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Activation Energy
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Today, we'll begin by discussing activation energy, denoted as Ea. Can anyone explain what activation energy means in terms of chemical reactions?
Isn't it the energy required for reactants to transform into products?
Exactly! Itโs the minimum energy barrier that must be overcome for a reaction to occur. Can someone tell me why this is vital for understanding reaction rates?
Because if the activation energy is high, fewer reactant molecules will have enough energy to react, making the reaction slower?
Right! A higher Ea means slower reactions at a given temperature. Remember, only the particles with energy equal to or greater than Ea can result in successful collisions. To help remember, think of a hillโreactants need enough energy to 'climb' it!
So can we change the activation energy?
Yes, we can! By using a catalyst, we can lower the activation energy required for the reaction without changing the products. Who can give me an example of a catalyst?
Enzymes in biological reactions!
Great example! Enzymes lower the Ea for chemical reactions in the body, accelerating metabolic processes. So, in summary, activation energy is crucial for determining how fast a reaction will proceed, and catalysts can significantly impact that. Who can summarize what we learned about Ea today?
Activation energy is the energy barrier for reactions, and lower Ea speeds up reactions, especially via catalysts.
The Arrhenius Equation
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Now, letโs dive into the Arrhenius equation, which is crucial for relating rate constants to temperature and activation energy. Does anyone remember the equation for that?
Is it k = A exp(โEa/(RT))?
Correct! In this equation, k represents the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Why do you think temperature is important in this equation?
Because changing the temperature changes how fast the molecules move, right?
Exactly! As temperature increases, more molecules have sufficient energy to overcome Ea, leading to more effective collisions. At what temperature range do reactions usually double in rate?
About every 10 to 20 degrees Celsius?
Yes! Thatโs an important rule of thumb. Can anyone recall how we could represent this relationship graphically?
By plotting ln k versus 1/T to create a straight line?
Exactly right! The slope will be -Ea/R. This shows how linearization helps visualize the relationship between reaction rate and temperature. To wrap up today, could someone summarize the Arrhenius equation for us?
The Arrhenius equation relates the rate constant to activation energy and temperature, showing how they affect reaction rates.
Catalysts
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Today, let's discuss catalysts. What is a catalyst, and how does it affect the reaction rate?
A catalyst speeds up a reaction by lowering the activation energy.
Correct! Can anyone explain the difference between homogeneous and heterogeneous catalysts?
Homogeneous catalysts are in the same phase as the reactants, while heterogeneous catalysts are in a different phase.
Absolutely right! An example of a homogeneous catalyst could be sulfuric acid in an esterification reaction, and an example of a heterogeneous catalyst is a metal catalyst that facilitates reactions at its surface. Why do you think catalysts are important in industry?
They help make processes faster and often more efficient, which is critical in large-scale manufacturing.
Exactly! Catalysts are crucial for economic efficiency in chemical manufacturing and are key to many biological processes. To summarize, what do we know about catalysts and their roles?
Catalysts speed up reactions by lowering activation energy and can be homogeneous or heterogeneous, making them essential in both biological and industrial processes.
Rate Laws
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Letโs explore rate laws. Who can define a rate law for me?
It's a mathematical expression that relates the reaction rate to the concentrations of reactants.
Great! And why are rate laws important in the context of chemical kinetics?
They help us understand how changing the concentrations of reactants affects the rate at which products are formed.
Right on! The rate law can be determined experimentally, and it reveals important information about the reaction mechanism. Can someone tell me how we might determine the order of a reaction?
By using methods like the initial-rate method, where we measure how changing the concentration of reactants affects the rate.
Excellent! This hands-on approach is key to understanding the behavior of complex systems. So, in summary, why are rate laws essential to our understanding of chemical reactions?
Rate laws relate reaction rates to reactant concentrations and provide insight into reaction mechanisms through experimental observation.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The glossary includes essential terminology used throughout the chapter on chemical kinetics. It features terms such as activation energy, rate constant, and both types of catalysts, offering concise definitions that facilitate understanding of kinetic principles in chemistry.
Detailed
Glossary of Important Terms
This glossary serves as a crucial reference for understanding the foundational concepts in chemical kinetics discussed throughout the chapter. Here, we define significant terms that help elucidate how reactions proceed, what factors influence their rates, and the theoretical frameworks used to explain these phenomena. Understanding these terms is essential for grasping the more complex interactions and equations that arise in the study of chemical kinetics.
- Activation Energy (Ea): The energy barrier that reactant molecules must overcome to form products. It is critical in determining the rate of a reaction, as only those molecules with sufficient energy can result in effective collisions.
- Arrhenius Equation: The equation, k = A exp(โEa/(R T)), relates the rate constant k to temperature T and activation energy Ea. This equation models how the rate of a reaction changes with temperature and provides insight into collision frequency and energy.
- Catalyst: A substance that increases the reaction rate by lowering the activation energy without being consumed in the overall reaction. Catalysts are essential in many industrial processes to enhance efficiency.
- Collision Frequency (Z_AB): The number of collisions per unit time per unit volume between species A and B in a gas. This term is pivotal in the study of reaction kinetics, as it correlates with the amount of reactant interaction over time.
- Elementary Step: A single-collision event (or unimolecular transformation) in a proposed mechanism, with a well-defined molecularity. This term is important for breaking down complex reactions into manageable parts for analysis.
- Half-Life (tโโโ): The time required for the concentration of a reactant to fall to half its initial value. It is a critical measure in determining reaction speed, especially in radioactive decay and other kinetic studies.
- Heterogeneous Catalyst: A catalyst that exists in a different phase than the reactants (e.g., a solid metal surface with gas reactants). Understanding such catalysts helps optimize reactions in industrial applications.
- Homogeneous Catalyst: A catalyst that exists in the same phase as the reactants (e.g., an acid dissolved in water). Many biochemical reactions involve homogeneous catalysis, especially in biological systems.
- Molecularity: The number of reactant particles that simultaneously collide or react in an elementary step: unimolecular (1), bimolecular (2), or termolecular (3). Molecularity helps classify reactions based on their mechanism.
- Pre-Equilibrium Approximation: The assumption that an early step in a mechanism is so fast it is effectively at equilibrium before the rate-determining step occurs. This approximation simplifies our understanding of reaction sequences.
- Rate Constant (k): The proportionality constant in a rate law; it is highly dependent on temperature and sometimes on catalysts. The rate constant is fundamental in calculating reaction kinetics and understanding reaction dynamics.
- Rate Law: A mathematical expression that relates the reaction rate to concentrations of reactants (and sometimes products or catalysts) and a rate constant. Understanding the rate law is essential to predict how changes in conditions affect reaction rates.
- Rate-Determining Step (RDS): The slowest elementary step in a multi-step mechanism, which controls the overall reaction rate. Identifying the RDS is crucial in understanding the kinetics of a reaction.
- Second-Order Reaction: A reaction whose rate law is either k [A]^2 (where two molecules of A collide) or k [A][B] (where one molecule each of A and B reacts). Second-order reactions often exhibit unique kinetic behavior compared to first-order reactions.
- Single-Exponential Decay: Characteristic of first-order kinetics: A = [A]_0 e^(โk t). This principle is central in radioactive decay and many unimolecular reactions.
- Steady-State Approximation: The assumption that the concentration of a reaction intermediate remains very small and approximately constant throughout most of the reaction, facilitating the analysis of complex reactions.
- Steric Factor (p): The fraction of collisions between reactant molecules that occur with the correct orientation to lead to reaction. This factor is crucial in understanding reaction dynamics and optimizing conditions for reactions to occur effectively.
- Temperature-Jump Technique: A method that perturbs a reaction at equilibrium by a rapid temperature increase and observes how the system relaxes back to equilibrium to obtain rate constants. This technique is often advanced and requires specialized equipment.
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Activation Energy (Ea)
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The energy barrier that reactant molecules must overcome to form products.
Detailed Explanation
Activation energy, denoted as Ea, refers to the minimum amount of energy that reactant molecules need to acquire in order to transform into products. It's like the initial push needed to get over a hill: without enough energy, the reaction won't happen. This concept is crucial because it helps explain why some reactions occur more easily than others; a reaction with a low activation energy can happen more spontaneously, while one with a high activation energy needs more energy input, like heat, to proceed.
Examples & Analogies
Imagine trying to push a car up a hill. If the hill is gentle (low activation energy), you can get the car moving with little effort. But if the hill is steep (high activation energy), you'll need a lot of force or help (like a tow truck) to get the car over the top. Similarly, in chemistry, reactions with high activation energies often need external energy sources to proceed.
Arrhenius Equation
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k = A exp(โEa/(R T)), relating the rate constant k to temperature T and activation energy Ea.
Detailed Explanation
The Arrhenius equation is a formula that shows how the rate constant (k) of a chemical reaction depends on temperature (T) and the activation energy (Ea). In this equation, A represents the frequency factor, which relates to how often molecules collide in a way that can lead to a reaction. The negative exponent tells us that as temperature increases or as activation energy decreases, the rate constant and hence, the reaction rate increases. This means that higher temperatures help more molecules overcome the energy barrier needed to react.
Examples & Analogies
Think about a game of marbles on a smooth board. If you gently roll a marble (representing low energy), it may not hit another marble hard enough to move it (just like a reaction that doesn't occur when energy is low). But if you roll it faster (higher temperature), it has a better chance of knocking into another marble hard enough to get it rolling too (like a successful reaction). The Arrhenius equation helps us calculate exactly how much faster reactions occur at different temperatures.
Catalyst
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A substance that increases the reaction rate by lowering the activation energy without being consumed in the overall reaction.
Detailed Explanation
A catalyst is a substance that speeds up a chemical reaction by providing an alternative reaction pathway with a lower activation energy. Importantly, catalysts are not consumed in the reaction, meaning they can participate in the process without being altered permanently. This means that a small amount of catalyst can be used over and over again to facilitate the reaction.
Examples & Analogies
Imagine a busy intersection where traffic is heavy. A police officer directing traffic (the catalyst) can help the cars (the reactants) move more smoothly and quickly through the intersection. The officer doesn't get stuck in traffic or go anywhere themselvesโthey just help the cars get past the intersection faster. In the same way, a catalyst helps chemical reactions occur quicker without becoming part of the final products.
Collision Frequency (Z_AB)
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The number of collisions per unit time per unit volume between species A and B in a gas.
Detailed Explanation
Collision frequency refers to how often reactant molecules collide with each other in a given volume over a certain period of time. For reactions to occur, molecules must collide. The greater the frequency of these collisions, the higher the likelihood of a reaction occurring. This concept is primary in collision theory, which states that the rate of reaction depends on how often molecules collide effectively.
Examples & Analogies
Think of a crowded room where everyone is mingling. The more people that bump into each other (collisions), the more conversations (reactions) will start. If the room is empty, very few interactions happen. Similarly, in a chemical reaction, a higher concentration of reactant molecules leads to more frequent collisions, increasing reaction rates.
Elementary Step
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A single-collision event (or unimolecular transformation) in a proposed mechanism, with a well-defined molecularity.
Detailed Explanation
An elementary step is the simplest part of a chemical reaction mechanism, representing a single event where reactant molecules collide and transform into products. Each step has a defined molecularity, which tells us how many molecules are involved (unimolecular, bimolecular, etc.). Understanding these steps helps chemists build comprehensive mechanisms for complicated reactions.
Examples & Analogies
Consider a complex dance performance. Each dancer's movement is like an elementary step in the performance. Each step must be correct for the entire dance to be successful. If one dancer misses their step (for example, colliding improperly or being out of sync), the whole routine can falter. In chemistry, each elementary step needs to occur correctly for the overall reaction to proceed smoothly.
Half-Life (tโโโ)
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The time required for the concentration of a reactant to fall to half its initial value.
Detailed Explanation
Half-life is a measure used in kinetics to quantify the time it takes for the concentration of a reactant to decrease to 50% of its original amount. This concept is particularly useful in studying first-order reactions, where the half-life remains constant regardless of the initial concentration. Over a series of equal time intervals, a first-order reaction consistently reduces the reactant concentration by half.
Examples & Analogies
Think of a candle burning down. If the candle takes an hour to burn halfway down, we know it will take another hour to reduce that remaining half down to a quarter left after two hours. The time taken for each reduction is consistent, similar to how half-lives work in certain reactions. Understanding half-lives helps predict how long it will take for a reactant to diminish significantly in a chemical reaction.
Molecularity
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The number of reactant particles that simultaneously collide or react in an elementary step: unimolecular (1), bimolecular (2), or termolecular (3).
Detailed Explanation
Molecularity indicates how many molecules participate in an elementary step of a reaction. It can be either unimolecular (involving one molecule), bimolecular (involving two), or termolecular (involving three). Understanding molecularity is crucial because it helps in determining the rate laws for reactions and the methods by which reactants interact.
Examples & Analogies
Imagine a game of catch. If only one person throws a ball to themselves, that's unimolecularโjust one participant. If two friends pass a ball back and forth, that's bimolecular, as both are involved in the action. If three friends try to juggle with one ball, that's termolecular. In chemistry, like in these games, the number of participants changes how well the process works.
Pre-Equilibrium Approximation
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The assumption that an early step in a mechanism is so fast it is effectively at equilibrium before the rate-determining step occurs.
Detailed Explanation
The pre-equilibrium approximation is a situation in multi-step reactions where a fast initial step reaches a state of balance (equilibrium) before a slower step takes place. This assumption simplifies the analysis of the reaction mechanism by allowing chemists to treat the concentration of intermediates as constant, streamlining the calculations involved in determining the overall reaction rate.
Examples & Analogies
Think of a busy restaurant. When customers enter quickly and are seated right away (fast step to equilibrium), they establish the amount of customers at the table before ordering (slow step). Even if new customers come in, the ones sitting have already settled into their seats, making the scene stable until they place their orders. In a chemical reaction, early steps can settle into a stable state quickly too, allowing for simpler calculations about what happens next.
Rate Constant (k)
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The proportionality constant in a rate law; depends strongly on temperature (and sometimes on catalyst). Units vary with overall reaction order.
Detailed Explanation
The rate constant, represented as k, is a direct reflection of how fast a reaction occurs under given conditions. It varies with temperature and the presence of catalysts. The units of k will change depending on the overall order of the reaction (whether itโs zero, first, or second order). Understanding the rate constant is vital for predicting how a reaction rate will change with different conditions.
Examples & Analogies
Imagine a baking recipe that calls for different baking times depending on how hot the oven is. A recipe might take longer when the oven is cooler and shorter at a higher heat. Similarly, in chemical reactions, k behaves like that. A higher temperature can speed up the reaction, just like a hotter oven speeds up baking.
Rate Law
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A mathematical expression that relates the reaction rate to concentrations of reactants (and sometimes products or catalysts) and a rate constant.
Detailed Explanation
A rate law is a formula that describes how the concentration of the reactants affects the speed of a chemical reaction. It details the relationship between reaction rate and reactant concentrations, often taking the form: Rate = k[A]^m[B]^n, where m and n are orders of the reaction with respect to reactants A and B respectively. The rate law is determined experimentally and is crucial for understanding the kinetics of the reaction.
Examples & Analogies
Consider a garden where plants grow at different rates depending on how much water they receive. If one plant (the rate law) grows faster when watered more frequently (higher concentration), it shows that its growth rate depends on how much water (concentration) it gets. Similarly, in reactions, the rate law reveals how reactant concentrations influence the reaction speed.
Rate-Determining Step (RDS)
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The slowest elementary step in a multi-step mechanism, which controls the overall reaction rate.
Detailed Explanation
The rate-determining step is the slowest step in a multi-step reaction mechanism and is crucial because it dictates the overall speed of the reaction. The overall reaction cannot go faster than this slowest step. Understanding which step is the rate-determining step helps chemists to focus on and potentially optimize that step to increase the reaction rate.
Examples & Analogies
Imagine a long line of cars waiting at a single toll booth on a highway. Even if all other lanes are clear, the overall traffic flow is limited by the slow toll booth process. If that line isnโt moving quickly, no cars can exit the highway at that point, just like a chemical process is slow if its rate-determining step is sluggish. Optimizing that booth could smooth things out, akin to speeding up the slow step in a reaction.
Second-Order Reaction
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A reaction whose rate law is either k [A]^2 (two molecules of A collide) or k [A] [B] (one molecule each of A and B).
Detailed Explanation
A second-order reaction is characterized by its rate being proportional to the product of the concentrations of two reactants, which could be two instances of the same reactant (k[A]^2) or one molecule each of two different reactants (k[A][B]). The rate depends significantly on the concentration of these reactants, meaning doubling a reactant's concentration could quadruple the reaction rate in the case of k[A]^2.
Examples & Analogies
Think of planting seeds in a garden. If you plant one seed (first-order), you get a certain amount of flowers. If you plant two seeds in the same spot (second-order), you might not just double the flowers; you could have a competition in the limited space that leads to even more because they help each other thrive or compete for sunlightโreflecting the reaction dynamics when concentration and interactions amplify each other.
Single-Exponential Decay
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Characteristic of first-order kinetics: A = [A]โ e^(โkt).
Detailed Explanation
Single-exponential decay describes how the concentration of a reactant decreases over time in a first-order reaction, where the rate of decay is proportional to its current concentration. This results in a graph that shows a steep decline that flattens out as time goes on, allowing chemists to understand how rapidly a substance might disappear.
Examples & Analogies
Imagine a clock where a hand is gradually moving downwards. The further down you go, the slower the movement becomes, signifying that less time remains. First-order reactions behave similarly: at first, there's a quick reduction in concentration, but as less reactant is available, the rate of decay slows, reflecting how exponential decay works in real life.
Steady-State Approximation
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The assumption that the concentration of a reaction intermediate remains very small and approximately constant throughout most of the reaction.
Detailed Explanation
The steady-state approximation allows chemists to simplify complex reactions by assuming that the concentrations of any intermediates involved remain constant during the reaction, even if they are technically changing. This assumption is particularly useful in multi-step reactions and makes it easier to derive rate laws since it doesn't require tracking every small change in concentration.
Examples & Analogies
Imagine a bakery with an assembly line for making cakes. Even as bakers constantly add ingredients and take out finished cakes, the number of cakes waiting to be frosted stays about the same (the steady state), allowing the bakers to maintain a consistent workflow. In chemistry, assuming intermediary concentrations are stable can help in drawing conclusions without being bogged down by every slight fluctuation.
Steric Factor (p)
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The fraction of collisions between reactant molecules that occur with the correct orientation to lead to reaction.
Detailed Explanation
The steric factor, denoted as p, quantifies how effective molecular collisions are regarding orientation. Not all collisions are productive; molecules need to be oriented correctly when they collide in order to form products. The steric factor ranges from 0 to 1, where 1 means all collisions are effective and 0 means no collisions lead to a reaction.
Examples & Analogies
Imagine a group of friends trying to play catch, but only some throw the ball directly to their partners. If everyone throws the ball with the intent to catch it (like effective collisions), then the game goes smoothly. But if many just toss the ball with no aim, few successful catches happen. The steric factor is like the accuracy of those throws: the better they are aimed, the more successful the game of catch will be!
Temperature-Jump Technique
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A method that perturbs a reaction at equilibrium by a rapid temperature increase and observes how the system relaxes back to equilibrium to obtain rate constants.
Detailed Explanation
The temperature-jump technique is a method used in chemical kinetics to quickly disturb a system at equilibrium by raising the temperature suddenly. Observing how the system responds as it returns to equilibrium allows chemists to measure forward and reverse rate constants. This technique is particularly useful in systems that are otherwise difficult to probe under standard conditions.
Examples & Analogies
Think of a teeter-totter in a playground. If you push one side down hard and quickly, the other side will naturally come up and then settle back down into balance. Similarly, in a chemical reaction, increasing the temperature is like pushing down hard on one side; you observe the reactions adjusting back to balance (equilibrium), allowing you to measure how fast things are responding to changes.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Activation Energy: The minimum energy required for a reaction to occur.
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Arrhenius Equation: Connects rate constant with temperature and activation energy.
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Catalyst: A substance that increases reaction rates by lowering activation energy.
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Rate Law: Describes how reaction rates relate to reactant concentrations.
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Half-Life: Time taken for the concentration of a reactant to be halved.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Enzyme action in the human body is a practical example of catalysis, where enzymes lower activation energy for biochemical reactions.
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In industrial processes, catalysts like platinum or palladium are often used to speed up reactions without being consumed.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
๐ต Rhymes Time
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For activation energy, think of a climb, A steep hill to cross, to make reaction chime.
๐ Fascinating Stories
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Imagine a race where all runners need to jump over a fence. The higher the fence (activation energy), the fewer will finish the race (reaction rate). But if a ladder (catalyst) is provided, more can jump the fence and win.
๐ง Other Memory Gems
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CAT = Catalyst Accelerates Temperature! Remember that catalysts work by lowering activation energy, increasing the reaction rate.
๐ฏ Super Acronyms
Ea = Effectively Activated
- The 'Ea' helps remember Activation energy is crucial for reactions.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Activation Energy (Ea)
Definition:
The energy barrier that reactant molecules must overcome to form products.
-
Term: Arrhenius Equation
Definition:
k = A exp(โEa/(R T)), relating the rate constant k to temperature T and activation energy Ea.
-
Term: Catalyst
Definition:
A substance that increases the reaction rate by lowering the activation energy without being consumed in the overall reaction.
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Term: Collision Frequency (Z_AB)
Definition:
The number of collisions per unit time per unit volume between species A and B in a gas.
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Term: Elementary Step
Definition:
A single-collision event (or unimolecular transformation) in a proposed mechanism, with a well-defined molecularity.
-
Term: HalfLife (tโโโ)
Definition:
The time required for the concentration of a reactant to fall to half its initial value.
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Term: Heterogeneous Catalyst
Definition:
A catalyst in a different phase than the reactants (e.g., a solid metal surface with gas reactants).
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Term: Homogeneous Catalyst
Definition:
A catalyst in the same phase as the reactants (e.g., an acid dissolved in water).
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Term: Molecularity
Definition:
The number of reactant particles that simultaneously collide or react in an elementary step: unimolecular (1), bimolecular (2), or termolecular (3).
-
Term: PreEquilibrium Approximation
Definition:
The assumption that an early step in a mechanism is so fast it is effectively at equilibrium before the rate-determining step occurs.
-
Term: Rate Constant (k)
Definition:
The proportionality constant in a rate law; depends strongly on temperature (and sometimes on catalyst).
-
Term: Rate Law
Definition:
A mathematical expression that relates the reaction rate to concentrations of reactants (and sometimes products or catalysts) and a rate constant.
-
Term: RateDetermining Step (RDS)
Definition:
The slowest elementary step in a multi-step mechanism, which controls the overall reaction rate.
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Term: SecondOrder Reaction
Definition:
A reaction whose rate law is either k [A]^2 (two molecules of A collide) or k [A][B] (one molecule each of A and B).
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Term: SingleExponential Decay
Definition:
Characteristic of first-order kinetics: A = [A]_0 e^(โk t).
-
Term: SteadyState Approximation
Definition:
The assumption that the concentration of a reaction intermediate remains very small and approximately constant throughout most of the reaction.
-
Term: Steric Factor (p)
Definition:
The fraction of collisions between reactant molecules that occur with the correct orientation to lead to reaction.
-
Term: TemperatureJump Technique
Definition:
A method that perturbs a reaction at equilibrium by a rapid temperature increase and observes how the system relaxes back to equilibrium to obtain rate constants.