Study Guide: Chemical Kinetics and Chemical Equilibrium

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical reactions occur and the factors that affect these rates. Understanding kinetics allows chemists to control reactions and predict how changes in conditions will influence the speed of a reaction.

• Reaction Rate: The change in concentration of a reactant or product per unit time. It is usually expressed in mol/L·s.

• Rate Law: An equation that relates the reaction rate to the concentrations of reactants, often in the form $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant and m, n are the reaction orders.

Determining the Rate of a Reaction

• With Respect to Reactant or Product: The rate can be measured by monitoring the decrease in concentration of a reactant or the increase in concentration of a product over time.

• Example: For the reaction $A \rightarrow B$, the rate can be expressed as $-\frac{d[A]}{dt}$ or $\frac{d[B]}{dt}$.

Effect of Concentration Changes

• Changing Reactant Concentration: If the concentration of one reactant is doubled while others remain constant, the effect on the rate depends on the order of the reaction with respect to that reactant.

• Example: If the rate law is $\text{Rate} = k[A]^2[B]$, doubling [A] increases the rate by a factor of 4.

Integrated Rate Laws

• First-Order Reactions: $[A] = [A]_0 e^{-kt}$

• Second-Order Reactions: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

• Zero-Order Reactions: $[A] = [A]_0 - kt$

• Use: Integrated rate laws allow calculation of reactant concentration at any time.

Graphical Interpretation of Rate Laws

• First-Order: Plot of $\ln[A]$ vs. time yields a straight line with slope $-k$.

• Second-Order: Plot of $1/[A]$ vs. time yields a straight line with slope $k$.

• Zero-Order: Plot of $[A]$ vs. time yields a straight line with slope $-k$.

Half-Life

• Definition: The time required for the concentration of a reactant to decrease by half.

• First-Order: $t_{1/2} = \frac{0.693}{k}$

• Second-Order: $t_{1/2} = \frac{1}{k[A]_0}$

• Zero-Order: $t_{1/2} = \frac{[A]_0}{2k}$

Reaction Mechanisms and Rate Laws

• Elementary Steps: Individual steps in a reaction mechanism.

• Rate-Determining Step: The slowest step in the mechanism, which controls the overall rate.

• Intermediates: Species produced and consumed during the reaction, not present in the overall equation.

Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products.

• Dynamic Equilibrium: Both forward and reverse reactions continue to occur, but there is no net change in concentrations.

The Equilibrium Constant (K)

• Expression: For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant is $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$.

• Kc: Equilibrium constant in terms of concentration (mol/L).

• Kp: Equilibrium constant in terms of partial pressures (atm).

• Relationship: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

Manipulating Equilibrium Expressions

• Reversing the Reaction: Inverts the equilibrium constant ($K' = 1/K$).

• Multiplying the Reaction: Raises $K$ to the power of the multiplier ($K' = K^n$).

• Adding Reactions: Multiplies the equilibrium constants ($K_{overall} = K_1 \times K_2$).

Le Châtelier’s Principle

• Definition: If a system at equilibrium is disturbed, it will shift to counteract the disturbance and restore equilibrium.

• Disturbances: Changes in concentration, pressure, or temperature can shift the position of equilibrium.

• Example: Increasing the concentration of a reactant shifts equilibrium toward products.

Relationship Between Q and K

• Reaction Quotient (Q): Calculated like $K$ but with initial concentrations or pressures.

• Comparison:

  • If $Q < K$, the reaction proceeds forward (toward products).

  • If $Q > K$, the reaction proceeds in reverse (toward reactants).

  • If $Q = K$, the system is at equilibrium.

Solving Equilibrium Problems

• ICE Tables: Used to organize initial concentrations, changes, and equilibrium concentrations.

• Quadratic Equations: Sometimes required to solve for unknown concentrations at equilibrium.

• Example: For $A \rightleftharpoons B$, if $K$ and initial [A] are known, set up an ICE table and solve for equilibrium concentrations.

Summary Table: Kc vs. Kp

Constant	Expression	Units	When Used
Kc	$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$	varies (often MΔn)	Concentration (mol/L)
Kp	$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$	varies (often atmΔn)	Partial pressures (atm)
Additional info: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ = moles of gaseous products - moles of gaseous reactants.

Practice and Application

• Arrhenius Equation: Relates the rate constant to temperature: $k = Ae^{-E_a/RT}$

• Reaction Mechanisms: Propose mechanisms and identify intermediates and rate-determining steps.

• Equilibrium Calculations: Use ICE tables and quadratic equations to solve for unknown concentrations or pressures at equilibrium.