Chem ch.12-13

Reaction rate

the change in concentration of a reactant or product per unit of time. Its always positive.

Average rate

Calculated over a time interval using initial and final concentrations.

Instantaneous rate

The rate at a specific point in time. It can be found from the slope of the tangent line to a concentration vs. time graph at that point.

Initial rate

The instantaneous rate at time zero.

Nature of reactants

The identity of the reacting substances.

State of reactants

Reactions occur at interfaces; smaller particle size (e.g., powders) leads to faster rates.

Temperature

Higher temperatures generally lead to faster reaction rates.

Catalyst

A substance that increases reaction rate without being consumed.

Concentration

Higher concentrations of reactants generally lead to faster reaction rates.

Rate law

An equation that relates the reaction rate to the concentration of reactants. It has the general form:

• Rate = k[A]x[B]y

• kk is the rate constant.

• xx and yy are the reaction orders with respect to reactants A and B, respectively.

• The overall reaction order is the sum of the individual orders (x+y).

Reaction order

Determined experimentally, not from stoichiometric coefficients. Usually integers (0, 1, 2), but can be fractional or negative. A zero-order reactant means its concentration does not affect the rate.

Zero order reaction

Rate = kk

• Concentration-Time Equation: [A]t=[A]0−kt

• Half-Life: t1/2=[A]02k

First order reaction

Rate = k[A]k[A]

• Concentration-Time Equation: ln[A]t​=−kt+ln[A]0​ or ln⁡([A]t[A]0)=−kt

• Half-Life: t1/2=ln⁡(2)k≈0.693 (independent of initial concentration)

Second order reaction

Rate = k[A^]2

• Concentration-Time Equation: 1/[A]t=kt+1/[A]0

• Half-Life: t_1/2=1/k[A]0​ (dependent on initial concentration)

Collide

The frequency of collisions depends on concentration. Requires equal energy to the activation energy (Ea). Molecules must collide in a specific spatial arrangement for bonds to break and form correctly.

Activation energy (Ea)

The minimum energy required for a reaction to occur. Represented by the energy barrier in a reaction coordinate diagram.

Reaction coordinate diagram

Shows the change in potential energy as reactants transform into products. It includes activation energy (Ea​) and the change in enthalpy (ΔH).

Arrhenius equation

Relates the rate constant (kk) to temperature (TT) and activation energy (EaEa​):

• k=Ae^−Ea​/RT

• AA is the pre-exponential factor (related to collision frequency and orientation).

• RR is the ideal gas constant (8.314 J/K·mol).

• The equation can be linearized: ln⁡k=−Ea/RT+ln⁡A. A plot of lnk vs. 1/T1/T yields a slope of −Ea/R.

Orientation factor

A modification to the Arrhenius equation, k=pAe^−Ea/RT, accounts for the probability of correct molecular orientation.

Reaction mechanism

The sequence of elementary steps by which a reaction occurs at the molecular level.

Elementary step

A single molecular event (e.g., a collision or a unimolecular decomposition).

Molecularity

• The number of reactant molecules involved in an elementary step (unimolecular, bimolecular, termolecular).

• The rate law for an elementary step can be written directly from its molecularity.

  • Unimolecular (A →→ products): Rate = k[A]

  • Bimolecular (A + B →→ products): Rate = k[A][B]

  • Bimolecular (A + A →→ products): Rate = k[A]²

Reaction intermediate

A species produced in one elementary step and consumed in a subsequent step. It does not appear in the overall balanced equation.

Rate-determining step (RDS)

The slowest elementary step in a reaction mechanism. The overall rate of the reaction is limited by the rate of the RDS.

Valid mechanism

1. The elementary steps must sum to the overall balanced equation.

2. The mechanism must be consistent with the experimentally determined rate law.

3. The elementary steps must be physically reasonable.

Homogenous catalysis

The catalyst is in the same phase as the reactants (e.g., liquid catalyst in a liquid reaction). Enzymes are biological homogeneous catalysts.

Heterogeneous catalysis

The catalyst is in a different phase from the reactants (e.g., a solid catalyst with gaseous reactants). This often involves adsorption of reactants onto the catalyst surface.

Effects on equilibrium

Catalysts increase the rates of both forward and reverse reactions equally. They allow the system to reach equilibrium faster but do not change the equilibrium position or the equilibrium constant (K).

Dynamic equilibrium

A state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction.

• Macroscopically, concentrations appear constant.

• Microscopically, forward and reverse reactions continue at equal rates.

Reversible reactions

Reactions that can proceed in both the forward and reverse directions. Represented by a double arrow (⇌).

Closed system

Essential for equilibrium; no substances can enter or leave.

Equilibrium misconceptions

• Concentrations of reactants and products are NOT necessarily equal at equilibrium.

• Equilibrium is a dynamic process, not a static one.

Heterogenous equilibria

Reactions involving species in different phases (e.g., solid, liquid, gas). The concentrations (or activities) of pure solids and pure liquids are NOT included in the equilibrium constant expression because they remain constant.

Le Châtelier's Principle

If a change of condition (stress) is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

Why does concentration affect equilibrium position?

• Adding a reactant shifts the equilibrium towards products.

• Adding a product shifts the equilibrium towards reactants.

• Removing a reactant shifts the equilibrium towards reactants.

• Removing a product shifts the equilibrium towards products.

Why does pressure/volume (for gaseous reactions) affect equilibrium position?

• Increasing pressure (decreasing volume) shifts the equilibrium towards the side with fewer moles of gas.

• Decreasing pressure (increasing volume) shifts the equilibrium towards the side with more moles of gas.

• If the number of moles of gas is the same on both sides (Δngas=0), pressure/volume changes have no effect on the equilibrium position.

• Adding an inert gas at constant volume does not affect the equilibrium position.

Why does temperature affect equilibrium position?

• For exothermic reactions (ΔH<0, heat is a product): Increasing temperature shifts equilibrium towards reactants (K decreases). Decreasing temperature shifts equilibrium towards products (K increases).

• For endothermic reactions (ΔH>0, heat is a reactant): Increasing temperature shifts equilibrium towards products (K increases). Decreasing temperature shifts equilibrium towards reactants (K decreases).

Why do catalyst affect equilibrium position?

A catalyst speeds up both the forward and reverse reactions equally. It helps the system reach equilibrium faster but does not change the equilibrium position or the value of K.