Collision Theory

Collision Theory ● Collision Theory states that in order to react, molecules must collide ● Bonds are being broken and reformed in a ratio, and atoms are exchanged/moved around ● Not all collisions result in a reaction because they must meet the two general criteria ○ If requirements are not met, no reaction will occur or even take place ● Every reaction has a different/unique threshold of activation energy ○ Lower 𝐸𝑎 = Faster reaction because there are more successful collisions ○ Higher 𝐸𝑎 = Slower reaction because there are many low energy collisions Requirements for Collision Requirement Qualitative Reasoning Sufcient Activation Energy (𝐸𝑎) The molecules must collide hard enough because to break bonds requires a large amount of energy Proper Orientation Molecules need to break and make bonds in order for a chemical reaction to occur, therefore, the alignment and position of the molecules is vital given that molecules bond in specic contexts Rate and Factors that Affect It ● The rate of a reaction is the speed at which a chemical process occurs ● Physical State of the Reactants (solid, liquid, gas, aqueous) ○ The more contact between reactants, the more collisions that will occur ■ We want to increase collisions and increase the energy of collisions ○ Gas mixtures and solutions react faster than solids and liquids (movement!) ■ It is preferable to make a solid/liquid into a gas for experimental data ○ Solids will react faster when in smaller pieces ● Concentration of Reactants (Molarity (M)) ○ Higher concentration of reactants will result in more collisions ● Temperature ○ Faster moving molecules collide more frequently and with greater force ■ At higher temperatures, high-energy collisions happen more frequently ● Presence of a Catalyst ○ Catalysts speed up reactions by changing the mechanism (steps) of the reaction ○ Catalysts are not consumed during the course of the reaction ○ Example: Catalysts can gather reactants and place them in the proper orientation with enough energy in order to collide with one another successfully Reaction Coordinate Diagrams ● These diagrams can also be called reaction pathway diagrams or energy diagrams ● Activation Energy (𝐸𝑎 ): The minimum amount of energy required to initiate a reaction ○ The reaction will not occur until it overcomes the 𝐸𝑎 (successful collisions) ○ Smaller Eₐ results in faster reactions and a smaller hill on the diagram ○ Larger 𝐸𝑎 results in slower reactions and a larger hill on the diagram ○ 𝐸𝑎 = 𝐸𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑆𝑡𝑎𝑡𝑒 - 𝐸𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 ● Change in Energy (∆𝐸): The difference in energy between reactants and products ○ The ∆𝐸 can be either positive or negative ○ ∆𝐸 = 𝐸𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 - 𝐸𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 ● Transition State/Activated Complex: Seen at the peak of the reaction coordinate diagram ○ It is at a low concentration and is very unstable because it may form a product, or it may fall back to the reactant state of matter ● Change: ∆ = Final - Initial ● Exothermic: Energy is released/given off during the reaction - Negative ∆𝐸 (exit) ● Endothermic: Energy is absorbed during the reaction - Positive ∆𝐸 (enter) ● Intermediate: A usually stable step of a reaction between the reactant and the product ○ When there is an intermediate, it is essentially multiple reactions in one ○ When a reaction has an intermediate, there are more transition states ○ We can determine which step of intermediate diagrams are faster (hill height) ○ We can determine overall exo v. endo between intermediates Types of Reaction Coordinate Diagrams Single-Step Multistep Boltzmann Distribution Curves ● Area under the curve represents all molecules in a reaction and their speed ● A particular activation energy is required for the reaction – shown by the vertical line ○ All collisions of this particular speed and above will have enough energy to react ○ The molecules with a speed to right of vertical line will have proper 𝐸𝑎 ○ Catalysts can shift the vertical line to the left, allowing more molecules to collide ● Higher temps lead to more molecules meeting energy required for a successful collision ○ Curves with higher temperatures will be more shifted to the right of the graph ● Approximate average represented by µ = ((𝑟𝑜𝑜𝑡)(𝑚𝑒𝑎𝑛)) 2 Catalysts ● Catalysts increase the rate of reaction by decreasing the activation energy ● Catalysts change the mechanism(s) by which the process occurs ● A lower 𝐸𝑎 would lead to a higher speed/rate ○ More molecules can get over the 𝐸𝑎 threshold, allowing more successful collisions ● Catalyzed reactions are often studied in terms of reaction coordinate diagrams Reaction Rates ● Rates of reactions can be determined by monitoring the change in concentration of a reactant or a product over time ○ Units: Molarity per second (M/s) - Square brackets around a compound is molarity ■ Example: [NO] ○ Remember: Molarity = mol/L ● We can watch the decrease of reactants or increase of products to analyze rates ○ Reactants are high in M at the beginning of a reaction, and then decrease ○ Products are low in M at the beginning of a reaction, and then increase ● In a reaction, the amount of moles does not change, so we can predict amounts ○ Conservation of Mass - Makes sense because if R turns to P, we haven't lost or gained any additional matter from the beginning Instantaneous versus Average Rates ● Instantaneous Rates: One moment in time of a reaction ● Average Rates: The rate of a reaction over a period of time ● The “rate” always refers to instantaneous, unless otherwise indicated Average Rate ● Average Rate (M/s): The change in concentration divided by the change in time ○ Equation: Average Rate = ∆𝑀 ∆𝑇 ● As the reaction advances, the average rate always decreases/slows down ○ Concept Check: This is because there are less reactants to react - lower probability Instantaneous Rate ● Instantaneous Rate: The rate of reaction at a specic time (not average) ● Graphs are used to plot the concentration versus the time ○ Instantaneous rate represented by slope of a line tangent to the curve at any point ● All reactions slow down over time - compare the steepness of the two slopes ○ The steeper the slope of the instantaneous rate, the faster the rate of change ● The best indicator of the “rate” of a reaction is the instantaneous rate near the beginning, when there are the most reactants ○ This is called the initial rate, which is a type of instantaneous rate ■ Initial rates are always positive Reaction Rate and Stoichiometry ● The rate of reactant appearance disappearance = rate of product ● Mole ratios can be created from diagrams in order to write balanced chemical equations ● We can also use reactions to nd rates of change of other reactants and/or products Rate Laws ● One way to examine how the [reactants] affect the rate of reaction is to do many experiments, vary the [reactant] one at a time, and measure the rate. 𝑥 𝑦 ● Rate Law Statement: Rate = k[𝐴] [𝐵] ○ The rate constant (k) changes with temperature and is different for every reaction ■ Temperature dependent ○ Only the reactants are included in the rate law statement ○ Exponents are the rate order - Not same as the coefcients from the equation ○ To nd the rate constant, plug in numbers and solve for k ■ Equation Units of k: 1 𝑡𝑥𝑀 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑂𝑟𝑑𝑒𝑟 − 1 ● Overall rate orders are found by adding up all of the orders of each reactant Table Logic ● Compare two experiments where one reactant changes and other stays constant ○ Analyze how the initial rate responds ● We can write rate laws based off of the orders found from the table Handy Log Rule ● Used for one reactant at a time and the other reactant must be held constant ● Useful when the numbers are not easily manipulated and/or hard to estimate ○ Equation: Order = 𝑙𝑜𝑔 (𝑟𝑎𝑡𝑒 𝑟𝑎𝑡𝑖𝑜) 𝑙𝑜𝑔 (𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜) ○ Make sure that the ratios come from the same row in the table and match Finding Rates with No Constants ● When given a table or information with no constant reactant, we have a way to nd ra ● Before using the equation, use table logic to nd the order of the obvious reactant ● Equation: 𝑟𝑎𝑡𝑒 1 𝑟𝑎𝑡𝑒 2 = 𝐴 𝑥 𝐵 𝑦 𝐴 𝐵 ( )( ) ○ After nding the order of one of the obvious reactants, simplify 𝑥 ○ Once in the simplied form it should look something like this: 1 = 0. 5 ○ Either guess and check for either 0, 1, or 2 by plugging in or use logBAE ■ logBAE: Click MATH button on calculator and go to logBASE (𝑎𝑛𝑠𝑤𝑒𝑟) ● 𝑙𝑜𝑔(𝑏𝑎𝑠𝑒) = exponent (order) Differential Rate Laws Summary ● Chemists cannot look at the stoichiometry of a chemical equation and know its rate law ● Rate laws MUST be determined experimentally ● Rate laws can be determined by observing the effect on rate when changing initial concentrations - How the speed of a reaction varies with concentration ● The orders are usually 0, 1, or 2, but they can be higher, fractional, or even negative ● How the speed of a reaction varies with the concentrations of the reactants, using differential rate laws. Differential versus Integrated Rate Laws ● Use the differential rate law when the data is given in concentrations and rates ● Use the integrated rate law when the darta is given in concentrations and time (not rates) ○ The equations are used to study only individual reactants Integrated Rate Law: 1st Order Equation: ln [𝐴]𝑡- ln [𝐴]0= -kt ○ Subscripts are treated as indicators and are not factored into equation Solve for any one of the four variables in equation when given the other three ○ Determine the concentration of some reactant remaining at any time after the reaction proceeds for some time ○ Calculate the time required for a reactant to drop to a particular level Graphing 1st Order Integrated Rate Laws ○ If the reaction is 1st order, plotting ln[A] vs time yields a linear graph ○ The slope tells you k (rate constants can NEVER be negative) ■ The slope will be negative ○ The y intercept is ln [𝐴]0(initial concentration) ○ 1st order reactions always have a constant half-life ○ The x-axis will be time and the y-axis will be ln concentration Integrated Rate Law: 2nd Order ● Equation: 1 [𝐴] 𝑡 1 [𝐴] = kt 0 ○ Subscripts are treated as indicators and are not factored into equation ● Paralleled with the equation for a straight line: y = mx + b ● Graphing 2nd Order Integrated Rate Laws ○ Plotting 1 [𝐴] vs time will give a linear graph 𝑡 ○ The slope tells you k (rate constants can NEVER be negative) ■ The slope will be positive ○ The y-intercept = 1 [𝐴] (initial concentration) 0 ○ The x-axis will be time and the y-axis will be Integrated Rate Law: 0th Order 1 [𝐴] 0 ● Equation: [𝐴]𝑡- [𝐴]0= -kt ○ Subscripts are treated as indicators and are not factored into equation ○ This is the same equation as the rst order without the natural logarithms ● Graphing 0th Order Integrated Rate Laws ○ Plotting [𝐴]𝑡vs time will give a linear graph ○ The slope tells you k (rate constants can NEVER be negative) ■ The slope will be negative ○ The y-intercept = [𝐴]𝑡 ○ The x-axis will be time and the y-axis will be [𝐴]𝑡 Half Life ● Half Life (𝑡1/2): Time required for the concentration to drop to half of its previous value ● Half life is a convenient way to describe how fast a reaction occurs ● Fast reactions have a short half life and slow reactions have a long half life ● Equation of Half-Life Only Applicable to 1st Order Reactions: 𝑡1/2= 0.693 𝑘 ○ First order reactions always have a constant half life (does not change/vary) ● Determining Half Life from 1st Order Graphs ○ Find the point where the original [A] drops to ½ the starting amount ● Chemists can also plug in half of given concentrations into equations to nd 𝑡1/2 ● Conceptual Remaining Reactant/Product: 100 → 50 → 25 → 12.5 → 6.25 → 3.125 →… ● There IS a difference between the amount of disappearance and the amount remaining Methods to Determine Reaction Order ● Table Logic can be applied to tables with concentrations and rates ● Graphs can be used when concentration and time is given ● Handy Log Rule can be applied to tables with concentrations and rates Methods to Determine Rate Constant (k) ● Identify the slope of linear graph ● Write rate law and plug in Methods to Determine Half-Life ● In 1st Order Reactions: 𝑡1/2= 0.693 𝑘 ● Plug in ½ of [𝐴]0 to [𝐴]𝑡 ● Estimate from graph (only applies to molarity vs time) Rate Laws and Half Life Summary 0th Order 1st Order 2nd Order Rate Law Rate = k Rate = k[A] Rate = k[𝐴] Integrated Rate Law [𝐴]𝑡- [𝐴]0= -kt ln [𝐴]𝑡- ln [𝐴]0= -kt Plot for Linear Graph Slope Half-Life [A] vs time -k 𝑡1/2= 2 ln[A] vs time 2𝑘 0 𝑡1/2= 1 [𝐴] 𝑡 1 [𝐴] -k [𝐴] 1 [𝐴] = kt 0 vs time 𝑡 k 0.693 𝑘 𝑡1/2= 1 𝑘 [𝐴] 0 Reaction Mechanisms ● Most chemical reactions do not occur in a single step as the balanced equation implies ● Reaction Mechanism: A series of individual steps in which a chemical reaction occurs ○ Elementary Step: Each individual reaction that describes molecular collision/event ○ The rate law of an elementary step can be deduced from the reaction stoichiometry ■ NOT true from overall balances reactions ● The rate law is directly related to how many molecules are involved in an elementary step ○ Unimolecular: 1 reactant (A → product and rate = k[A]) 2 ○ Bimolecular: 2 reactants (2A → P (rate = k[𝐴] ) OR A+B → P (rate = k[A][B])) 2 ○ Termolecular: 3 reactants (2A + B → P and rate = k[𝐴] [B] ■ Hard to meet requirements, so not likely (Bad proposed mechanism) Reaction Mechanism: Slow 1st Step ● Chemists cannot determine the rate law from the overall balanced reaction ○ Chemists must see a proposed mechanism ● The slow step determines the rate ○ When the slow step is 1st...the rate law includes only the reactants of that 1st step ■ “The team is only as strong as its weakest member” ○ Do not cross anything off to come up with the rate law ○ If only one step is given as a proposed mechanism, assume it is the slow step ● Intermediate: The product in the rst step and the reactant in the second ● Catalyst: Does not get used in reaction and appears on reactant of 1st AND 2nd steps ● Writing Rate Laws + Overall Reactions from Reaction Mechanisms with a Slow 1st Step ○ 1. Circle reactants of the rst step - The rate law only includes these reactants ○ 2. Find orders using stoichiometric relationships (coefcients) ○ 3. Write rate law ○ 4. Determine intermediates and catalysts and cross them out ○ 5. Determine catalysts and cross them out ○ 6. Write what remains in the mechanisms to determine overall reaction ■ Remember to write the number of times the R/P appear in BOTH steps Reaction Mechanism: Slow 2nd Step ● The rate determining mechanism will be the second step because the second is slow ● Intermediate: The product in the rst step and the reactant in the second ● Catalyst: Does not get used in reaction and appears on reactant of 1st AND 2nd steps ● Writing Rate Laws + Overall Reactions from Reaction Mechanisms with a Slow 2nd Step ○ 1. Cross off the intermediates and catalysts ○ 2. Include the reactants up to and including the slow step (do not use last fasts steps) ○ 3. Any products before the slow step (in the fast step) show up in the denominator (shown as a negative exponent) Arrhenius Equation ● Equation: k = Ae −𝐸 𝑎 𝑅𝑇 ○ k = rate constant ○ A = frequency factor – frequency of collisions between molecules ○ 𝐸𝑎 = activation energy ○ R = 8.314 J/mol-K ○ T = temp in Kelvin ● Know conceptual basis of equation: Puts together the rate constant and collision theory ○ Shows that the rate constant is temperature dependent ● Increasing rate with increasing temp is non-linear - Depends on fraction of molecules with enough energy the number of collisions, and proper orientation Beer-Lambert Law ● Lab: A way to measure the concentration of a colored solution ○ Visualizing the rate of reaction that only works with a color that changes over time ● Equation: A = ϵ𝑏𝑐 ○ A = Absorbance of the light of the beam being shot through the analyte ■ Units are in AU ○ ϵ = Molar absorptivity (constant based on the chemical/analyte being tested) ○ b = path length (constant based on the side of the container) ○ c = concentration (this is what we are looking for) ■ A or proportional to c, allowing us to use them interchangeably (A/time) ● See which is linear over time to determine the rate of reaction ● Spectrophotometer: A piece of lab equipment used in the lab ○ Allows us to select the complementary color of the analyte to use as a beam ■ This will create a certain type of wavelength specic to the solution ■ This further maximizes the absorption to gather most accurate results ○ Transmittance: How much light comes out of analyte (opposite of absorbance) ■ Low concentration results in low absorbance ■ Low concentration results in high transmittance ● Darker colors have a higher absorbance (black shirt in sunny day) ● Absorbance decreases over time ● Wavelength of the beam is determined by the color - Specic wavelength used in the lab ● A calibration curve is necessary to convert between correct units ● We can take any absorbance from the lab graph and nd corresponding concentration Multiple Choice Tips ● Spend at most 1.5 minutes on each MC and return to it when done with MC if incomplete ● Process of Elimination: Identify the answers you for sure know are incorrect ● Remember that not having a calculator is actually helpful ○ These questions are not intended for extremely difcult calculations ○ Look at the answers to the question and rule out any that seem extremely far from what you think the answer is ● Use use the information given to you, but remember that not all of it is always useful ○ Sometimes, questions are testing your ability to pick out most useful information ● MC question applications specic to Unit 4 ○ Visualize molecules with correct orientation ○ Use conceptual checks when dealing with energy distribution graph proles ○ Use shorthand stoichiometry to nd rates when given at equation ○ Remember what effects what (EX: Activation energy doesn't depend on temperature) ○ When concentrations are doubled, double the order and multiply them to nd overall ○ Resort to table logic when given a table and look for hints like ln or 1/[A] ○ Remember basic denitions (EX: Catalysts do not get consumed