Chapter 14 - Kinetics PDF

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Kinetics : study of motion, rate Instantaneous rate: slope (concen/time) → slope of tangent line (line drawn for one point) A+B→C First Order with respect to A Trial One

[A] = 1

Rate = 1

Trial Two

[A] = 2 (concent changes)

Rate = 2 (rate doubles)

Reactant decreases → rate slows down as rxn proceeds Second Order with respect to A Trial One

[A] = 1

Rate = 1

Trial Two

[A] = 2 (concent changes)

Rate = 4 (rate quadruples)

Trial One

[A] = 1

Rate = 1

Trial Two

[A] = 2 (concent changes)

Rate = 1 (rate is unchanged)

Relationship is quadratic Zero Order with respect to A

Rate is independent of reactant concentration Negative First Order with respect to A Trial One

[A] = 1

Rate = 1

Trial Two

[A] = 2 (concent changes)

Rate = 1/2 (rate is halved)

A+B→C ᵐFirst order w/respect to A +   First order w/respect to B = second overall order Rate Law: aA + bB + cC → dD +eE Rate = k[A]ᵐ[B]฀[C]ᴾ m = rxn order with respect to A (m≠a) n = rxn order with respect to B (n≠b) p = rxn order with respect to C (p≠c) Initial Rate Data: 2NO + O2 → 2NO2 [NO]initial(M)

[O2]initial(M)

Rate (M/s)

Trial 1

0.100

0.250

0.04

Trial 2

0.200

0.250

0.16

Trial 3

0.100

0.500

0.08

1. For trial one and two, O2 concentrations are constant, the rate is quadrupled → so the rxn order would be second order with respect to NO 2. For trial one and three, No concentrations are constant, the rate is doubled → so the rxn order would be first order with respect to O2 3. Furthermore → rate = k[NO]²[O2 ] a. This is a coincidence, the stoichiometric coefficients for each reactant will not match the rxn order for each reactant Rate constant Units - If you know the rate constant → look at units of k → match units to rxn order Integrated Rate Law - Discern rate law at any given time - Relationship b/w concent. Of reactants and time - [A0] - initital concent Half life - First order: independent of [A]0 - Half life is constant as concent changes - Second order: depends on [A]0 - Zero order: depends on [A]0 - Half life gets shorter as concent decreases Kinetic Relationships - Rxn order and rate law is determined experimentally - The rate law relates the rate of rxn to the concent of reactants - The IRL relates to concent of the reactants to time - The half life is the time it takes concent of the reactant to fall to ½ of its [A]0 - The ½ of first order rxn is independent of the [A]0 - The half lives of zero and second order rxns depend on [A]0 Order

Rate

Integrated Rate Law **

Half Life

0

k[A]⁰

[A]t = -kt + [A]0

t1/2 = [A]0/2k

1

k[A]

ln [A]t = -kt + ln[A]0

t1/2 = ln(2)/k

2

k[A]²

1/[A]t = kt +1/[A]0

t1/2 = 1/k[A]0

**IRL can be plotted in y=mx+b Half life is constant: first order Each successive half life is double the previous half life (initial half life: 0.25, successive half life: 0.50) Zero Order graph: decreasing slope, straight line First Order graph: decreasing slope, straight line Second Order graph: increasing slope, straight line (inverse of concent/time)

The Rate Constant The rate constant and the activation energy tell us how fast the reaction proceeds(moles/sec), not whether it is spontaneous. Rate constant (k) is not actually constant - It is dependent on temperature, and presence of catalyst It i measurable Huge variation of k - so much variation in chemical mechanisms In first order - half life and k constant are independent of concentration If the temperature is changed or a catalyst is added → the rate constant is changed Increase in temperature → increases the rate constant → increases rate of rxn → (+) Ea As the temperature increases, the rate constant approaches the pre-exponential factor (E/T approaches zero). Breaking a bond requires energy (endo) and making a bond releases energy (exo) KE increases w/ increasing temp Rate of reaction increases w/ increasing temp Increase in concentration → increases the rate but not the rate constant Greater number of particles → greater concent. → greater # of collisions Rate of reaction depends on concentration (greater initial amt → greater rate: Ludwig) A catalyst will provide a route for the reaction with a lower activation energy. Temp rises → speed of molecules increase → increase in collision frequency The catalysed reaction is still going to be a lot faster than the uncatalysed one because of the huge increase in sufficiently energetic molecules. More molecules colliding → consent of reactants go down → concent of products go up Collisions does not mean a rxn will occur → it has to have enough energy and it has to be aligned in a specific way - Every rxn has a minimum amount of energy required to get it started - to start collisions (activation energy). This needs to happen for anything to happen after - This activation energy - kinetic energy, actual speed of particles Faster particles move → harder collision because of more energy Needs to be positioned correctly to cause a rxn as well (you can keep banging velcro together but it has to be on the right side to stick Reaction rate - rate at which consent of reactants decrease -- experimentally Rate law - mathematical relationship b/w the concentrations of the reactants and the rate of reaction Equilibrium - when a rxn forward (reactants make products) is perfectly balanced to the reverse (products make reactants) are equal to each other Reverse rxn has such a high Ea that the collisions are almost always ineffective → that is why we use the forward more often A multi step rxn can only happen as fast as the slowest step takes - Rate determining step (rate limiting step) - very slow, controls how fast everything else can go. - Has the highest Ea - If the particles have a hard time getting over that part of the energy hill → they will have a hard time making it over the other steps no matter how fast the rest are

-

That is why we don't consider any other step after the rate limiting step (slow step) Need a rxn to happen faster → introduce a catalyst - chemical that lowers the Ea of rxn, which speeds up the rxn - Catalyst does not actually change the rxn - They can be a chemical, piece of metal, or gas - Most common is an enzyme: biological catalysts in body Collision theory - for molecules to react, they must collide in the correct orientation and with more KE than the Ea of the rxn - Ea - amt of energy that has to provided for the rxn to proceed - energy barrier that must be surmounted for the reactants to be tranadformed unto products - Catalysts decreses this barrier (Ea) so that the reactants can surpass the barrier and become products at a faster rate - Kinetic energy that the mo;ecules must collide with in order for to reach transition state - Reaches transition state (peak pt) → rxn will occur - The rxn that can't get over the transition state → rxn does not exists Delta H - change in energy between the reactants and products - Products sit lower - exothermic (needs to releases energy for rxn to occur) - Products sit higher - endothermic (needs to absorb energy for rxn to occur) Catalyst - Speeds up rxn - Lowers the Ea - Rxn with catalyst results in a faster rate of rxn - Catalysts does affect the delta H - Not used up stoichiometrically in a rxn - Must be present in 1st step and the regenerated in second step (product) so it is not used up - Faster rates at higher temperatures because more heat energy means faster moving molecules which means more KE - Higher KE → easier to surpass the Ea → rxn will be faster Arrhenius Equation - Temp dependence of the rate constant - K = Ae^(Ea/RT) - Shows that rate constant depends on Ea - A - frequency factor - # of times the reactants approah Ea/unit time - Most of the approaches do not have enough energy to make it over activation barrier (transiition state) - Higher barrier → greater temp senssitivty of rate - As temp increases → # of molecules having enpough thermal energy to surmount AB increases - Can be turned into → ln(k2 /k1) = Ea /R(1/T1 -1/T2 ) - Use this to calculate Ea - R=8.315 lne^x = x

The orientation factor represents the fraction of collisions having an orientation that allows the reaction to occur. The reaction with the smallest orientation factor is the one where collisions have the smallest chance of having a favorable orientation . Exponential factor (e^(Ea/RT) - Depends on both temp and Ea of rxn - Low Ea + high temp → (-) exponent small → Ef approaches 1 - Ea = 0 → exponenet is 0 →. Is exactly 1 - Large Ea + low temp → (-) exponbent large → Ef is small Reaction Mechanism Consist of: NO2 + F2 → NO2F + F SLOW F + NO2 → NO2F FAST

Rate Law = k [NO2] [F2]

Elementary Steps 

Slow Step = the rate determining (limiting) step - Rate primarily depends on this step since the other steps are negligibly small (rate law will probably look like slow step) Reaction Intermediate - species found in elementary steps but not in the overall equation Reaction Quotient To figure out concentration of other substances in equilibrium : use ice table Kc is the equilibrium constant, referring to when the reactants and products are in terms of molarity. Kp is the equilibrium constant when the products and reactants are given in terms of atm (usually when they're gases) - it's known as the equilibrium constant of partial pressures. Qc refers to molarity and Qp refers partial pressure - instead of equilibrium, they refer to at some point in time of the reaction. It could be before, after, or even at the equilibrium depending on whether or not Q is equal to K. 2PCl5

PCl3

Cl2

Initial amt

1.00 mol

0

0

Change

-2x

+x

+x

Equilibrium amt

1.00 - 2x

x

x

Reactants = (-) Products = (+) aA +bB → cC + dD Equilibrium constant Expression (Kc) Kc = ([C]^c[D]^d) / ([A]^a[B]^b) products/reactants

This tells us whether the products or reactants are favored in the equilibrium Kc >> (much greater than) 1 → the numerator bigger, creating more product Kc Qc → Q is more on the reactant side → shifts right → more products equilibrate Kc < Qc → Q is more on the product side → shifts left → more reactants equilibrate Kc = Qc → system is at equilibrium

2HI

H2

I2

Initial amt

0.10 M

0

0

Change

-2x

+x

+x

Equilibrium amt

(x^2) / (0.10 - 2x)^2 x=0.010 0.080

0 + 0.010 0.010

0 + 0.010 0.010

Reactant concent decreases w/ time becauses reactants are consumed in rxn Products concent increases w/ time because products are formed in rxn Average rate of reaction decreases as rxn proceeds reactants → products: concentration → rxn slows down → rate of rxn slows down A chemical reaction at equilibrium:   X. The rate of the forward reaction equals the rate of the reverse reaction.   Y. There is no observable change in macroscopic properties of the system. reaction quotient Q and the equilibrium constant K: - The larger the value of K, the farther the forward reaction proceeds toward completion. - The concentrations of pure solids and pure liquids are omitted from the expression for Q, because they do not change during the course of a chemical reaction. - Q must be equal to K at equilibrium. - By comparing the value of Q with K one can predict the direction of change for a system not initially in equilibrium.

Slope of graph = -Ea/R...