MCAT General Chemistry Chapter 5- Chemical Kinetics

Spontaneous reactions do not imply that the reaction will occur

*spontaneous reactions do not imply the reaction will occur fast - most important biochemical reactions happen so slowly that without the aid of enzymes or catalysts, measurable progress would not happen over the course of a human lifetime (without enzymes or catalysts, most reactions would take forever)

Homogenous catalysts

-same phase as the reactants -solid, liquid, gas

Arrhenius equation

- best a mathematical way of representing collision theory k=Ae^(-Ea/RT) where k is rate constant of reaction, A is frequency factor, Ea is activation energy, R is ideal gas constant, and T is temp in Kelvins *relationships between the variables and exponent rules that govern the equation are important - As the frequency favor increases, the rate increases directly -If T were to increase to infinity, while other variables were constant, the value of the exponent would have a magnitude less than 1 *note the presence of the negative sign -as the magnitude of the exponent gets smaller, it actually moves from a more negative value towards 0 -the exponent becomes more positive which means the rate constant increases -this should make sense because the rate of a reaction should increase with temperature *low activation energy and high temperatures make the negative exponent of the Arrhenius equation smaller in magnitude and this increase the rate constant k

Broken-order reactions

- fractions or noninterger orders often in mixed order reactions

Activation energy

-Ea, energy barrier -the minimum energy of collision necessary for a reaction to take place

Experimental Determination of Rate Law

-The values of k,x, and y in the rate law equation (rate=k[A]^x[B]^y) must be determined experimentally for a given reaction at a given temperature -data usually provided in chart that includes initial concentrations of reactants ad product formation as a function of reactant concentrations -data for 3-4 rials are often included -identify a pair of trials in which the concentration of one of the reactants is changed while the concentrations of all the other reactants remain constant -under these conditions, any change in the rate of product formation from one trial to another is fully attributable to the change in concentration of that one reactant -ex. A+B=C -if A is constant and the concentration of B doubles, if the rate of formation of product C quadruples, then the exponent on [B] must be two based on the generic rate law (rate =k[A]^x[B]^y) -2^Y = 4, y = 2 -repeat this process for the other reactant using the data from a different pair of trials making sure the concentration of only that reactant we are looking at is changed while the concentrations of all others are constant -once the orders are determined, the rate law can be completed by replacing the exponents x and y with numbers -to determine k, the rate constant, plug in actual numbers from one of the trials - pick whichever trial has the most arithmetically convent numbers

Higher order reactions

-There are very few noteworthy reactions which a single reaction step involves a third order rate (termolecular process) -Far more rare for 3 particles to collide simultaneously with correct orientation to undergo a reaction

Frequency factor

-aka the attempt frequency -a measure of how often molecules in a certain reaction collide, with unit s^-1 -can be increased by increasing the number of molecules in the vessel - when there are more molecules, there are more opportunities for collision

Transition state

-also called activated complex -greater energy than both reactants and products -denoted by two positive symbols on top of each other -energy required to reach this state is called activation energy -can either dissociate into products or revert to reactants without addition energy input

Why must you be careful in reading the temperature of reactions? What does this diagram show?

-apparently raising the temperature by 10C in a reaction will result in doubling the reaction rate -this is not always true but is generally for biological systems but not for others -if the biological system gets too a high, the catalyst can denature - plummeting the reaction rate -the reaction here is optimal between 35-40 at normal body temperature and falls shortly after 40C at which it denatures

Concentration of radioactive substance A (equation)

-based on the first order rate law, the rate of decrease of the amount of radioactive isotope A is proportional to the amount of A - rate = - delta [A]/delta time = k[A] Therefore the concentration of radioactive substances A at any time t can be expressed as: -[A]t=[A]o*e^(-kt) -[A]t=concentration of A at time t -[A]o=initial concentration of A - k is rate constant

Gibbs Free Energy

-determines whether the reaction is spontaneous or non-spontaneous -also called delta G -determines if a reaction will occur by itself without outside assistance

Heterogeneous catalysts

-different phase from the reactants

How are transition states different from reaction intermediates?

-distinguished from reaction intermediates in that its theoretically constructed (can't be isolated) to exist at the max point of energy rather than distinct identities with finite lifetimes

Collision theory

-for a reaction to occur, molecules must collide with each other -a reaction rate is proportional to the number of effective collisions between the reacting molecules (rate increases with more collisions) *not all collisions result in chemical reaction -for a collision to be effective, the molecules must be in the proper orientation and have a sufficient kinetic energy to exceed the activation energy/break existing bonds to form new ones -only a fraction of colliding particles have enough kinetic energy to exceed activation energy -this means that only a fraction of all collisions are effective

First-order reaction

-have a nonconstant rate that depends on the concentration of a reactant -rate directly proportional to that one reactant such that doubling the concentration of that reactant results in doubling of the reaction rate of formation of the product -the rate law = k [A]^1 or k[B]^1 -occurs with radioactive decay -first order rate laws with single reactants imply that the reaction begins when the molecule undergoes chemical change by itself without chemical interaction, usually without a physical interaction other molecules -concentration vs time curve of first-order reaction is nonlinear -the curve indicates that the rate of formation of product is dependent on concentration of a reactant -slope of a ln[A] vs. time plot (straight line) is -k -the slope of such line is the opposite of the rate constant k (rate constant opposite of slope) -k has units s^-1

Second-order reactions

-have a nonconstant rate that depends on the concentration of reactant -rate proportional to either the concentrations of two reactants or the square of the concentration of a single reactant -implies physical collision between two reactant molecules, especially if the rate law is first order with respect to each of the reactants -concentration vs. time curve is nonlinear with respect to one single reactant -curve shows that the rate of formation of product is dependent on concentration of reactant -slope of a 1/[A] vs. time plot (straight line) is k reveals a linear curve -slope of such curve is equal to rate constant k -k has units M^-1s^-1

Why are rate problems important?

-helps with understanding of proportionality and variable relationships

Enzyme saturation

-high substrate conditions saturate the active sites of the enzyme, leading to maximal turnover -adding more substrate will not increase the rate considering all enzymes are already taken

By what factors do enzymes enhance the rate of the reaction?

-increase the rate by about 10^2 to 10^12 depending on the reaction over other thermo dynamically feasible reaction pathways -also talked about in Chapter 2 of Biochemistry

4 Factors affecting reaction rate

-increasing concentration of reactant will increase reaction rate because there are more effective collisions per unit time (except for zero-order reactions) -dads to increase in frequency factor, relating to Arrhenius equation *for reactions in gaseous state, partial pressure of gas reactants serve as a measure of concentration -increase temp. will increase reaction rate because temperature is a measure of a particles' average kinetic energy, therefore increasing temp increases avg kinetic energy of molecules -portion of reactants with enough energy to surpass the activation energy and thus capable of undergoing a reaction will increase with higher temperature -all reactions, including nuclear, are temperature dependent *optimal temperature is needed for efficient activity -changing medium can increase or decrease reaction rate, depending on how reactants interact with medium -some molecules are more likely to react with each other in aqueous environments while others are more likely to react in non aqueous solvents such as DMSO (dimethyl sulfoxide) or ethanol -the physical state of the medium (liquid, gas, solid) can have an effect -polar solvents are generally preferred because their molecular dipole tends to polarize the bonds of the reactants, thereby lengthening and weakening them, permitting the reaction to occur faster -adding a catalysts increase reaction rate because it lowers the activation energy of both the forward and reverse reactions -no impact on free energies of reactants or products (thermodynamics), therefore only alters the rates of the reactions (kinetics; forward and reverse) by the same factor -no impact on equilibrium position or measurement of Keq *can not transform a nonspontaneous reaction into a spontaneous one - will only make spontaneous reactions move more quickly toward equilbrium -substances that increase the reaction rate without being consumed - enzymes specifically -interact with reactants by absorption or the formation of intermediates to stabilize them to reduce the Ae necessary for the reaction to proceed (faster) -return to chemical state after product formation -increases frequency of collisions between reactants by changing relative orientation, increasing the percentage -can donate electron density to reactants -can reduce intramolecular bonding with reactant -has two classifications: homogenous and heterogenous

Rate constant

-k -technically not a constant because its particular value for any specific chemical reaction will depend on the activation energy for that reaction and the temp. at which the reaction takes place -however, for specific reaction, at specific temp., the rate constant is indeed a constant

Rate for general reaction aA + bB --> cC + dD

-lower case letters are the stoichiometric coefficients rate= -Δ[A]/aΔt=-Δ[B]/bΔt=Δ[C]/cΔt=Δ[D]/dΔt -expressed in units of molarity per second (M/s) OR moles per liter per second (mol/L x s)

Rate law

-must be determined from experimental data =k[A]^x[B]^y where x and y are the orders of A and B respectively - k is the proportionality constant k or the reaction rate coefficient/rate constant -for nearly all forward irreversible reactions, the rate is proportional to the concentration of the reactants with each concentration raised to some experimentally determined exponent -the rate is proportional to =k[A]^x[B]^y -also measured in units of concentration over time (molarity per second or moles per liter per second) -exponents in rate law are not equal to stoichiometric coefficients unless the reaction occurs via a single step mechanism -note product concentration never appear in rate law - do not confuse with equilibrium expressions *whenever a question asks to determine the rate law for a reaction, look for its experimental data first

Chemical mechanism, intermediate, rate determining step

-propose a series of steps or pathways that make up the overall reaction -many reactions proceed by more than one step -accompanied by the sum of which gives the overall reaction -helps explain the reaction rate, position of equilibrium, and thermodynamic characteristics -must coincide with rate data from experimental observation -major topic in organic chemistry and metabolism (5-10 Organic Chemistry, 9-11 Biochemistry) -ex. A2 +2B => 2AB This reaction would take place in two steps: Step 1: A2 + B => A2B (slow) Step 2: A2B + B => 2AB (fast) -these two steps will give the overall net reaction -A2B does not appear in the overall reaction is deemed as the intermediate -intermediates are often difficult to detect because they can be consumed after formed - proposed mechanism that includes the intermediate can be supported through kinetic experiments -the rate determining step is the slowest step -acts as a kinetic bottle neck -limits the maximum rate at which the reaction can proceed -prevents the overall reaction from proceeding any faster than that slowest step **the rate of the whole reaction is only as fast as the rate determining step

Zero-order reactions

-rate of formation of product C is independent of changes in concentration of any reactants (A or B) -have a constant reaction rate that does not depend on the concentration of reactant; rate is equal to the rate constant or rate coefficient of K -rate law = =k[A]^0[B]^0 = kt + [A]0 -k has units of molarity/seconds -can only be affected by changing the temp. or adding a catalyst (lowers Ea to increase k) considering that the rate constant is dependent on those two factors -concentration vs. time curve is a straight line, with slope equal to -k -k has units of M/s -rate of the reaction or k is the opposite of the slope

Free energy diagram

-shows relationship between the activation energy, the delta G of the system, and delta G of the reaction -Delta G of rxn: difference between free energy of products and reactants *negative free energy change indicates exergonic reactions (energy released; -delta G) while positive implies endergonic (energy gained; +delta G) -activation energy of forward reactions: difference between free energy between the transition state and reactants -activation energy of reverse reactions: difference between free energy between the transition state and products -transition state is at the peak of the energy diagram *free energy of product (thermodynamics) can be raised or lowered thereby changing the value of delta G without affecting the value of forward Ea (kinetics) - shows that kinetics and thermodynamics should be considered separately *diagrams that peak down are usually exergonic while those rising up are endergonic *depending on context, reaction profiles either use Gibbs free energy or enthalpy for the y axis *uncatalyzed reactions usually have higher transition states and Ae forward and reverse

Reaction orders

-the power to which the concentration of a reactant is raised in a rate law -includes first, second, higher, or mixed on the basis of kinetics -generic reaction mechanism can be used

Mixed-order reactions

-those that have a rate order that changes over time -refer to non interference orders/fractions in other cases to reactions with rate orders that vary over the course of the reaction -includes broken order reactions *also known as reactions that change over time on MCAT - know both terms -rate law = k1 [C][A]^2/k2 + k3[A] -A is a single reactant -C is a catalyst -large value for [A] at the beginning of the reaction is that k3[A]>>k2 and the reaction will appear to be first order with respect to A -at the end, when [A] is low, k2>> k3[A], making the reaction appear second order with respect to A -concentration of A changes the reaction order *overall reaction and mechanism are beyond the scope as well as the derivation *understand what is implied here: how the rate order changes as the reactant concentration changes

Reaction coordinate

-traces the reaction from reactants to products

Transition state theory

-when molecules collide with energy equal to or greater than the activation energy, they form a transition state in which the old bonds are weakened and the new bonds begin to form -molecules form a transition state or activated complex during a reaction in which the old bonds are partially dissociated into products and the new bonds are partially formed -from transition state, reaction can proceed toward products or revert back to reactants -transition state is the highest point on a free energy reaction diagram

Some symptoms of hyper and hypothermia are related to changes in

Metabolism caused by changes in temperature and reaction kinetics.

What type of reactions usually include kinetic limitations?

Multi step reactions like in substrate level and oxidative phosphorylation in Biochemistry -usually the intermediate steps

Rate of reaction expression Based on collision theory

Rate = Z x f -Z is total number of collisions occurring per second -f is the fraction of collisions that are effective

Stoichiometric coefficients for the overall reaction are often different from those for the...

Rate law and will therefore not be the same as the order of the reaction.

Overall order of reaction rate law

Sum of X and y -exponents can be integers or fractions and must be determined experimentally *MCAT will focus mainly on zero, first, second and third order reactions *will primarily be interferes

Reaction rates of dissociation and synthesis can be affected by aspects like

Temperature

The stoichiometric coefficients for the reaction are not equal which means

That the rates of change of concentrations are not equal -ex. Two moles of A are consumed for every B molecule consumed - the rate of consumption of A is twice the rate of B = every 2 moles of A consumed, only one molecule of C is produced - rate of consumption of A is twice the rate of production of C -rate of B would be equal to rate of C production

Common Traps and confusions in chemical kinetics, law of mass action

The assumption that orders of a reaction are the same as the stoichiometric coefficients in balanced equations -the values are usually never the same -orders are experimental -when they do match, the rxn mechanism is a single step and the balanced overall reaction is reflective of the entire chemical process OR when the complete reaction mechanism is given and the rate determining step is indicated -the stoichiometric coefficients on the reactant side of the rate determining step are equal to the orders -This becomes tricky when the rate determining step involves an intermediate as a reactant in which one must derive the intermediate molecule's concentration by the law of mass action (equilibrium constant expression) for the step that produced the intermediate Mistaking the equilibrium constant expression/law of mass action for the rate law -they both look similar -the expression for equilibrium includes the concentrations of all the species in the reaction, both reactants and products -the expression for chemical kinetics - the rate law expression - includes the reactants -Keq indicates where the reaction's equilibrium position lies -the rate indicates how quickly the reaction will get there K, the rate constant, is not constant -its value for specific reactions will depend on the activation energy for that reaction and temperature at which the reaction takes place -HOWEVER, for reactions that are specific and are at a specific temperature, it indeed becomes a constant -reversible reactions, the Keq is equal to the ratio of the rate constant for the forward reaction K divided by the rate constant for the reverse reaction, k-1 Principles of equilibrium apply to the system only at the end of the reaction after the system has reached equilibrium -while the reaction rate can theoretically be measured at any time, it is usually measured at or near the beginning of the reaction to minimize effects of the reverse reactions

Chemical kinetics

The study of reaction rates, the effects of reaction conditions on these rates, and mechanisms implied by such observations -molecular basis of reactions provides framework of reaction chemistry

Two theories of the molecular basis of chemical reactions

Transition state theory and collision theory of chemical kinetics

Reaction rates are measured in terms of...

the rate of disappearance of a reactant or appearance of a product because reactants by definition are being consumed in the process of the formation of products -negative signs are placed at the front of the rate of reactants

Exponents in the rate law are not equal to the stoichiometric coefficients, unless...

the reaction occurs via a single step mechanism

Rate order of reaction is...

the sum of all individual rate orders in the rate law