GEN CHEM II - Section 2 chemical kinetics

What is rate defined as and the equation for it?

Chemical reaction over time → can be expressed in stoich

Change in conc of reactant / change in time interval

What is instantaneous rate?

Rate of reaction at specific time

• time zero is referred as “initial rate”

Rate of formation or decomp sign

Formation = positive

Decomposition = negative

Collision Theory and the 3 postulates/rules

• Chemical reactions need 2+ molecules to run into each other to make and break bonds

1. Rate of reaction proportional to rate of reactant collisions

REACTION RATE x (# of collisions / unit of time)

2. Reactants must collide and be in contact at a specific orientation for atoms to become bonded to make product

3. Collisions must occur with enough activation energy to allow mutual penetration (disrupt e- structures) of reactant valence shells, so that their electrons can be rearranged and form new bonds

If activation energy is less than avg KE of molecules? more than avg KE?

• if less → slower

• if more → faster

Arrhenius Equation

k = Ae - (^E_a / RT)

This equation indicates how rate constant (k) is affected by activation energy and temperature …

(Ea/RT) shows fraction of collisions that provide enough energy to break activation barrier

R → ideal gas constant (8.314 J/molK)

T → temp in kelvin

E_a→ activation energy (J/mol)

e → constant (2.7183)

A → frequency factor (relates to freq of collisions and orientation of reactants)

What happens when two reactions are at equal temp? Higher temp?

The one with higher activation energy will have a lower rate constant and a slower rate

HIGHER TEMP = KE more than Ea (activation energy)

HIGHER TEMP = Lower activation energy x rate constant proportional to freq factor

What occurs with larger E_a and smaller E_a ?

Larger → smaller e^-Ea/RT slower reaction since smaller energy to break barrier

Smaller → larger e^-Ea/RT faster reaction since energy large enough to break barrier

Factors affecting reaction rates

1. Chemical nature of reactants

2. State of subdivision of reactants (rapid reaction to slower reaction as it is a mixture)

3. Temperature of reactants

4. Concentration of reactants (proportional to rate)

5. Presence of catalyst (lowers down activation energy)

Rate Laws

Mathematical expressions that describe relationship between rate of chem reaction v. conc of reactants

rate = k [A]^m [B]ⁿ [C]^y

k → rate constant

[ ]→ (in brackets) molar conc of reactants

the exponents are generally between 1 - 3; positive for reaction order (reaction order means ratio between conc of reactants x rate)

Sum of total orders of reactants is…

Overall reaction order

How would you mainly solve for reaction order?

Look at rates if directly proportional or doubles when conc is constant…

• You want to check when specific conc is changing but the other is constant and vice versa, then do rate # / rate # —> LOOK ONLY AT THE SPECIFIC CONC WHERE IT IS CHANGING AND IF THE OTHER IS CONSTANT. FOCUS ON THAT

Integrate Rate Laws

Determination of amt of reactant/product after period of time needed for reaction to happen

1. First order reactions

2. Second order reactions

First order reactions

Equation for rate constant to initial and present-after concentration

ln ([A]_t / [A]₀) = -kt or kt

OR

[A] = [A]₀ e^-kt

OR TO STANDARD LINEAR EQ FORMAT for graphing y = mx + b

ln[A] = -kt + ln[A]₀

Second order reactions

rate = k[A]²

differential rate law

1/[A] = kt + 1/[A]₀

integrated rate law

Zero order

rate = k[A]⁰

differential rate law

[A] = -kt + [A]₀

integrated rate law (y + mx = b)

Half-Life of Reaction

Considered time required for half given reactant to be consumed

• specific for each order of reactions

First order half life, rate constant

s^-1

t_1/2 = 0.693 / k

Zero order half life, unit constant

t_1/2 = [A]₀ / 2k

m s-1

unable to calculate rate constant from half life

Second order half life, unit constant

t_1/2 = 1 / k[A]₀

m^-1s^-1

unable to calculate rate constant from half life

How to determine Ea needed via Alternate Version of Arrhenius

plot of ln(k) v. 1/t gives straight line with slope -Ea/R where Ea may be found

y intercept → value of ln(A)

SLOPE CAN THEREFORE BE FOUND

change of ln(k) / change of 1/t

Ea = -R [ lnk2 - lnk1 / (1/T2 - 1/T1) ]

Ea can be found via slope x R

Reaction mechanism

Process/path where reaction occurs, each step in process is called “elementary reaction” which cant be broken down simpler → adds to overall reaction

3 types of elementary reactions and definitions/equations each

Unimolecular: rearrangement of single reactant to produce 1+ molecules of product

Rate = k[A]

Bimolecular: collision and combo of 2+ molecules to form activated complex

1. 2 reactant molecules are different and first order

Rate = k[A][B]

2. 2 identical molecules collide and react (second order) Rate = k[A]²

3. 3+ molecules/atoms/ions collide at the same time (but really rare)

Rate Limiting Step

One step in multi-step reaction that is significantly slower and limits the rate of overall reaction

• if RDS is first step, overall rate law matches rate law of that step

• If equilibrium step precedes RDS, rate law more complex

Equilibrium and how to solve

RATE _forward = RATE _reverse

• Intermediates can’t appear in final overall rate law

1. Identify rate limiting step

2. Write preliminary rate law for each reaction

3. Eliminate intermediates

4. Simplify

Catalysis

Catalyst speeds rate of reaction by lowering activation energy; catalyst regenerates in the process; lower energy may involve multiple steps and have intermediates

Homogenous Catalysts

Occurs in same phase as reactants to help form intermediates that decompose or reacts with another reactant to regenerate catalyst and form product

Heterogenous Catalyst

Occurs in different phase (usually) solid than reactants; catalysis occurs on active surface where reaction can occur esp for gas + liquid phase reactions

Has four steps. . .

1. Absorption of reactant onto surface of catalyst

2. Activation of absorbed reactant

3. Reaction of absorbed reactant

4. Diffusion of product from surface into gas/liquid phase (deabsorption)

ANY may be RDS STEP, but overall rate may be faster esp if gas/liquid phase

Lock and key model vs induced fit model

Lock and key: shape of enzyme active site matches substrate

Induced Fit: active site is flexible and changes shape to bond with substrate