Chemical Kinetics and Reaction Dynamics Review

Collision Theory and Reaction Dynamics

• Fundamental Requirements for Reaction:

  • Particles must physically collide with one another.

  • Colliding particles must possess energy equal to or greater than the activation energy ($E \ge E_a$).

  • Colliding particles must adopt a favorable molecular orientation during collision.

• Pressure Effects on Gas-Phase Reactions:

  • Increasing pressure at constant temperature compresses the gas into a smaller volume, increasing particle concentration per unit volume.

  • Higher particle concentration leads to a higher frequency of collisions per unit time, thereby accelerating the reaction rate.

• Influence of Chemical Bond Strength:

  • Reactions involving strong bonds within reactant molecules exhibit high activation energies ($E_a$).

  • Even under elevated temperature and pressure conditions, a reaction can maintain a low rate if reactant bond strength creates a substantial kinetic energy barrier.

• Mechanisms of Catalytic Action:

  • A catalyst provides an alternative reaction pathway featuring a lower activation energy ($E_a$).

  • It does not alter the average kinetic energy of colliding molecules (which depends exclusively on temperature).

  • It increases the reaction rate by:

  • Increasing the proportion of molecular collisions possessing sufficient energy to overcome the reduced activation energy barrier.

  • Increasing the proportion of collisions occurring in the correct geometric orientation.

  • A catalyst remains chemically unchanged in composition and mass at the completion of the reaction.

Maxwell–Boltzmann Energy Distributions

• Definition and Axes:

  • Represents the statistical distribution of kinetic energy among gas molecules in a sample at a given temperature.

  • Horizontal axis ($x$-axis): Kinetic energy ($E_k$ or $Ke$).

  • Vertical axis ($y$-axis): Probability or fraction of molecules possessing a specific kinetic energy.

• Key Mathematical Features:

  • Origin: The curve starts at $(0,0)$ because no molecules have zero kinetic energy.

  • Peak Value ($A$): Represents the most probable kinetic energy of the molecules.

  • Activation Energy ($B$): The specific energy value ($E_a$) marked along the horizontal axis necessary for a reaction to occur.

  • Area under the Curve beyond $E_a$ ($C$): Represents the total proportion or fraction of molecules with kinetic energy equal to or exceeding activation energy ($E \ge E_a$).

  • Probability Value at Activation Energy ($D$): The height of the curve corresponding to the activation energy threshold.

• Effect of Temperature Variation ($T_1 > T_2$):

  • When temperature increases from $T_2$ to $T_1$ ($T_1 > T_2$):

  • Average kinetic energy shifts to higher values.

  • The curve peak shifts to the right and flattens downward.

  • The total area under the curve remains constant (equal to $1.0$ or $100\%$ of molecules).

  • The high-energy tail rises, significantly enlarging the area under the curve beyond $E_a$, meaning a larger fraction of molecules possess sufficient energy to react.

Factors Influencing Reaction Kinetics

• Surface Area and Solid Particle Size:

  • Reducing particle size (e.g., crushing solid lumps into powder) exposes a greater surface area for reactant collisions.

  • Increased surface area increases collision frequency between solid reactants and dissolved ions or gas particles, elevating the initial reaction rate.

  • Cutting magnesium ribbon into smaller pieces speeds up reaction rate, whereas increasing overall ribbon length without changing cross-sectional area per unit mass does not increase rate.

• Concentration and Dilution:

  • Adding water to hydrochloric acid ($\text{HCl}(aq)$) dilutes the solution, decreasing hydrogen ion ($\text{H}^+$) concentration.

  • Fewer reactive ions per unit volume decrease collision frequency, lowering the reaction rate.

  • Doubling reactant concentration doubles initial collision frequency and doubles the initial rate of reaction.

• Monitoring Kinetics via Gas Evolution Mass Loss:

  • Reactions producing gases (such as $\text{CO}_2(g)$ or $\text{H}_2(g)$) in open systems lose mass as gas escapes.

  • Continuous mass measurement on an electronic balance yields mass versus time decay curves.

• Analyzing Mass Loss Curves Under Varied Reaction Conditions:

  • Baseline Reaction (Curve I): Excess $\text{CaCO}_3(s)$ reacting with $100\,cm^3$ of $0.50\,mol\,dm^{-3}$ $\text{HCl}(aq)$ at $25\,^{\circ}\text{C}$.

  • Halving Acid Volume at Fixed Concentration: Using same mass and size of $\text{CaCO}_3(s)$ and $50\,cm^3$ of $0.50\,mol\,dm^{-3}$ $\text{HCl}(aq)$ at $25\,^{\circ}\text{C}$:

  • Initial concentration is unchanged ($0.50\,mol\,dm^{-3}$), maintaining the exact same initial gradient/rate as Curve I.

  • Halving acid volume halves total moles of limiting reactant ($\text{HCl}$), yielding half the total mass loss of gas, flattening out at half the overall mass drop (Curve C).

• Doubling Acid Concentration with Excess Reactant:

  • Doubling $\text{HCl}$ concentration doubles initial rate, producing a much steeper initial decline.

  • If solid reactant ($\text{CaCO}_3$) is limiting, total mass lost remains constant, reaching the same plateau level faster (Curve B).

Investigation: Acid Deposition Effects on Limestone

• Experimental Design and Setup:

  • Target substrate: Limestone (primarily calcium carbonate, $\text{CaCO}_3$).

  • Procedure setup:

  • Beakers 1, 2, 3: $200.0\,cm^3$ of $0.100\,mol\,dm^{-3}$ nitric acid, $\text{HNO}_3(aq)$.

  • Beakers 4, 5, 6: $200.0\,cm^3$ of $0.100\,mol\,dm^{-3}$ sulfuric acid, $\text{H}_2\text{SO}_4(aq)$.

  • Six similarly sized pieces of limestone weighed daily over 5 days after being removed, washed, dried with paper towels, and replaced.

• Limestone Mass Decay Data ($\text{HNO}_3$ Treatment):

  • Day 0: $48.08\,g$

  • Day 1: $47.97\,g$

  • Day 2: $47.94\,g$

  • Day 3: $47.91\,g$

  • Day 4: $47.91\,g$

  • Day 5: $47.91\,g$

• Graph Construction and Initial Rate Determination:

  • Best-fit line rule: Must be drawn as a smooth best-fit curve. Straight line segments connecting individual points or straight linear fits are invalid.

  • Initial Rate Calculation:

  • Construct a tangent line to the curve at time $t = 0\,\text{days}$.

  • Calculate initial gradient: $\text{Rate} = \left|\frac{\Delta \text{mass}}{\Delta \text{time}}\right|_{t=0}$.

  • Expected initial rate value range: $0.13 - 0.20\,g\,day^{-1}$ (e.g., $0.16\,g\,day^{-1}$).

  • Equivalent rate expressions: $1.5 \times 10^{-6} - 2.3 \times 10^{-6}\,g\,s^{-1}$, $7.5 \times 10^{-8} - 1.2 \times 10^{-7}\,mol\,dm^{-3}\,s^{-1}$, $4.5 \times 10^{-6} - 6.9 \times 10^{-6}\,mol\,dm^{-3}\,min^{-1}$, or $9.0 \times 10^{-5} - 1.4 \times 10^{-4}\,g\,min^{-1}$.

• Kinetic Rate Plateau Explanation:

  • Rate decreases over time as $\text{HNO}_3$ concentration decreases, causing less frequent collisions between $\text{H}^+$ ions and $\text{CaCO}_3(s)$.

  • Rate reaches zero at Days 3–5 because $\text{HNO}_3$ is completely consumed (acid is the limiting reactant).

• Comparative Acid Evaluation (Nitric Acid vs. Sulfuric Acid):

  • Theoretical Hypothesis: Sulfuric acid ($\text{H}_2\text{SO}_4$) should cause greater mass loss than nitric acid ($\text{HNO}_3$).

  • Theoretical Justification: $\text{H}_2\text{SO}_4$ is diprotic (dibasic), releasing two $\text{H}^+$ ions per molecule ($\text{H}_2\text{SO}_4 \rightarrow 2\text{H}^+ + \text{SO}_4^{2-}$), whereas $\text{HNO}_3$ is monoprotic ($\text{HNO}_3 \rightarrow \text{H}^+ + \text{NO}_3^-$). At equal molar concentration ($0.100\,mol\,dm^{-3}$), $\text{H}_2\text{SO}_4$ supplies double the $\text{H}^+$ ion concentration.

  • Experimental Total Mass Loss Data:

  • Nitric acid samples (1, 2, 3): $0.17\,g$, $0.14\,g$, $0.15\,g$

  • Sulfuric acid samples (4, 5, 6): $0.10\,g$, $0.07\,g$, $0.08\,g$

  • Solubility Explanation for Anomaly:

* Reaction equations:

      $\text{CaCO}_3(s) + 2\text{HNO}_3(aq) \rightarrow \text{Ca(NO}_3\text{)}_2(aq) + \text{CO}_2(g) + \text{H}_2\text{O}(l)$       $\text{CaCO}_3(s) + \text{H}_2\text{SO}_4(aq) \rightarrow \text{CaSO}_4(s) + \text{CO}_2(g) + \text{H}_2\text{O}(l)$ * Solubility differences: * Calcium carbonate ($\text{CaCO}_3$): Insoluble. * Calcium nitrate ($\text{Ca(NO}_3\text{)}_2$): Soluble. * Calcium sulfate ($\text{CaSO}_4$): Slightly soluble. * Calcium sulfate ($\text{CaSO}_4$) forms a slightly soluble/deposited layer that coats the surface of the limestone. * This protective layer prevents underlying $\text{CaCO}_3$ from coming into contact with remaining $\text{H}_2\text{SO}_4(aq)$, terminating the reaction prematurely and resulting in smaller total mass loss.

• Sources of Methodological Error:

  • Surface area across limestone pieces was non-uniform.

  • Variable composition or impurities present in limestone samples.

  • Limestone absorbed water during washing, increasing measured mass.

  • Solution/acid lost when limestone was removed from beakers.

  • Loss of limestone due to crumbling during drying.

  • Paper towel fibers adhering to limestone surfaces.

  • Uncovered beakers permitting solvent evaporation.

  • Ambient temperature was not controlled during the experiment.