Chem 1C Midterm

Thermodynamics

Focuses on the final and initial states (reactants and products), only considers the speed of the reaction, and the reaction pathway

Activation Energy

• minimum amount of energy needed to start the reaction

• helps determine the rate at which a reaction occurs.

Large Ea

slow rate of reaction

Small E_a

fast rate of reaction

Rate of Reaction units

(mol/L *s) or (M/s)

Avg. Rate of Reaction:

Formula: ∆M/∆t

• can be done by finding the slope between two points

Instantaneous rate of reaction

the rate of a reaction at a specific moment in time, calculated as the derivative of concentration with respect to time.

t= 0 initial rate

Rate of reaction signs

Reactants = -

Products = +

Comparing Instantaneous Rates:

aA+bB -> cC+ dD

-1/a (∆[A]/∆t) = -1/b (∆[B]/∆t) = 1/c (∆[C]/∆t) = 1/d (∆[D]/∆t)

This equation represents the relationship between the change in concentration of reactants and products over time for a reaction, allowing for the comparison of instantaneous rates across different species.

Rate Law:

• Rate = k[A]^m[B]ⁿ

• K = rate constant (can be slope)

• N = order of reaction, can be an integer, a fraction, or 0

• ONLY FOUND EXPERIMENTALLY

Overall Order

sum of m+n

Integrated Rate Law:

• Has a corresponding equation for the dependence of concentration and time

• Involves TIME, does not involve rate

• Used to determine the rate constant and reaction order

Ex: [A]-[A]₀= -kt

Differential Rate Law Ex:

• Formula: Rate = k[A]ⁿ

• How the rate changes with concentration

• Finding reaction mechanisms

• No time in formula, just concentrations + rate

Zero-Order Reactions:

“Zero is Chill”

• Rate = k [A] ⁰

• Integrated rate law = [A]-[A]₀=-kt → [A] = -kt+[A]₀

• Plot = [A] vs. t → negative slope 

• Half Life: t_1/2= [A]₀/2k

• Units of k: M/s

Pseudo Rate Constant

"Flood one to freeze one."

Flood A or B to freeze its effect so you can isolate the other's order.

A rate constant that appears in the rate law of a reaction when one or more reactants are present in large excess, simplifying the rate expression as if only one reactant is influencing the rate.

• used to help find order??

1st Order Reactions:

“First logs in”

(First order = ln appears in the equation.)

“Half-life is constant!”

Only first-order has a constant half-life, independent of [A]₀.

• Rate = k[A]¹

• Integrated Rate law = ln[A]-ln[A]₀=-kt

• Plot = ln[A] vs. t -> negative slope 

• Half life: t_1/2= 0.6931/k

• Units of k: 1/s

2nd Order Reactions:

“Second is Inverse”:

(Second-order = 1 over [A])

“Half-life gets longer.”

As [A]₀ gets smaller, second-order half-life gets longer.

• Rate = k [A]²

• Integrated Rate law = 1/[A] - 1/[A]₀ = kt

• Plot: 1/[A] vs. t -> positive slope

• t_1/2 = 1/k[A]₀

• Units of k= M^-1S^-1

Elementary Step

Basic step in a reaction

Intermediate Step:

a species is neither a ractant or a product

Each step in a mechanism

is an elementary step —> directly caused by atoms

Rate of elementary step:

proportional to the products of its reactants = raised to the power of their stoichiometric coefficients.

• For elementary steps, the stoichiometric coefficient = exponent in the rate law. (Only true for elementary steps!)

Molecularity:

elementary step ( # of species that must collide to produce a reaction event)

• Unimolecular: 1

• Biomolecular: 2 (most common)

• Termolecular: 3 (rare)

Rate Determining Step (Or Rate Limiting)

The slowest step controls the overall reaction rate.
Like a traffic jam — the whole highway moves at the speed of the slowest car.

"A reaction is only as fast as its slowest step."

“Mechanism must match the math.”

the slowest step in a reaction mechanism, which dictates the overall reaction rate.

• Overall step can NOT be faster than its slowest step

  • If the first step is fast enough compared to the rate-determining step, then the first step will reach equilbrium

Rate Mechanism

• is the storyline — it shows the steps it takes to get there

can never be proven

Factors that Increase the Rate of Reaction:

🐱 C — Concentration

More particles = more chances to collide

🔥 A — Activation Energy (Ea)

Lower Ea = faster reaction

Big hill = slow. Small hill = fast.

🌡 T — Temperature

Higher temp = more energetic collisions

🎯 S — Steric Factors

Correct orientation needed during collision

• Also Catalyst (lowers Ea or raise Arrhenius factor A)

Arrhenius formula:

• Ln (k) = -Ea/R (1/T)+ lnA

• Ln (K2/K1) = Ea/R (1/T1-1/T2)

Chemical Equilibrium:

• Two reactions take place at the same rate, forwards and reverse reactions continue even after equilibrium

• no change of concentration when equilibrium is reached

Equilibrium Constant (K)

[Products]^coefficients / [Reactants]^coefficients

• Each reactant is expressed in M

Homogenous Equilibria

reactant and products are all in the same phase

Heterogenous equilibria:

reactants and products are more than one phase

What happens at a given temperature?

K is a constant

K_p (Equilibrium Constant with Partial Pressure):

• partial pressure of gas is proportional to molar concentrations

• K_c: Equilibrium Constant in terms of molarity (Concentration)

• K_p: Equilibrium constant in terms of partial pressures (Pressure).

  • Units: atm

  • Calculated the same as K_c

K_p Formula

K_p= K_c (RT)^∆n

Manipulating Equilibrium Constants:

• Reversing a chemical reaction inverts K

• Multiplying a chemical equation by a coefficient raises K to that coefficient.

• Adding multiple equations to get an overall reaction → overall equilibrium constant is found by multiplying the constants of the beginning equations’ constants

Interpreting K:

• If K >>1 : [products]>> reactants

  • Forward reaction takes place for a long time, equilibrium to the right

• If K<<1 = [reactants] >>> products 

  • Equilibrium lies towards reactants to the left

• If K = 1: Reactants and products are approximately equal, reaction proceeds halfway before equilibrium is started

Q Reaction Quotient:

• Reactants and products are mixed together out of equilibrium: use Q

• Q or Q_p= [Products ₀^{(Whatever the coefficients are}] / [Reactants₀]^{Whatever the coefficients are}

• Use the initial instead of the equilibrium concentrations

K and Q

• Trick is to write K and Q

• K=Q : Reaction is at equilibrium

• Q=K → You’re at equilibrium

• K > Q: Reaction shifts to the products (Follow the arrow) → Has to make Q increase to K

  • Q<K → Not enough products → reaction shifts right (to products)
    

• K < Q: Reaction shifts left to reactants → make Q decrease to K 

  • Q>K → Too many products → reaction shifts left (to reactants)

Percent Decomposition:

[Change]/[Intial reactant] * 100

Ice Table

• Use an ICE table to find equilibrium concentrations from initial value 

  • Initial, Change, Equilibrium

Approximation:

% =  x/1.00 M *100

Le Chatelier’s Principle

• a system at equilibrium that is stressed will react in a way that will counteract that stress

  • Bouncing BACK!!

Stresses on Equilibrium

CRaP TV

• C = Concentration
  
  

• R = Removal (of a product/reactant)
  
  

• P = Pressure (or volume)
  
  

• T = Temperature
  
  

V = Volume (connected to pressure)

Adding a Concentration (Reactant/Product)

• “Add it? It runs away. Take it? It replaces.”

• Add reactant → shift to products

• Add product → shift to reactants
  

Removing a Product/Reactant

• “Add it? It runs away. Take it? It replaces.”

• Remove product → shift to products

• Removing reactant → shift to reactants

Increase / Decreasing Pressure and Volume (ONLY FOR GASES)

• More pressure, fewer moles. Less pressure, more rolls/moles."

• Decrease volume (increase pressure) → shift to the side with fewer moles of gas

• Increase volume (decrease pressure) → shift to the side with more moles of gas

• If moles are equal on both sides → no effect
  

Adding an Inert Gas

• If volume is constant, no change (just extra space-filler).

• If inert gas is added at constant pressure, volume increases → same as pressure drop!

🧠 Think: “Inert = irrelevant… unless volume changes.”

Temperature Endothermic (Heat = reactant)

• Endothermic (Heat = reactant): 

  • Increase temp -> shifts right

    • K gets larger

  • Decrease temp -> shifts left

    • K gets smaller

• Adding head shifts away from heat, removing heat shifts toward heat

• K follows the direction of the shift  (K is bigger when shift is forward, K decreases when shift is left)

Temperature Exothermic (Heat = product)

• Exothermic (Heat = product):

  • Increase temp -> shifts left 

    • K Gets smaller

  • Decrease Temp -> shifts right

• Adding head shifts away from heat, removing heat shifts toward heat

• K follows the direction of the shift  (K is bigger when shift is forward, K decreases when shift is left)

∆G and Equilbrium:

• ∆G < 0 = spontaneous → ready to go

• ∆G>0 = nonspontaneous —> needs energy

• ∆G=0 = equilibrium

∆G Formula

∆G = ∆H -T∆S

∆Gºrxn:

• ∆Gºrxn = n_p∆Gº_p - n_r∆Gº_r

• difference in free energy of pure product and reactants in standard states

∆Grxn:

• ∆Grxn = ∆Gºrxn+RTlnQ

• molar reaction free energies at a fixed composition of reaction mixture

∆G and Equilbrium:

• ∆Gºrxn = -RTlnK

  • If K>1 = ∆Gºrxn < 0

  • If K<1 = ∆Gº rxn > 0

Equibrium Constant: DOES NOT GIVE concentration of GASES K_c but K_p

K_c= K_p(RT)^∆n

Relating change of equilibrium constant to Temperature

• “Endo wants heat → give it heat, it goes!”
  “Exo hates heat → give it heat, it stops!”

• If ∆H < 0: K decreases as T increases

• If ∆H > 0: K increases as T increases