Grade 11 Chemistry Study Notes: Chemical Kinetics and Equilibrium

UNIT 4: CHEMICAL KINETICS

Chemical kinetics is the branch of chemistry concerned with reaction rates, which refers to the speed at which a chemical change occurs. It involves monitoring the change in concentration of a reactant or product over a period of time. Movements or changes are inherent to kinetics.

THE RATE OF A CHEMICAL REACTION

The rate of a chemical reaction measures the change in concentration of a reactant or product per unit time, determining how rapidly these concentrations fluctuate.

• General Reaction Equation: For a reaction $Reactants \rightarrow Products$, molecules of reactants are consumed while products are formed.

• Simple Case ($A \rightarrow B$): The rate is monitored by the decrease in concentration of $A$ or the increase in concentration of $B$.

• Mathematical Expression:     $Rate = \frac{\Delta c}{\Delta t}$     where $\Delta$ denotes the difference between final and initial states.

• Sign Convention:

  • For reactants: $Rate = -\frac{\Delta[A]}{\Delta t}$ (The minus sign makes the rate a positive value since $\Delta[A]$ is negative).

  • For products: $Rate = \frac{\Delta[B]}{\Delta t}$.

• Complex Stoichiometry: For a reaction $aA + bB \rightarrow cC + dD$, the rate expression incorporates stoichiometric coefficients to ensure the rate is consistent across all species:     $Rate = -\frac{1}{a} \frac{\Delta[A]}{\Delta t} = -\frac{1}{b} \frac{\Delta[B]}{\Delta t} = \frac{1}{c} \frac{\Delta[C]}{\Delta t} = \frac{1}{d} \frac{\Delta[D]}{\Delta t}$

COLLISION THEORY AND PRE-CONDITIONS FOR REACTION

Chemical reactions are explained via the Collision Theory, which possets that reactions take place due to collisions between molecular species.

• Collision Frequency: The rate of reaction is directly proportional to the number of collisions per second. However, not all collisions result in a reaction.

• Pre-conditions for Effective Collisions:

  1. Proper Orientation: Reactant molecules must collide in a specific spatial orientation to allow for bond breaking and formation.

  2. Activation Energy ($E_a$): This is the minimum amount of energy required to start a chemical reaction. If colliding molecules lack sufficient energy to overcome this barrier, no reaction occurs.

• Kinetic Molecular Theory Connection: The average kinetic energy of particles is directly proportional to absolute temperature. Increased temperature leads to more frequent and energetic collisions, raising the reaction rate.

FACTORS AFFECTING THE RATE OF REACTION

Several specific factors influence how quickly reactants are converted into products:

• Nature of Reactants:

  • Reactions involving the combination of oppositely charged ions in aqueous solutions are extremely rapid (e.g., $H_3O_{(aq)}^{+} + OH_{(aq)}^{-} \rightarrow 2H_2O_{(l)}$).

  • Molecular reorganization reactions (e.g., decomposition of $H_2O_2$) are slower than ionic reactions.

  • Specific chemical reactivity matters: Sodium reacts with water almost explosively, while Calcium reacts at a moderate rate.

• Surface Area:

  • In heterogeneous reactions (different phases), the reaction occurs at the interface.

  • Finely divided solids (powders) react faster than Large blocks because they provide a greater surface area for contact.

• Concentration/Pressure:

  • Increasing the concentration of reactants increases the frequency of collisions.

  • For gases, increasing pressure increases the concentration and thus the reaction rate. Pressure has no effect on solid or liquid phase rates.

• Temperature:

  • A rise in temperature increases the average kinetic energy of molecules.

  • A common rule of thumb: The rate of reaction in a homogeneous system approximately doubles for every $10\,^{\circ}C$ increase in temperature.

• Catalysts:

  • A catalyst is a substance that increases the reaction rate by providing an alternative pathway with a lower activation energy ($E_a$).

  • They are not consumed in the reaction and can be recovered.

  • Positive Catalysts: Lower $E_a$ and increase the rate (e.g., $V_2O_5$ in $SO_3$ production).

  • Negative Catalysts (Inhibitors): Increase $E_a$ and decrease the rate (used to extend food shelf-life).

  • Enzymes: Highly specific biochemical catalysts found in living organisms.

DETERMINATION OF REACTION RATE

Rate is measured through change in observable properties over time, such as color, temperature, pressure, mass, or the volume of gas evolved.

• Average Rate: The rate measured over a specific time interval ($\Delta t$).

• Instantaneous Rate: The rate at a specific moment in time ($t$). It is determined by calculating the slope of the tangent to the concentration-time curve at that specific point.

• Initial Rate: The instantaneous rate measured at the very start of the reaction ($t = 0$), determined from the slope of the tangent at the origin.

• Case Study ($N_2O_5$ Decomposition): $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$.

  • Pressure increases as 2 gas moles produce 5 gas moles.

  • The brown color intensity of $NO_2$ can be monitored.

  • Data at $55\,^{\circ}C$ shows that rate is high initially and decreases as reactants are depleted.

UNIT 5: CHEMICAL EQUILIBRIUM

Chemical equilibrium occurs when at least some of the reactants remain after the reaction reaches a steady state.

• Irreversible Reactions: Proceed in one direction until reactants are exhausted ($C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)}$).

• Reversible Reactions: Proceed in both forward and reverse directions concurrently. Represented by a double arrow ($\rightleftharpoons$).

THE DYNAMIC NATURE OF EQUILIBRIUM

Equilibrium is a dynamic state where microscopic changes continue, even though macroscopic properties (concentration, pressure, color) remain constant.

• Definition of Equilibrium: The state where the Rate of the Forward Reaction ($r_f$) equals the Rate of the Reverse Reaction ($r_r$).

• Establishment: Initially, $r_f$ is high and $r_r$ is zero. As products form, $r_f$ decreases and $r_r$ increases until they match.

• Characteristics:

  • Closed system required.

  • No net change in concentrations of reactants or products.

  • Dynamic on a molecular level.

THE LAW OF MASS ACTION AND EQUILIBRIUM CONSTANTS

Proposed by Guldberg and Waage (1864), this law states that the rate of a reaction is proportional to the product of the concentrations of reactants raised to their stoichiometric powers.

• The Equilibrium Constant ($K_{eq}$): For $aA + bB \rightleftharpoons cC + dD$:     $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• Types of Constants:

  • $K_c$: Concentration-based equilibrium constant (used for solutions and gases).

  • $K_p$: Pressure-based equilibrium constant (used for gas-phase reactions).

• Relationship between $K_p$ and $K_c$:     $K_P = K_C(RT)^{\Delta n}$     where $R$ is the gas constant ($0.0821\,L\,atm\,K^{-1}\,mol^{-1}$), $T$ is temperature in Kelvin, and $\Delta n = (c+d) - (a+b)$ for gaseous species.

HETEROGENEOUS VS HOMOGENEOUS EQUILIBRIUM

• Homogeneous Equilibrium: All species are in the same physical state (e.g., all gases).

• Heterogeneous Equilibrium: Species exist in different phases (e.g., solids and gases).

• Rules for Expressions: The concentrations of pure solids and pure liquids are constant and are omitted from the equilibrium constant expression. Only aqueous ($aq$) and gaseous ($g$) species are included.

  • Example: $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$

  • Expression: $K_c = [CO_2]$ or $K_p = P_{CO_2}$.

PREDICTING THE DIRECTION OF A REACTION

• Reaction Quotient ($Q$): Calculated using the same expression as $K$, but with concentrations at any stage of the reaction (not necessarily equilibrium).

• Predictions:

  • If $Q = K$: System is at equilibrium.

  • If Q < K: Reaction shifts forward (to the right) to reach equilibrium.

  • If Q > K: Reaction shifts backward (to the left) to reach equilibrium.

• Extent of Reaction:

  • K > 10^{10}: Reaction goes nearly to completion.

  • K < 10^{-10}: Reaction occurs to a negligible extent.

LE CHATELIER’S PRINCIPLE

If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change.

• Concentration:

  • Add reactant: Shifts forward.

  • Remove reactant: Shifts backward.

• Pressure (Volume Change):

  • Increase Pressure (Decrease Volume): Shifts toward the side with fewer moles of gas.

  • Decrease Pressure (Increase Volume): Shifts toward the side with more moles of gas.

  • Adding an inert gas (e.g., Argon) at constant volume has no effect on equilibrium.

• Temperature:

  • Exothermic Reaction (\Delta H < 0): Heat is a product. Increasing temperature shifts equilibrium to the left (reactants).

  • Endothermic Reaction (\Delta H > 0): Heat is a reactant. Increasing temperature shifts equilibrium to the right (products).

• Catalysts: A catalyst reaches equilibrium faster but does not change the equilibrium position or the value of $K$.

INDUSTRIAL APPLICATIONS: HABER AND CONTACT PROCESSES

1. The Haber Process (Ammonia Synthesis):

• Equation: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) + 92\,kJ$

• Conditions: High pressure ($200-400\,atm$) and moderate temperature (approx. $500\,^{\circ}C$).

• Catalyst: Iron ($Fe$).

• Optimization: Continuous removal of $NH_3$ liquid shifts equilibrium forward according to Le Chatelier's Principle.

2. The Contact Process (Sulfuric Acid Production):

• Ket Step: Oxidation of $SO_2$ to $SO_3$: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$.

• Conditions: $450\,^{\circ}C$, atmospheric pressure.

• Catalyst: Vanadium (V) oxide ($V_2O_5$).

• Steps:

  1. Burning sulfur: $S + O_2 \rightarrow SO_2$.

  2. Catalytic oxidation: $SO_2$ to $SO_3$.

  3. Formation of Oleum: $SO_3 + H_2SO_4(conc) \rightarrow H_2S_2O_7$.

  4. Dilution: $H_2S_2O_7 + H_2O \rightarrow 2H_2SO_4$.

QUESTIONS & DISCUSSION

Q: Why does the burning of paper take less time than the ripening of a banana?

• A: Burning paper is a high-speed combustion reaction that occurs in seconds, whereas the biochemical maturation of a banana involves complex cellular processes that take days.

Q: Does sugar dissolve faster in hot or cold tea?

• A: Sugar dissolves faster in hot tea because the increased temperature increases the kinetic energy and collision frequency between water molecules and sugar crystals.

Q: What is the outcome of adding more water to a reaction where water is the solvent?

• A: Adding more water increases the volume, thereby decreasing the concentration of the reactants, which generally results in a slower reaction rate.

Q: How do you calculate the rate of formation of product if given the rate of disappearance of a reactant?

• A: Use the stoichiometric ratio from the balanced equation. For example, in $2NO + 2H_2 \rightarrow N_2 + 2H_2O$, the rate of formation of $N_2$ is half the rate of disappearance of $NO$.

Q: Why is iron chopped into smaller pieces to facilitate a fire?

• A: Chopping wood (or using iron filings instead of blocks in experiments) increases the surface area exposed to oxygen, leading to higher collision rates and faster combustion/reaction.

Q: What happens if you add a catalyst to the Contact process?

• A: The catalyst ($V_2O_5$) speeds up the rate at which $SO_3$ is formed by lowering the activation energy, but it does not change the total amount of $SO_3$ at equilibrium.