CHMA11 UTSC Midterm/ Final textbook notes. Chemistry University Notes. Midterm reviews and final reviews

  CHMA11 ~ TEXTBOOK NOTES

10.2 VESPR Theory: The Five Basic Shapes (400-403)

·       valence shell electron pair repulsion (VESPR) theory: allows prediction of shapes of molecules based on idea that electrons- either as lone pairs or as bonding pairs- repel one another.

·       based on idea that electron groups repel one another through coulombic forces

¾    electron groups: lone pairs, single bonds, multiple bonds, or lone electrons in a molecule

·       repulsions between electron groups on interior atoms of a molecule determine geometry of molecule

·       preferred geometry of a molecule is one where electron groups have max separation (min energy) possible

·       for molecules with one interior (central) atom, molecular geometry depends on

¾    number of electron groups around central atom

¾    how many of those electron groups are bonding and how many are lone pairs

Two Electron Groups: Linear Geometry

·       linear geometry: molecular geometry of 3 atoms with 180° bond angle due to repulsion of 2 electron groups

·       molecules that form only 2 single bonds, with no lone pairs, rare because they don’t follow octet rule

·       same geometry observed in all molecules that have 2 electron groups and no lone pairs

·        

Three Electron Groups: Trigonal Planar Geometry

·       trigonal planar geometry: molecular geometry of four atoms with 120° bond angles in a plane

·       double bond contains more electron density than single bond, exerts slightly greater repulsion on single bonds

·        

Four Electron Groups: Tetrahedral Geometry

·       tetrahedral geometry: molecular geometry of 5 ato       ms with 109.5° bond angles

·        

Five Electron Groups: Trigonal Bipyramidal Geometry

·       trigonal bipyramidal geometry: molecular geometry of 6 atoms with 120° bond angles between 3 equatorial electron groups and 90° bond angles between the two axial electron groups and the trigonal plane

·        

Six Electron Groups: Octahedral Geometry

·       octahedral geometry: molecular geometry of 7 atoms with 90° bond angles

·        

10.8 Molecular Orbital Theory: Electron Delocalization (432-)

·        

11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.11, 11.12, 12.2, 12.3, 12.4, 12.5, 12.6, 12.7

CHAPTER 13

13.2 The Rate of a Chemical Reaction (564-569)

·       if chemical reaction has slow rate, only relatively small fraction of molecules react to form products in given period of time; fast rate means large fraction of molecules react

·       rate of chemical reaction measured as change in amounts of reactants or products (usually in concentration units) divided by change in time

·       reaction rate: negative of change in concentration of a reactant divided by change in time

¾    negative sign usually part of definition when reaction rate is defined in terms of a reactant because reactant concentrations decrease a reaction proceeds; change in concentration of a reactant is negative

¾    negative sign makes overall rate positive

·       change in concentration of a product positive; no negative sign when rate defined in respect to product

·       definition of rate with respect to each reactant and product must reflect stoichiometric coefficients of reaction

The Average Rate of the Reaction

·       calculate average rate of reaction using:  –Δ [A]/Δt (M/s)

·       rate is average rate within given time interval

Instantaneous Rate of the Reaction

·       rate at any one point in time; represented by instantaneous slope of curve at that point

·       can be determined from slope of tangent to curve at point of interest

·       rate is same whether we use one of reactants or product for calculation

·       generic reaction: aA + bB → cC + dD

rate of reaction:

·       example on page 567

Measuring Reaction Rates

·       polarimetry: measuring degree of lighting passing thorough a reacting solution

·       spectroscopy: most common; light of specific wavelength passed through sample, intensity of transmitted light (depends on how much light absorbed by sample) is measured and recorded

·       reactions in which number of moles of gaseous reactants and products changes as reaction proceeds can be readily monitored by measuring changes in pressure

13.3 The Rate Law: The Effect of Concentration on Reaction Rate (569-572)

·       rate law: relationship between rate of reaction and concentration of reactants; rate = k [A]ⁿ

¾    k= rate constant: constant of proportionality

¾    n= reaction order: determines how rate depends on concentration of reactants

®    if n=0, reaction is zero order, rate independent of concentration of A

®    if n=1, reaction is first order, rate directly proportional to concentration of A

®    if n=2, reaction is second order, rate proportional to square of concentration of A

®    other orders possible, including non-integers, but these most common

Zero-Order Reaction

·       rate = k[A]⁰ = k

·       rate constant because reaction doesn’t slow down as concentration of A decreases

·       rate same at any concentration of A

·       occur under conditions where amount of reactant available for reaction unaffected by changes in overall quantity of reactant

First-Order Reaction

·       rate = k[A]¹

·       rate slows down as reaction proceeds because concentration of reactant decreases

·       rate directly proportional to concentrations

Second-Order Reaction

·       rate = k[A]²    

·       rate more sensitive to reactant concentration

Determining the Order of Reaction

·       order of reaction can be determined only by experiment

·       method of initial rates: initial rate measured by running reaction several times with different initial reactant concentrations to determine effect of concentration on rate

·       can determine value of k by solving rate law for k and substituting concentration and initial rate from any one of the measurements

·       for 0 order reaction concentration doubles as initial rate stays constant, for 1^st order reaction, concentration doubles as initial rate doubles, for 2^nd order concentration doubles as initial rate quadruples

·      

·       rate constant for 0 order reaction is Ms^-1, 1^st order reaction is s^-1, 2^nd order reaction is M^-1s^-1

·       example on page 570

Reaction Order for Multiple Reactants

·       consider reaction aA + bB → cC + dD

·       as long as reverse reaction negligibly slow, rate = k [A]^m [B]ⁿ

·       overall order: sum of orders of all reactants in a chemical reaction

·       rate law for any reaction must be determined experimentally

·       example of rate law and rate order on page 572

13.4 The Integrated Rate Law: The Dependence of Concentration on Time (573-580)

·       integrated rate law: relationship between concentrations of the reactants in a chemical reaction and time

First-Order Integrated Rate Law

·       in A → products, rate directly proportional to concentration

·       rate = k [A]

·        ; aka differential rate law

·       first order integrated rate law: ln[A]_t = -kt + ln[A]₀ or

¾    [A]_t = concentration of A at any time, k= rate constant, [A]₀= initial concentration of A

·       for 1^st order reaction, plot of natural log of reactant concentration as function of time yields straight like with slope of –k and y-intercept of ln[A]₀

·       example on page 575-576

Second-Order Integrated Rate Law

·       in A → products, rate proportional to square of concentration of A

·       rate = k [A]²

·      

·       second order integrated rate law:

·       for straight line, plot inverse of concentration of reactant as function of time; slope of k, intercept of 1/[A]0

·       example on page 577

Zero Order Integrated Rate Law

·       rate proportional to constant

·       rate = k [A]⁰ = k

·      

·       zero order integrated rate law: [A]_t = -kt + [A]₀

·       for straight line, plot concentration of reactant as function of time; slope of k, intercept of [A]₀

The Half-Life of a Reaction

·       half-life (t_1/2): time required for concentration of reactant or amount of radioactive isotope to fall to one-half of its initial value

·       half-life expression: defines dependence of half-life on rate constant and initial concentration; different for different reactions

First-Order Reaction Half-Life

·       integrated rate law:

·       half-life of first-order reaction:

·       t_1/2 independent of initial reaction

·       constant half-life unique to first order reactions

·       example on page 579

Second-Order Reaction Half-Life

·       integrated rate law:

·       half-life of second-order reaction:

·       half-life depends on initial concentration

·       half-life continues to get longer as concentration decreases

Zero-Order Reaction Half-Life

·       integrated rate law: [A]_t = -kt + [A]₀

·       half-life of first order reaction:

·       half-life depends on initial concentration

13.5 The Effect of Temperature on Reaction Rate (581-588)

·       temperature dependence of reaction rate contained in k

·       k only constant when temperature constant

·       increase in temperature generally results in  increase in k, resulting in faster rates

·       Arrhenius equation: relates rate constant of reaction to temperature, activation energy, and frequency factor

¾     ; k= rate constant, T=temperature (K)

¾    R= gas constant= 8.34 J/molK

¾    frequency factor (A): aka pre-exponential factor; number of times that reactants approach activation energy per unit time

¾    activation energy (E_a): energy barrier in chemical reaction that must be overcome for reactants to be converted into products

The Activation Energy                                                         

·       activated complex (transition state): high-energy intermediate state between reactant and product

·       activation energy is energy required to reach activated complex

·       higher E_a, slower reaction rate (at given temperature)

The Frequency Factor

·       approaching activation barrier not equivalent to surmounting it

·       most approaches don’t have enough total energy to make it over activation barrier

The Exponential Factor

·       exponential factor: number from 0-1 that represents fraction of molecules that have enough energy to pass activation barrier on given approach

·       fraction of approaches that are successful and result in product

·      

·       as temperature increases, number of molecules having enough thermal energy to pass activation barrier increases

Arrhenius Plots: Experimental Measurements of the Frequency Factor and the Activation Energy

·        

·       Arrhenius plot: plot of natural log of rate constant (ln k) versus inverse of temperature in kelvins (1/T) that yields a straight line with slope of –E_a/R and y-intercept of ln A

·       example on page 584-585

·       when either data are limited or plotting capabilities absent, can calculate activation energy if we know rate constant at 2 different temperatures

·       2-point form of Arrhenius equation:

·       example on page 585-586

 The Collision Model: A Closer Look at the Frequency Factor

·       consider 2 gas phase reactants: A_(g) + B_(g) → products

·       collision model: model of chemical reactions in which reaction occurs after a sufficiently energetic collision between two reactant molecules

·       each approach to activation barrier is a collision between the reactant molecules

·       frequency factors of most gas-phase chemical reactions tend to be smaller than number of collisions that occur per second

·      

¾    orientation factor (p): fraction of sufficiently energetic collisions

¾    collision frequency (z): number of collisions that occur per unit time; can be calculated for a gas-phase reaction from pressure of gases and temperature of reaction mixture

·       under typical conditions, single molecule undergoes on the order of 10⁹ collisions every second

·       small orientation factor indicates that orientational requirements for this reaction very stringent

·       reactions between individual atoms usually have orientation factor of ~1 because atoms spherically symmetric

·       if orientation factor greater than 1, collisions aren’t needed for reaction

·       harpoon mechanism: positive charge on potassium and negative charge on bromine cause 2 species to attract each other and form a bond without a collision

13.6 Reaction Mechanisms (588-591)

·       overall equation doesn’t show intermediate steps

·       reaction mechanism: series of individual chemical steps by which an overall chemical reaction occurs

·       elementary step: an individual step in a reaction mechanism; can’t be broken down into simpler steps

·       individual steps in mechanism add to overall reaction

·       reaction intermediates: species that are formed in step of a reaction mechanism and consumed in another

·       can piece together a reaction mechanism by measuring kinetics of overall reaction and working backward to write a mechanism consistent with measured kinetics

Rate Laws for Elementary Steps

·       molecularity: number of reactant particles involved in elementary step; unimolecular and bimolecular most common

·       unimolecular: describes a reaction that involves only one particle that goes on to form products

·       bimolecular:  an elementary step in a reaction that involves two particles, either the same species or different, that collide and go on to from products

·       termolecular: an elementary step of a reaction in which three particles collide and go on to form products; rare because probability of three particles colliding simultaneously is small

·       rate law for overall chemical reaction can’t be deduced from balanced chemical equation

·       rate law proportional to product of concentration of particles in elementary step

Rate-Determining Steps and Overall Reaction Rate Laws

·       rate-determining step: step in a reaction mechanism that occurs much slower than any of the other steps’ limits overall rate of reaction, determining rate law for overall reaction

·       for proposed reaction mechanism to be valid:

¾    elementary steps in mechanism must sum to overall reaction

¾    rate law predicted by mechanism must be consistent with experimentally rate law

·       valid mechanism not proven mechanism because other mechanisms may also fulfill both above requirements

Mechanism with a Fast Initial Step

·       with slow initial step, rate law predicted by mechanism normally contains only reactants involved in overall reaction

·       when mechanism begins with fast initial step, some other subsequent step in mechanism is rate limiting step

·       rate law predicted by rate limiting step may contain reaction intermediates

·       rate law containing intermediates cannot generally correspond to experimental law

·       products of first step can build up, rate at which they’re consumed limited by slower step further down; as products build up, can begin to react with one another to re-form reactants

·       as long as first step is fast enough compared to rate-limiting stem, first-step reaction will reach equilibrium

·       indicate equilibrium:

reactants                 products

·       if equilibrium reached, rate of forward reaction equals rate of reverse reaction

·       example on page 592-593

13.7 Catalysis (593-598)

·       catalyst: substance that is not consumed in a chemical reaction, but increases rate of reaction by providing an alternate mechanism in with rate-determining step has a smaller activation energy

·       activation energy for rate-limiting step much smaller than for first, uncatalyzed pathway, so faster reaction

Homogenous and Heterogeneous Catalysis

·       homogenous catalysis: catalysis in which the catalyst exists in same phase as reactants

·       heterogeneous catalysis: catalysis in which catalyst and reactants exist in different phases

·       hydrogenation: the catalyzed addition of hydrogen to alkene double bonds to make single bonds; heterogeneous

·       ex. of hydrogenation: in presence of finely divided platinum, palladium, or nickel, reaction between ethene and hydrogen (relatively slow at normal temperature) happens rapidly

¾    1. adsorption reactants are adsorbed onto metal surface

¾    2. diffusion: reactants diffuse on the surface until they approach each other

¾    3. reaction: the reactants react to form the products

¾    4. desorption: the products desorb from the surface into the gas

¾    large activation energy of hydrogenation reaction greatly lowered when reactants adsorb onto surface

Enzymes: Biological Catalysts

·       enzymes: biochemical catalyst made of protein that increases rates of biochemical reactions; usually large protein molecules with complex 3D structures

·       active site: the specific area of an enzyme at which catalysis occurs; properties and shape just right to bind reactant molecule

·       substrate: the reactant molecule of a biochemical reaction that bonds to an enzyme at the active site

¾    fits into active site like key fits into lock

·       when substrate binds to active site of enzyme, activation energy of reaction greatly lowered, allowing reaction to occur at much faster rate

·       by allowing otherwise slow reactions to occur at reasonable rates, enzymes give living organisms tremendous control over which reactions occur, and when they occur

·       each enzyme very specific (catalyzes only single reaction) and efficient

·       many substances that inhibit action of enzymes are highly toxic

CHAPTER 14

14.2 The Concept of Dynamic Equilibrium (615-617)

·       reversible: as applied to a reaction, the ability to proceed in either the forward or reverse direction

·       reversible reaction: a reaction that achieves the theoretical limit with respect to free energy and will change direction upon an infinitesimally small change in a variable related to the reaction

·       dynamic equilibrium: the point at which the rate of the reverse reaction or process equals the rate of the forward reaction or process; forward and reverse occurring at same rate

·       concentrations of reactants and products no longer change at equilibrium, doesn’t meant concentration of reactants and products are equal to one another at equilibrium

14.3 The Equilibrium Constant (K) (618-622)

·       equilibrium constant (K): ratio, at equilibrium, of concentrations of products of a reaction raised to their stoichiometric coefficients, to concentrations of reactants raised to their stoichiometric coefficients

·       law of mass action: relationship between balanced chemical equation and expression of equilibrium constant

¾         products/ reactants

Expressing Equilibrium Constants for Chemical Reactions

·       to express equilibrium constant for chemical reaction, apply law of mass action to balanced chemical equation

·       coefficients in chemical equation become exponents in expression of equilibrium constant

·       example on page 618

The Significance of the Equilibrium Constant

·       large equilibrium constant (K>>1) indicates that numerator (number of products at equilibrium) is larger than denominator (amount of reactants at equilibrium); reaction favoured; forward reaction essentially completes

·       equilibrium constant only says how far reaction has proceeded once equilibrium is reached, not how fast

·       (K<<1) indicates reverse reaction favoured; high concentration of reactants, low concentrations of products; forward reaction doesn’t proceed very far

·       K ≈ 1 means neither direction favoured; forward reaction proceeds about halfway

Relationships between the Equilibrium Constant and the Chemical Equation

·       if chemical equation modified in some way, equilibrium constant for equation must be changed to reflect modification

·       if you reverse equation, invert equilibrium constant

¾    consider A + 2B ↔ 3C                      

¾    reversed to 3C ↔ A + 2B                 

·       if you multiply coefficients in equation by a factor, raise equilibrium constant to same factor

¾    consider A + 2B ↔ 3C                                        

¾    multiply by n to get nA + 2nB ↔ 3nC       

·       if you add 2 or more individual chemical equations to obtain an overall equation, multiply corresponding equilibrium constants by each other to obtain overall equilibrium constant

¾    consider A↔ 2B                                                   2B ↔ 3C              

¾    2 equations sum as follows               A↔ 2B

                                                                        2B ↔ 3C                                     <- product of K₁ and K₂

                                                                          A ↔ 3C

·       example on page 622

14.4 Expressing the Equilibirum Constant in Terms of Pressure (622-624)

·       for gaseous reactions, partial pressure of a gas is proportional to its concentrations of reactants and products

·       can express equilibrium constant in terms of partial pressures of reactants and products

·       consider 2SO3(g) ↔ 2SO2(g) + O2(g)                     ; K_C= K with respect to concentration in molarity

¾    K_P= K in respect to partial pressures in atmospheres; partial pressures of each gas instead of conc.

®   

·       since partial pressure of a gas in atmospheres not same as concentration in molarity, value of K_P for a reaction necessarily equal to value of K_C

·            [A]= concentration of ideal gas, n_A=moles of A, V= volume in litres

·       ideal gas law: P_A= partial pressure of A                  R= gas constant= 8.34 J/molK

·      

¾    if total number of moles of gas is same before and after reaction, then Δn = 0, and K_P equal to K_C

·       example on page 624

Units of K

·       as long as concentration units expressed in molarity for K_C and pressure units expressed in atmospheres for K_P, we can enter quantities directly into equilibrium expression, dropping their corresponding units

14.5 Heterogeneous Equilibria: Reactions Involving Solids and Liquids (625-626)

·       concentration of a solid doesn’t change because solid doesn’t expand to fill its containiner; concentration depends only on density

·       pure solids and pure liquids not included in equilibrium expression (K_C equation)

·       example on page 626

14.6 Calculating the Equilibrium Constant from Measured Equilibrium Concentrations (626-628)

·       most direct way to obtain experimental value for equilibrium constant of a reaction is to measure concentrations of reactants and products in a reaction mixture at equilibrium

·       equilibrium constant will always be same at given temperature, regardless of initial concentrations

·       in most cases, only need to know initial concentrations of reactant(s) and equilibrium concentration of any one reactant or product; other equilibrium concentrations can be deduced from stoichiometry of reaction

·       consider A_(g) ↔ 2B_(g) ;

¾    initial [A] is 1.00 M, initial [B] is 0.00 M; when equilibrium reached, concentration of A is 0.75 M

¾    A changed by -0.25 M, so based on stoichiometry, [B] changed by 2 x (+ 0.25 M) or +0.50 M

	[A]	[B]
Initial	1.00	0.00
Change	-0.25	+0.50
Equilibrium	0.75	0.50

¾    to calculate equilibrium constant, use balanced equation to write expression for equilibrium constant, then substitute concentrations from the ICE table

¾   

·       examples on page 628

14.7 The Reaction Quotient: Predicting the Direction of Change (629-631)

·       reaction quotient (Q_C): ratio, at any point in the reaction, of concentrations of products of a reaction raised to their stoichiometric coefficients to the concentrations of the reactants raised their stoichiometric coefficients

·       for gases with amounts measured in atmospheres, reaction quotient uses partial pressures in place of concentrations, and is called Q_P

·       reaction quotient depends on current state of reaction and has many different values as reaction proceeds

·       consider aA + bB ↔ cC + dD                           

¾    in reaction mixture containing only reactants, Q_C= 0

¾    in reaction mixture containing only products, Q_C=

¾    in reaction mixture containing both reactants and products, each at a concentration of 1 M, Q_C=1

·       value of Q relative to K is measure of reaction toward equilibrium

·       at equilibrium, reaction quotient is equal to equilibrium constant

·       Q < K reaction goes to right (toward products)

Q > K reaction goes to left (toward reactants)

Q = K reaction is at equilibrium

·       example on page 631

14.8 Finding Equilibrium Concentrations (631-640)

Finding Equilibrium Concentrations When We Know the Equilibrium Constant and All but One of the Equilibrium Concentrations of the Reactants and Products

·       can use the equilibrium constant to calculate equilibrium concentration of one of the reactants or products, given the equilibrium concentrations of the others

·       example on page 632

Finding Equilibrium Concentrations When We Know the Equilibrium Constant and Initial Concentrations or Pressures

·       set up ICE chart, chances in concentration represented by variable x

·       consider A_(g) ↔ 2B_(g)

	[A]	[B]
Initial	1.0	0.00
Changed	-x	+ 2x
Equilibrium	1.0-x	2x

¾    solve for x using quadratic equation

·       examples on page 634-635

·       when initial conditions given in terms of partial pressures (instead of concentrations) and equilibrium, constant given as K_P instead of K_C, use same procedure, but substitute partial pressures for concentrations

·       examples on page 636-637

Simplifying Approximations in Working Equilibrium Problems

·       if equilibrium constant relatively small, reaction won’t proceed very far to right; if initial reactant concentration relatively large, can assume x is small relative to initial concentration of reactant;

·       if x much smaller than 1, then denominator can be approximated as 1.0

·       consider above example (in ICE chart), this time, K= 3.3 x 10^-5

·       to check validity: ratio of s to number it’s subtracted from should be <0.05

·       examples page 638-640

14.9 Le Châtelier’s Principle: How a System at Equilibrium Responds to Disturbances (641-648)

·       Le Châtelier’s Principle: when a chemical system at equilibrium is disturbed, the system shifts in a direction that minimizes the disturbance

The Effect of a Concentration Change on Equilibrium

·       increasing concentration of one or more of the reactants (making Q<K) shifts reaction to right

·       increasing concentration of one or more of the products (making Q>K) shift reaction left

·       decreasing concentration of one or more of the reactants (making Q>K) shifts reaction left

·       decreasing concentration of one or more of the products (making Q<K) shifts reaction right

·       example on page 644

The Effect of a Volume (or Pressure) Change on Equilibrium

·       decrease in volume causes an increase in pressure, vice versa

·       decreasing volume causes reaction to shift in direction that has fewer moles of gas particles

·       increasing volume causes reaction to shift in direction that has greater number of moles of gas particles

·       if reaction has equal number of moles of gas on both sides of chemical equation, change in volume produces no effect on equilibrium

·       adding an inert gas to mixture at a fixed volume has no effect on equilibrium

·       example on page 645

The Effect of a Temperature Change on Equilibrium

·       changing temperature changes value of equilibrium constant

·       increasing temperature causes exothermic reaction to shift left; equilibrium constant (K) decreases

·       decreasing temperature causes exothermic reaction to shift right; K increases

·       increasing temperature causes endothermic reaction to shift right; K increases

·       decreasing temperature causes endothermic reaction to shift left; K decreases

example on pa