CSEC Chemistry: Rate of Reaction

Cheatsheet Content

1. Definition of Rate of Reaction The rate of reaction is the change in concentration of a reactant or product per unit time. It measures how fast reactants are consumed or products are formed. Units: mol $dm^{-3} s^{-1}$ or $g s^{-1}$ or $cm^3 s^{-1}$. Formula: Rate $= \frac{\text{Change in quantity}}{\text{Time taken}}$ Example: If $20 \text{ cm}^3$ of $CO_2$ gas is produced in $10 \text{ seconds}$, the rate of reaction is $\frac{20 \text{ cm}^3}{10 \text{ s}} = 2 \text{ cm}^3\text{/s}$. 2. Collision Theory For a reaction to occur, reactant particles must: Collide: Particles must come into contact with each other. Have sufficient energy: Collisions must have energy greater than or equal to the activation energy ($E_a$). Correct orientation: Particles must collide in the correct geometric alignment for bonds to break and form. Activation Energy ($E_a$): The minimum amount of energy required for a reaction to occur. A higher frequency of effective collisions leads to a faster rate of reaction. 3. Factors Affecting Rate of Reaction 3.1. Concentration of Reactants Effect: Increasing the concentration of reactants increases the rate of reaction. Explanation: More particles per unit volume mean a higher frequency of collisions, leading to a higher frequency of effective collisions. Example: $0.5 \text{ mol dm}^{-3}$ $HCl$ reacts faster with magnesium ribbon than $0.1 \text{ mol dm}^{-3}$ $HCl$. Example: Burning wood splint glows brighter in pure oxygen than in air (which is only ~21% oxygen). 3.2. Surface Area of Solid Reactants Effect: Increasing the surface area of solid reactants increases the rate of reaction. Explanation: When a solid reacts, only the particles on its surface are exposed to the other reactant. Crushing a solid into a powder increases the exposed surface area, allowing more particles to collide simultaneously. Example: Granulated sugar dissolves faster in water than a sugar cube. Example: Powdered zinc reacts much faster with dilute sulfuric acid than a large piece of zinc of the same mass. 3.3. Temperature Effect: Increasing the temperature increases the rate of reaction. Explanation: Particles gain more kinetic energy and move faster, leading to a higher frequency of collisions. A larger proportion of particles will have energy equal to or greater than the activation energy, leading to a higher frequency of effective collisions. Rule of thumb: For many reactions, a $10^\circ C$ rise in temperature roughly doubles the reaction rate. Example: Food spoils faster at room temperature than in a refrigerator because the reactions causing spoilage are slower at lower temperatures. Example: A glow stick glows brighter when placed in hot water compared to cold water. 3.4. Presence of a Catalyst Effect: A catalyst increases the rate of reaction without being chemically changed at the end of the reaction. Explanation: A catalyst provides an alternative reaction pathway with a lower activation energy ($E_a$). This means more reactant particles will have sufficient energy to react upon collision. Catalysts are specific to certain reactions. Types: Homogeneous catalyst: Same phase as reactants (e.g., $Fe^{2+}$ ions catalyzing the reaction between peroxydisulfate and iodide ions). Heterogeneous catalyst: Different phase from reactants (e.g., finely divided iron in the Haber process for ammonia synthesis; platinum/rhodium in catalytic converters in cars). Example: Manganese(IV) oxide ($MnO_2$) speeds up the decomposition of hydrogen peroxide ($2H_2O_2 \rightarrow 2H_2O + O_2$). Without $MnO_2$, the reaction is very slow. Inhibitors: Substances that slow down or stop a reaction. (e.g., preservatives in food slow down spoilage). 3.5. Pressure (for gaseous reactants) Effect: Increasing the pressure of gaseous reactants increases the rate of reaction. Explanation: Increasing pressure means the gas particles are closer together (higher concentration per unit volume). This leads to a higher frequency of collisions and thus more effective collisions. Example: In industrial processes like the Haber process ($N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$), high pressure is used to increase the rate of ammonia formation. Example: Propane burns faster under higher pressure. 4. Measuring Reaction Rates Methods involve monitoring a change in a measurable property over time. Common techniques: Change in volume of gas produced: Use a gas syringe or by displacement of water. Example: Reacting magnesium with hydrochloric acid: $Mg(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + H_2(g)$. Collect $H_2$ gas over time. Example: Reacting calcium carbonate with acid: $CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$. Collect $CO_2$ gas over time. Change in mass: If a gas is evolved and allowed to escape, the total mass of the system decreases. Example: The reaction of $CaCO_3$ with $HCl$ (as above). Place reaction mixture on a balance and measure mass loss as $CO_2$ escapes. Change in concentration: Titration: Take samples at intervals, quench reaction, then titrate. Colorimetry: If a reactant or product is coloured (e.g., the reaction of $I_2$ with thiosulfate, where $I_2$ is brown). Conductivity: If ions are formed or consumed. Change in turbidity/light transmission: For reactions that produce a precipitate, measure the time taken for a certain amount of precipitate to form. Example: The "disappearing cross" experiment: $Na_2S_2O_3(aq) + 2HCl(aq) \rightarrow 2NaCl(aq) + SO_2(g) + H_2O(l) + S(s)$. Sulfur (S) precipitate forms, making the solution cloudy. Measure time until a cross drawn under the beaker can no longer be seen. Graphing: Plot quantity (e.g., volume of gas) vs. time. The slope (gradient) of the curve at any point gives the instantaneous rate of reaction. The steepest slope (usually at the beginning) indicates the fastest rate. The curve flattens out as reactants are used up and the rate decreases. 5. Energy Profile Diagrams Illustrate the energy changes during a reaction. Axes: Y-axis = Potential Energy, X-axis = Reaction Pathway/Progress. Exothermic Reaction: Products have lower energy than reactants. Energy is released ($\Delta H$ is negative). Reaction Pathway Potential Energy Reactants Products Transition State $E_a$ $\Delta H$ Endothermic Reaction: Products have higher energy than reactants. Energy is absorbed ($\Delta H$ is positive). Reaction Pathway Potential Energy Reactants Products Transition State $E_a$ $\Delta H$ Effect of Catalyst: A catalyst lowers the activation energy ($E_a$) but does not change the $\Delta H$ of the reaction.