are solids. The most common are transition metals such as platinum or nickel. Catalysts of this type undergo adsorption of reactants unto their surface. The catalyst energizes the reactants and holds them in a position that allows easy interaction between them and other reacting species.

Monitoring property of the reaction mixture

If the amount of a reactant or product can't be monitored directly a chemist can monitor some property of the reacting mixture that correlates in a known manner with the quantity of reactant or a product. If a reaction is occurring in aqueous solution the solutions color and pH are properties that might indicate the quantity of reactant or product present. Reactions involving color changes may be colorimetrically analyzed using a spectrophotometer. A pH electrode is one type of ion selective electrode that can be used to measure acidity. The concentrations of many types of ions can be measured with different ISE's the ions concentration correlates with the charge that builds up as the ion diffuses across the ISE's membrane. It is simplest if only one chemical involved in the reaction affects the monitored property. If the property is influenced by more than one chemical, then their relative influences must be known.

Energy of collisions

If the collision does take place with the correct orientation there is still no guarantee that a reaction will occur, the collision must also occur with the sufficient energy to result in product formation. When reactant species collide with both proper orientation and adequate energy they combine to form an unstable species called an activated complex or a transition state. These species are very short lives and usually undetectable by most analytical instruments, in some cases sophisticated spectral measurements have been used to observe transition states.

Graphical determination of an integrated rate law

In many applications it is important to know how long a reaction must proceed to reach a predetermined concentration of some reactant or product or what reactant or product concentrations will be left after a given period of time. The integrated rate law shows how reactant concentration depends on time.

method of initial rates

In this method you compare experimentally determined initial rates (slope of tangent at time = 0.0 s) with the different initial concentrations of reactants. Measuring the initial rate of a reaction involves determining very small changes in concentration of a reactant or product over a very short period of time, An alternative approach is to use an integrated rate law, which expresses the concentration of a reactant as a function of time.

Calculating initial reaction rate

In this method you compare experimentally determined initial rates with different initial concentration of reactants. Measuring the initial rate of a reaction involves determining very small changes in concentration of a reaction or product over a very short time interval.

Temperature effects on rate of reaction

In unit 10 we learned about the qualitative relationship between temperature and kinetic energy. Mathematically speaking K = 1/2RT where R is a constant having the value 8.31 J/Mol K, and Tis the temperature in kelvins. From this relationship we see that temperature and kinetic energy are directly related to one another. If the temperature is doubled the kinetic energy is doubled. An increase in temperature will lead to particles striking one another with more energy. In other words, an increase in temperature means that the same particles are traveling faster. Consequently they hit each other more frequently and more forcefully. As a result temperature is the most significant factor that affects reaction rate. Another thing we learned in unit 10 is within any substance there is a normal distribution of kinetic energy among the particles that make up the system due to their random collisions.

Several factors effect the rate of a reaction

Increase in surface area makes rate faster Increase in temperature makes rate faster Adding a catalyst makes rate faster

When deciding what to measure for a reaction rate chemists need to consider these things

Is there a measurable property associated with the change in quantity of a reactant or product you might use to determine the rate? Exactly how might you measure the quantity of reactant or product in the laboratory Finally what units would be associated with the quantity you measure and consequently what units will represent the reaction rate?

activation energy

Minimum amount of energy needed for reactants to form a product during a collision between reactants is called the activation energy. How this energy compares to the kinetic energy provided by colliding reactant molecules is a primary factor affecting the rate of a chemical reaction. If the Activation energy is much larger than the average kinetic energy of the molecules, the reaction will occur slowly since only a few fast moving molecules will have enough energy to react If the Activation energy is much smaller than the average kinetic energy of the molecules, a large fraction of molecules will be adequately energetic and the reaction will proceed rapidly since most of the fast moving molecules will have enough energy to react. The reaction energy diagram below shows how the energy of the reaction between carbon monoxide and oxygen as it undergoes a reaction according to the equation.

Surface area effects on rate of reaction

Most reactions in the lab are carried out in solution or in the gas phase. In these states the reactants can intermingle on the molecular or atomic level and contact each other easily. When reactants are present in different states in a reacting system, we say the reaction is heterogenous. Most heterogenous systems involve the reaction of a solid with a solution or a gas. In heterogenous reactions the reactants can come into contact with each other only where they meet at the interface between the two phases. The size of the area of contact determines the rate of the reaction. Decreasing the size of the pieces of solid reactant will increase the area of contact. More collisions between reacting particles results in faster reaction rate.

Temperature of reacting particles vs kinetic energy Unit 11 pdf slide 26

Note that some particles have very little energy and others have a lot. The x axis value associated with the peak of the curve indicates the kinetic energy of most of the particles. The second curve indicates how the distribution would change if the temperature were increased. The area under the curves represents the total number of particles and therefore should be the same for both curve. The gray area represents the particles that have sufficient energy to collide successfully and produce a product. Notice that this has increased with an increase in temperature. A common generalization is that an increase of 10 degrees C will double the reaction rate. This is true for some reactions around room temperature.

Reaction rates may be determined by

Observing either the rate of disappearance of a reactant or the appearance of a product.

Calculating reaction rate

Once the chemist has decided what quantity of a particular chemical species to measure, they can begin to gather data. The data can then be used to calculate the rate of chemical reaction. Data may be presented graphically to monitor the rate throughout the entire reaction, or initial and final data may be used to determine the reactions average rate.

aliquot

Portion of specimen used for testing

first order differential rate law

Rate = k[A]

Rate of reaction

Rate is a measure of how some property varies with time Speed is a familiar rate that expresses the distance traveled by an object in a given amount of time Wage is a rate that represents the amount of money earned by a person for working a given amount of time Chemical reaction rate is a measure of how much reactant is consumed or how much product is produced by a reaction in a given amount of time

solving for rate constant

Rate=k[A]^n1[B]^n2 n1 = rate order of A n2 = rate order of B Plug in values and solve for k

Intermediates in a mechanism

Since we cant actually see reacting partivles colliding, flying apart and reassembling the mechanisms we use to describe chemical reactions are really just theoretical models. Chemists determine the models by altering the concentration of species involved in the mechanism and examining the effect these alterations produce Computer models are also very useful in understanding mechanisms In any multistep reaction mechanism, the first collisions or decompositions of an energized reactant, always produces some product that is consumed in a later step of the mechanism. Such species is called a reaction intermediate. An intermediate is a species that is formed in an early step and consumed in a later step of a mechanism and so does not appear in the overall reaction

Reaction rates are positive quanities

So negative rates should be multiplied by -1

Factors affecting the rates of reaction

Surface area of reactants: The greater the surface area of solid reactants (smaller the particles) the more molecules there are on the surface to collide, so the faster the reaction Reactant concentration/pressure: The more concentrated the reactants the more likely the reactants will come together (collide) producing products so the faster the reaction Temperature: The higher the temperature the faster the reaction because the reactants have more kinetic energy so they collide more frequently and with greater energy. It is commonly accepted that for every increase in temperature if 10degrees C the reaction rate doubles Nature of reactants: State of matter of reactants (s, l, g, or aq) Catalysts: Catalysts are substances that speed up a chemical reaction but they themselves are not changed in the reaction. Catalysts usually appear above the yield arrow in a chemical reaction

For a collision to be successful in causing a reaction:

The atoms that will be bonded together in the product should be oriented towards each other or else it is unlikely a collision will occur.

Reaction diagrams

The diagram depicts the reactions activation energy Ea as the energy difference between the reactants and the transition state The enthalpy is estimated as the energy difference between the reactants and products.

Reaction energy profiles

The easiest way to follow the changes that occur during a chemical reaction is to use the visual profile of energy changes that occur during the reaction. The potential energy diagram is a graphical representation of the energy changes that occur during a chemical reaction. The axis is not a time axis. We are simply following the energy profile as the reaction proceeds from reactants to activated complex to products. Increasing the rate of the reaction does not change the length of the x axis. The activation of energy Ea, is the difference between the potential energy of the activated complex and the total potential energy of the reactant molecules. It represents the amount of energy the reacting molecules must gain to form an activated complex It is important to note that the net energy evolved or absorbed during the reaction is independent of the activation energy. The enthalpy change is the difference between the total potential energy of the products and the total potential energy of the reactants. While altering factors such as the reactant concentrations surface area, temperature or adding a catalyst will affect the rate of a chemical reaction they will not affect the appearance of a a potential energy diagram of a reaction.

calculating half life of a first order reaction

The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value. The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t1/2 = 0.693/k

Rate laws

The rate of a reaction is often affected by the concentration of reactants. Rate laws (sometimes called differential rate laws or rate equations are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants.

Relative rates of reaction

The rate of a reaction may be expressed as the change in concentration of any reactant or product. For any given reaction these reaction rate expressions are all related simply to one another according to reaction stoichiometry. The rate of the general reaction: Rate = -(1/a)(ΔA/Δt) = (1/b)(ΔB/Δt)

Concentration/pressure effects on rate of reaction

The rates of all reactants are affected by the concentrations of the dissolved or gaseous reactants. When more solute is placed in the same volume of solvent, the solutions concentration is increased. When more gas particles are placed in the same container the partial pressure of the gas has increased. Always remember the concentration of pure solids and liquids cannot be increased because adding more substance increases both the moles and liters so the molarity remains constant. Also remember that crushing or breaking solids increases surface area. However it is impossible to cut a piece of liquid or gas into smaller bits. The surface area of liquids can be increased by spreading them over a larger area though.

Reaction measuring techniques

The technique used to measure the change in the quantity of reactant or product varies greatly depending on the reaction involved and the available apparatus 1. Reactions in solution The concentration of a reactant in solution may be determined from time to time as the reaction proceeds by the titration of an aliquot of the reacting species 2. Gas forming reactants If a gas is being formed in a closed system a manometer may be used to measure the change in pressure. A manometer measures the pressure of a gas formed in a reaction during a reaction Gas production might also be measured using a pneumatic trough and a gas volume measuring tube called a eudiometer. A eudiometer measures the volume of gas produced If a gas being formed is leaving an open system, there will be a change in mass that could easily be measured using a balance

Effects of magnitude of activation energy, Ea on reaction rates

Two shaded areas under the curve represent the numbers of molecules possessing adequate energy (RT) to over come barriers (Ea). A lower activation energy results in a greater fraction having the activation energy required, leading to a faster reaction. Reactions with lower activation energies occur more quickly because more of the collisions have the required Ea.

Atoms must collide to react with eachother

We should not be surprised that reacting atoms molecules or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This simple premise is the basis for a very powerful theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.

What happens when there is a catalyst

What happens is that catalysts are consumed during an intermediate step in a reaction and regenerated in a later step.

Deriving a rate law for a mechanism when the slow step is preceded by a fast equilibrium

When the rate determining step of a mechanism is preceded by a step involving a rapid reversible reaction the rate law is more challenging to derive. A reversible reaction is at equilibrium when the rates of the forward and revers reactions are equal. Since intermediate species concentrations are not used in formulating rate laws for overall reactions this approach is always necessary when deriving the rate law for a mechanism, where slow step is preceded by a fast equilibrium.

when to use the method of initial rates and when to use the graphical approach

Whether you use method of initial rates or graphical approach is determined by the type of data that can be collected conveniently and accurately. Once you have determined either type of rate law (differential or integrated) you can write the other for a given reaction. Integrated rate laws are commonly determined for reactions involving one reactant (decomposition) the data you would need to determine the order of a reaction with a single reactant is Molarity, M Vs time

integrated rate law zero order

[A]t = -kt + [A]0

activated complex

a transitional structure that results from an effective collision and that persists while old bonds are breaking and new bonds are forming

to determine the order of a reactant or product in a reaction

calculate and graph these 3 things (A is the reactant or product being tested) 1: [A] vs time 2: ln[A] vs time 3: 1/[A] vs time if graph 1 is linear the order of the reaction is 0 if graph 2 is linear the order of the reaction is 1 if graph 3 is linear the order of the reaction is 2

Average reaction rate equation

change in measurable quantity of a chemical species (P, M, g, mol, pH) / Change in time change in measurable quantity of a chemical species (P, M, g, mol, pH) divided by Change in time

Integrated rate law is used to

determine the amount of reactant or product present after a period of time estimate the time required for a reaction to proceed to a certain extent. (for example, an integrated rate law is used to determine the length of time a radioactive material must be stored for its radioactivity to decay to a safe level) Using calculus, the diferential rate law for a chemical reaction can be integrated with respect to time to give an equation that related the amount of reactant or product in a reaction mixture to the elapsed time of the reaction. This process can either be very straight forward or very complex, depending on the complexity of the differential rate law.

differential rate law

expression that gives the rate of a reaction as a function of concentrations; often called rate law

determining k from integrated rate law graphs

for 0 order reaction k = -slope of line for 1 order reaction k = -slope of line for 2 order reaction k = +slope of line

overview of rate laws

https://drive.google.com/file/d/1Jk6TyM2DJJ4eqVGpPM6bDX9SRLpDkVX3/view page 90

rate orders

if whatever change you make to reactant concentration has no effect on reaction rate, the order = 0 if whatever change you make to reactant concentration has the same change on reaction rate, the order = 1 if whatever change you make to reactant concentration has the change (change[])^2 on reaction rate, the order = 2

Integrated rate law - two ore more reactants present

if you wish to analyze the kinetics of a reaction that involves two or more reactants using an integrated rate law approach (reactant concentration vs time data) you need to ensure that the reactant you are NOT studying is present in very high concentrations (at least 10X the molarity of the reactant you are studying) this ensures that as the reactant you are studying goes down the change in the concentration of the reactant you are not studying is negligible, and therefore does not impact kinetics.

Reaction rate

is the change in the amount of a reactant or product per unit of time. Reaction rates are determined by measuring the time dependence of some property that can be related to reactant or product amounts. If you consider familiar reactions like the explosion of a firecracker, the metabolism of the lunch you ate today and the rusting of your bicycle, it is evident that chemical reactions occur at a wide variety of rates.

The overall order for a reaction

is the sum of the orders with respect to each reactant

first order integrated rate law

ln[A] = - kt + ln[A]0

Titration

process in which a solution of known concentration is used to determine the concentration of another solution

the greater the order of reactant (0,1,2,3)

the greater the change in reaction rate

For homogenous reactions, both the reactants and products are present in the same solution and thus occupy the same volume, so...

the molar amounts can be replaced with molar concentrations

half-life of a reaction

time required for half of a given amount of reactant to be consumed